From 3eae466486d92e035b126e9fdd60d79936bed66d Mon Sep 17 00:00:00 2001 From: Dianjin Wang Date: Fri, 7 Nov 2025 16:18:19 +0800 Subject: [PATCH] Rafactor: new MADlib site using MKDocs --- .github/workflows/publish-madlib-site.yml | 149 + .gitignore | 18 +- .htaccess | 2 - README.md | 69 + _media/bg.png | Bin 219 -> 0 bytes _media/home-panel-bg-blue.jpg | Bin 20465 -> 0 bytes _media/home-panel-bg.jpg | Bin 29986 -> 0 bytes _media/icons/community-portal.png | Bin 2344 -> 0 bytes _media/icons/document.png | Bin 461 -> 0 bytes _media/list-item.png | Bin 117 -> 0 bytes _media/logo-tricolor.png | Bin 1782 -> 0 bytes _media/logo.png | Bin 1782 -> 0 bytes _media/new.png | Bin 1394 -> 0 bytes _media/video-community.png | Bin 5719 -> 0 bytes _media/video-product.png | Bin 6010 -> 0 bytes _media/video-thumb-madlib-project.jpg | Bin 278461 -> 0 bytes community.html | 226 - data/.Rhistory | 4 - docs/.htaccess | 2 - docs/api/index.md | 104 + docs/api/linear-regression.md | 168 + docs/asf/index.md | 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docs/mathjax/README.md create mode 100644 docs/team/history.md create mode 100644 docs/team/index.md delete mode 120000 docs/v1.19.0/latest delete mode 100644 documentation.html delete mode 100644 download.html delete mode 100644 index.html delete mode 100644 jquery-1.10.2.min.js delete mode 100644 master.js create mode 100644 mkdocs.yml delete mode 100644 product.html delete mode 100644 skins/default/lightbox-close.png delete mode 100644 skins/default/lightbox-next.png delete mode 100644 skins/default/lightbox-prev.png delete mode 100644 style.css diff --git a/.github/workflows/publish-madlib-site.yml b/.github/workflows/publish-madlib-site.yml new file mode 100644 index 00000000..cd0ebb0c --- /dev/null +++ b/.github/workflows/publish-madlib-site.yml @@ -0,0 +1,149 @@ +# Licensed to the Apache Software Foundation (ASF) under one +# or more contributor license agreements. See the NOTICE file +# distributed with this work for additional information +# regarding copyright ownership. The ASF licenses this file +# to you under the Apache License, Version 2.0 (the +# "License"); you may not use this file except in compliance +# with the License. You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, +# software distributed under the License is distributed on an +# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY +# KIND, either express or implied. See the License for the +# specific language governing permissions and limitations +# under the License. + +# publish-madlib-site.yml +# +# This workflow builds and publishes the Apache MADlib website to +# madlib.apache.org. +# The site is built using MkDocs and published to the asf-site branch, +# which Apache infrastructure then serves at madlib.apache.org +# +# Triggered by: +# - Push to master branch: Builds and publishes to asf-site +# - Pull requests: Builds only (no publish) to verify changes +# +# Requirements: +# - Python project with MkDocs and Material theme +# - .asf.yaml file in repository root +# +# Notes: +# - Publication only occurs on push events, not pull requests +# - The asf-site branch is protected - only this workflow should modify it +# - Build artifacts are placed in ./site directory + +name: Publish MADlib Site + +on: + push: + branches: [ master ] + pull_request: + +jobs: + publish: + runs-on: ubuntu-latest + permissions: + contents: write + steps: + - uses: actions/checkout@v4 + + - uses: actions/setup-python@v5 + with: + python-version: 3.x + + - name: Cache MkDocs dependencies + run: echo "cache_id=$(date --utc '+%V')" >> $GITHUB_ENV + + - uses: actions/cache@v4 + with: + key: mkdocs-material-${{ env.cache_id }} + path: ~/.cache + restore-keys: | + mkdocs-material- + + - name: Install MkDocs and Material theme + run: | + echo "📦 Installing MkDocs and Material theme..." + pip install mkdocs mkdocs-material + + - name: Build site + run: | + echo "🏗️ Building MkDocs site..." + mkdocs build 2>&1 | tee build.log + echo "✅ Build completed" + + - name: Check for broken links in build + id: link-check + run: | + echo "🔍 Checking for broken internal links..." + + # Check if build.log exists + if [ ! -f build.log ]; then + echo "❌ build.log file not found!" + echo "has_link_errors=false" >> $GITHUB_OUTPUT + exit 0 + fi + + # Display some build.log content for debugging + echo "📄 Build log contains $(wc -l < build.log) lines" + echo "🔍 Searching for link errors..." + + # Search for error patterns (MkDocs might report different errors than Docusaurus) + if grep -i "error\|warning\|broken" build.log | grep -i "link\|reference\|anchor"; then + echo "❌ Found potential link issues!" + + # Save all possible link errors to temporary file + grep -i "error\|warning\|broken" build.log | grep -i "link\|reference\|anchor" > link_errors.txt || true + + # Write to Summary + { + echo "## 🔗 Issues Found" + echo "" + echo "The following issues were detected during the MkDocs build:" + echo "" + echo '```' + cat link_errors.txt + echo '```' + } >> $GITHUB_STEP_SUMMARY + + echo "has_link_errors=true" >> $GITHUB_OUTPUT + else + echo "✅ No obvious link issues found" + + # Write success information to Summary + { + echo "## ✅ Build Check Passed" + echo "" + echo "Site built successfully with no obvious link errors!" + } >> $GITHUB_STEP_SUMMARY + + echo "has_link_errors=false" >> $GITHUB_OUTPUT + fi + + - name: Copy ASF config + run: cp .asf.yaml site/.asf.yaml + + # Deploy to asf-site for production + - name: Deploy to production + if: github.event_name == 'push' && github.ref == 'refs/heads/master' + uses: peaceiris/actions-gh-pages@v4 + with: + github_token: ${{ secrets.GITHUB_TOKEN }} + publish_dir: ./site + publish_branch: asf-site + + # Final step: fail if there were link errors + - name: Report check results + if: always() + run: | + if [[ "${{ steps.link-check.outputs.has_link_errors }}" == "true" ]]; then + echo "❌ Workflow completed but with issues detected!" + echo "Please fix the issues before merging." + echo "Check the Summary tab above for detailed error information." + exit 1 + else + echo "✅ All checks passed successfully!" + fi \ No newline at end of file diff --git a/.gitignore b/.gitignore index c95dd103..1e90e096 100644 --- a/.gitignore +++ b/.gitignore @@ -3,7 +3,7 @@ *.o *.pyc - # Meta data of Mac OS X's Finder.app +# Meta data of Mac OS X's Finder.app .DS_Store # tags @@ -17,3 +17,19 @@ .Rhistory eproject.cfg *.project.vim + +# MkDocs build output +site/ +.cache/ + +# Python virtual environment +venv/ +env/ +.venv/ + +# IDE files +.vscode/ +.idea/ +*.swp +*.swo +*~ diff --git a/.htaccess b/.htaccess deleted file mode 100644 index 6f99509b..00000000 --- a/.htaccess +++ /dev/null @@ -1,2 +0,0 @@ -ErrorDocument 500 http://madlib.incubator.apache.org -ErrorDocument 404 http://madlib.incubator.apache.org diff --git a/README.md b/README.md new file mode 100644 index 00000000..a80c5721 --- /dev/null +++ b/README.md @@ -0,0 +1,69 @@ +# Apache MADlib Website + +This is a restructured version of the Apache MADlib website using Material for MkDocs framework. + +## Project Structure + +``` +├── mkdocs.yml # Main configuration file +├── docs/ # Documentation source files +│ ├── index.md # Homepage +│ ├── documentation/ # User guides and documentation +│ ├── api/ # API documentation +│ ├── community/ # Community resources +│ ├── blog/ # Blog posts and announcements +│ ├── team/ # Team information +│ ├── asf/ # ASF related information +│ ├── download.md # Download page +│ └── assets/ # Static assets (CSS, JS, images) +├── community-artifacts/ # Jupyter notebooks and examples +└── README.md # This file +``` + +## Installation & Usage + +1. **Install MkDocs and Material theme:** + ```bash + pip install mkdocs mkdocs-material + ``` + +2. **Navigate to project directory:** + ```bash + cd madlib-site + ``` + +3. **Serve locally for development:** + ```bash + mkdocs serve + ``` + +4. **Build for production:** + ```bash + mkdocs build + ``` + +## Customization + +### Styling +- Custom CSS in `docs/assets/stylesheets/extra.css` +- Material theme configuration in `mkdocs.yml` + +### Content +- All content is in Markdown format +- Easy to edit and maintain +- Supports Material for MkDocs extensions + +## Assets Required + +The website assets are located in the `docs/assets/` directory. + +## Configuration + +The `mkdocs.yml` file contains: +- Site metadata and branding +- 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Community

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Apache MADlib is an open source project that endeavors to adhere in all respects to the principles of The Apache Way.

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MADlib grew out of discussions between database engine developers, data scientists, IT architects and academics interested in new approaches to scalable, sophisticated in-database analytics. These discussions were written up in a paper in VLDB 2009 that coined the term “MAD Skills” for data analysis. The MADlib software project began the following year as a collaboration between researchers at UC Berkeley and engineers and data scientists at EMC/Greenplum (later Pivotal).

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In September 2015 MADlib was accepted into the Apache Software Foundation Incubator and graduated to a Top Level Project in July 2017.

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Some of the past and present participants in this project are:

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Providing core development and scalability testing

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Providing key research and development of scalable estimators

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Providing key research in the area of convex optimization

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Providing key research into text analytics

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Providing key research in artificial neural networks on distributed systems

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If you are interested in joining our project please consider joining our User or Developer mailing lists. Everyone is welcome.

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Reporting Issues

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We need your feedback, so if you find a bug, would like to suggest an improvement, or create a request then please follow the steps below to let us know.

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User Resources

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Our online user forum open to discuss any topics of interest to users of the product.

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Developer Resources

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Our online developer forum open to discuss any topics of interest to open source contributors.

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Contribution Guide

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Step by step instructions guiding you through tho MADlib contribution model

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Source Code Repository

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- Copyright © The Apache Software Foundation, Licensed under the Apache License, Version 2.0. -
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- - diff --git a/data/.Rhistory b/data/.Rhistory deleted file mode 100644 index 8ae6061f..00000000 --- a/data/.Rhistory +++ /dev/null @@ -1,4 +0,0 @@ -x = c(1, 2, 3) -sum(x) -if (sum(x) == 0){ print("yes")} -if (sum(x) == 0){ print("yes") } else {print("no")} diff --git a/docs/.htaccess b/docs/.htaccess deleted file mode 100644 index b2eb4aef..00000000 --- a/docs/.htaccess +++ /dev/null @@ -1,2 +0,0 @@ -ErrorDocument 500 http://madlib.incubator.apache.org/docs/latest -ErrorDocument 404 http://madlib.incubator.apache.org/docs/latest diff --git a/docs/api/index.md b/docs/api/index.md new file mode 100644 index 00000000..942297f7 --- /dev/null +++ b/docs/api/index.md @@ -0,0 +1,104 @@ +# API Reference + +Apache MADlib provides comprehensive API documentation for all algorithms and functions. The documentation is organized by functional areas and includes detailed examples, syntax, and usage patterns. + +## Quick Navigation + +### Supervised Learning +- [Linear Regression](../versions/latest/group__grp__linreg.html) - Linear regression analysis +- [Logistic Regression](../versions/latest/group__grp__logreg.html) - Binary and multinomial logistic regression +- [Elastic Net](../versions/latest/group__grp__elasticnet.html) - Regularized linear and logistic regression +- [Support Vector Machines](../versions/latest/group__grp__svm.html) - Classification and regression with SVMs +- [Decision Trees](../versions/latest/group__grp__decision__tree.html) - Tree-based classification and regression +- [Random Forest](../versions/latest/group__grp__random__forest.html) - Ensemble tree methods +- [XGBoost](../versions/latest/group__grp__xgboost.html) - Gradient boosting framework + +### Unsupervised Learning +- [k-Means Clustering](../versions/latest/group__grp__kmeans.html) - Partitional clustering algorithm +- [DBSCAN](../versions/latest/group__grp__dbscan.html) - Density-based clustering +- [Principal Component Analysis](../versions/latest/group__grp__pca.html) - Dimensionality reduction +- [Latent Dirichlet Allocation](../versions/latest/group__grp__lda.html) - Topic modeling + +### Deep Learning +- [Multi-Layer Perceptron](../versions/latest/group__grp__nn.html) - Neural networks +- [Keras Integration](../versions/latest/group__grp__keras.html) - Deep learning with Keras/TensorFlow +- [Model Selection](../versions/latest/group__grp__model__selection.html) - AutoML and hyperparameter tuning +- [GPU Configuration](../versions/latest/group__grp__gpu__configuration.html) - GPU setup and management + +### Graph Analytics +- [PageRank](../versions/latest/group__grp__pagerank.html) - Web page ranking algorithm +- [Single Source Shortest Path](../versions/latest/group__grp__sssp.html) - Graph shortest paths +- [Weakly Connected Components](../versions/latest/group__grp__wcc.html) - Graph connectivity +- [Graph Measures](../versions/latest/group__grp__graph__measures.html) - Graph analysis metrics + +### Statistics and Data Analysis +- [Descriptive Statistics](../versions/latest/group__grp__summary.html) - Summary statistics +- [Correlation Analysis](../versions/latest/group__grp__correlation.html) - Correlation and covariance +- [Hypothesis Testing](../versions/latest/group__grp__stats__tests.html) - Statistical tests +- [Association Rules](../versions/latest/group__grp__assoc__rules.html) - Market basket analysis + +### Data Preprocessing +- [Data Transformation](../versions/latest/group__grp__datatrans.html) - Data preparation utilities +- [Encoding Categorical Variables](../versions/latest/group__grp__encode__categorical.html) - Categorical data handling +- [Train/Test Split](../versions/latest/group__grp__train__test__split.html) - Data splitting utilities +- [Sampling](../versions/latest/group__grp__sampling.html) - Data sampling methods + +### Model Validation +- [Cross Validation](../versions/latest/cross__validation_8sql__in.html) - Model validation techniques +- [Prediction Metrics](../versions/latest/pred__metrics_8sql__in.html) - Model evaluation metrics + +## Complete API Reference + +### Markdown Documentation (Developer-Friendly) + +For easy-to-maintain Markdown documentation of the latest versions: + +[**Latest Version (v2.1.0)**](latest/index.md){ .md-button .md-button--primary } +[**Version 2.0.0**](v2.0.0/index.md){ .md-button } + +### HTML Documentation (Full-Featured) + +For the complete, searchable API documentation with full navigation and examples: + +[**Browse Complete HTML Documentation**](../docs/latest/index.html){ .md-button } + +## Version-Specific Documentation + +- [Latest (2.1.0)](../docs/latest/index.html) +- [Version 2.0.0](../docs/v2.0.0/index.html) +- [Version 1.21.0](../docs/v1.21.0/index.html) +- [All Versions](../documentation/versions.md) + +## Getting Started + +If you're new to MADlib, we recommend starting with: + +1. **[Installation Guide](../documentation/installation.md)** - Set up MADlib +2. **[Quick Start](../documentation/quick-start.md)** - Your first MADlib model +3. **[Examples](../documentation/examples.md)** - Common use cases +4. **API Reference** (this page) - Detailed function documentation + +## Search and Navigation + +The complete API documentation includes: + +- **Full-text search** across all functions and examples +- **Interactive navigation tree** for browsing by category +- **Cross-references** between related functions +- **Syntax highlighting** for SQL code examples +- **Mathematical formulas** rendered with MathJax + +## Contributing to Documentation + +The API documentation is automatically generated from source code comments. To improve the documentation: + +1. **Report Issues**: Use [MADlib JIRA](https://issues.apache.org/jira/browse/MADLIB) for documentation bugs +2. **Contribute Examples**: Submit pull requests with improved examples +3. **Improve Comments**: Enhance source code documentation + +For more information, see our [Contributing Guide](../community/contributing.md). + +--- + +!!! tip "Pro Tip" + Use the search function in the complete API documentation to quickly find specific functions or examples. The search supports partial matches and function names. \ No newline at end of file diff --git a/docs/api/linear-regression.md b/docs/api/linear-regression.md new file mode 100644 index 00000000..ec63df06 --- /dev/null +++ b/docs/api/linear-regression.md @@ -0,0 +1,168 @@ +# Linear Regression + +Linear regression models the relationship between a scalar dependent variable and one or more explanatory variables using linear predictor functions. + +## Overview + +Linear regression is one of the most fundamental algorithms in machine learning and statistics. MADlib provides a robust implementation that works efficiently with large datasets in PostgreSQL and Greenplum Database. + +## Key Features + +- **Scalable**: Handles large datasets efficiently using parallel processing +- **Robust**: Includes options for heteroskedasticity-consistent standard errors +- **Flexible**: Supports various input formats and grouping variables +- **Statistical**: Provides comprehensive statistical output including R², p-values, and confidence intervals + +## Basic Usage + +### Training a Model + +```sql +SELECT madlib.linregr_train( + 'source_table', -- Input table + 'output_table', -- Output model table + 'dependent_var', -- Y variable + 'ARRAY[1, x1, x2]' -- Independent variables (include 1 for intercept) +); +``` + +### Making Predictions + +```sql +SELECT madlib.linregr_predict( + (SELECT coef FROM output_table), + ARRAY[1, new_x1, new_x2] +) as prediction; +``` + +## Parameters + +| Parameter | Type | Description | +|-----------|------|-------------| +| `source_table` | TEXT | Name of the table containing training data | +| `out_table` | TEXT | Name of the output table for model | +| `dependent_varname` | TEXT | Name of the dependent variable column | +| `independent_varname` | TEXT | Expression for independent variables | +| `grouping_cols` | TEXT | Optional grouping columns | +| `heteroskedasticity_option` | BOOLEAN | Enable robust standard errors | + +## Output + +The trained model includes: + +- **coef**: Coefficient vector +- **r2**: R-squared value +- **std_err**: Standard errors +- **t_stats**: T-statistics +- **p_values**: P-values for significance testing +- **condition_no**: Condition number for numerical stability + +## Examples + +### Simple Linear Regression + +```sql +-- Create sample data +CREATE TABLE housing AS +SELECT + random() * 1000 + 500 as sqft, + random() * 100000 + 200000 as price +FROM generate_series(1, 1000); + +-- Train model +SELECT madlib.linregr_train( + 'housing', + 'housing_model', + 'price', + 'ARRAY[1, sqft]' +); + +-- View results +SELECT * FROM housing_model; +``` + +### Multiple Linear Regression + +```sql +-- Multiple predictors +SELECT madlib.linregr_train( + 'housing', + 'housing_multi_model', + 'price', + 'ARRAY[1, sqft, bedrooms, bathrooms]' +); +``` + +### Grouped Regression + +```sql +-- Separate models by region +SELECT madlib.linregr_train( + 'housing', + 'housing_by_region', + 'price', + 'ARRAY[1, sqft]', + 'region' +); +``` + +## Advanced Features + +### Robust Standard Errors + +```sql +-- Heteroskedasticity-consistent standard errors +SELECT madlib.linregr_train( + 'housing', + 'housing_robust', + 'price', + 'ARRAY[1, sqft]', + NULL, -- no grouping + TRUE -- robust standard errors +); +``` + +### Model Diagnostics + +```sql +-- Check model quality +SELECT + r2, + CASE WHEN r2 > 0.7 THEN 'Good fit' + WHEN r2 > 0.5 THEN 'Moderate fit' + ELSE 'Poor fit' END as fit_quality +FROM housing_model; +``` + +## Performance Tips + +1. **Include intercept**: Always include 1 in the independent variables array for the intercept term +2. **Scale features**: Consider scaling features if they have very different ranges +3. **Check condition number**: High condition numbers (>1000) may indicate multicollinearity +4. **Use appropriate data types**: FLOAT8 is recommended for numerical stability + +## Related Functions + +- [Logistic Regression](../versions/latest/group__grp__logreg.html) - For binary/categorical outcomes +- [Elastic Net](../versions/latest/group__grp__elasticnet.html) - Regularized regression +- [Robust Regression](../versions/latest/group__grp__robust.html) - Outlier-resistant regression + +## Complete Documentation + +For detailed syntax, additional parameters, and more examples: + +[**View Complete Linear Regression Documentation**](../versions/latest/group__grp__linreg.html){ .md-button .md-button--primary } + +## Mathematical Background + +Linear regression finds the best-fitting line through data points by minimizing the sum of squared residuals: + +$$\min_{\beta} \sum_{i=1}^{n} (y_i - X_i\beta)^2$$ + +Where: +- $y_i$ is the dependent variable +- $X_i$ is the vector of independent variables +- $\beta$ is the coefficient vector to be estimated + +The solution is given by the normal equation: +$$\hat{\beta} = (X^TX)^{-1}X^Ty$$ \ No newline at end of file diff --git a/docs/asf/index.md b/docs/asf/index.md new file mode 100644 index 00000000..625713e7 --- /dev/null +++ b/docs/asf/index.md @@ -0,0 +1,15 @@ +--- +hide: + - 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navigation + - toc +--- + +# MADlib Blog + +Welcome to the Apache MADlib blog! Here you'll find the latest news, release announcements, tutorials, and insights from the MADlib community. \ No newline at end of file diff --git a/docs/blog/posts/madlib-1.17.0-release.md b/docs/blog/posts/madlib-1.17.0-release.md new file mode 100644 index 00000000..79e090e2 --- /dev/null +++ b/docs/blog/posts/madlib-1.17.0-release.md @@ -0,0 +1,57 @@ +--- +date: 2020-04-09 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 1.17.0 Release + +On April 9, 2020, MADlib completed its seventh release as an Apache Software Foundation Top Level Project. + + + +## New Features + +### Deep Learning Advancements +- **Model selection framework for Keras with TensorFlow backend**: Comprehensive framework for model architecture search and hyperparameter optimization with GPU acceleration +- **Support for heterogeneous clusters**: Enhanced support for clusters where GPUs are attached to only certain segment hosts, enabling flexible deployment scenarios +- **Support inference for imported models**: "Bring your own model" capability - perform inference on models not trained in MADlib +- **Support transfer learning for multiple model fit function**: Advanced transfer learning capabilities for leveraging pre-trained models +- **Generate model selection table for grid search or random search**: Automated model selection with comprehensive result tracking +- **Helper function to get GPU type and configuration**: Utility functions for GPU discovery and configuration management + +### Clustering Enhancements +- **k-Means clustering - Select optimal number of centroids**: Automated cluster number selection using elbow or silhouette methods for optimal clustering results + +### Platform Support +- **PostgreSQL 12 support**: Extended compatibility to PostgreSQL 12 for broader deployment options + +## Improvements + +### Algorithm Enhancements +- **Association rules - Add option to set number of posterior rules**: Enhanced control over association rule mining output +- **Correlation and covariance - Improve memory usage with large number of groups**: Better memory management for statistical computations with many grouping variables + +### Deep Learning Performance +- **Improve performance of mini-batch preprocessor and fit functions**: Significant performance improvements for neural network training workflows + +### Documentation and Infrastructure +- **Docs - Improve installation guide on wiki**: Enhanced installation documentation for better user experience +- **Graph - SSSP should not show vertices in output table that are unreachable**: Cleaner output for Single Source Shortest Path algorithm +- **LDA - Add stopping criteria on perplexity**: Better convergence control for Latent Dirichlet Allocation + +## Download and Installation + +You are invited to [download the 1.17.0 release](https://dist.apache.org/repos/dist/release/madlib/1.17.0/) and [review the release notes](https://github.com/apache/madlib/blob/master/RELEASE_NOTES). + +For more details about the new deep learning features, please refer to the [Apache MADlib deep learning notes](https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning) and the [Jupyter notebook examples](https://github.com/apache/madlib-site/tree/asf-site/community-artifacts/Deep-learning). + +## What's New + +This release marks a significant milestone in MADlib's deep learning capabilities, introducing a comprehensive model selection framework that automates the often complex process of finding optimal neural network architectures and hyperparameters. The support for heterogeneous GPU clusters makes MADlib more flexible for real-world deployment scenarios. + +The "bring your own model" feature opens up new possibilities for integrating MADlib with existing machine learning workflows, while the enhanced k-means clustering with automatic cluster selection makes unsupervised learning more accessible. + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/blog/posts/madlib-1.18.0-release.md b/docs/blog/posts/madlib-1.18.0-release.md new file mode 100644 index 00000000..7b48724c --- /dev/null +++ b/docs/blog/posts/madlib-1.18.0-release.md @@ -0,0 +1,55 @@ +--- +date: 2021-04-05 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 1.18.0 Release + +On April 5, 2021, MADlib completed its eighth release as an Apache Software Foundation Top Level Project. + + + +## New Features + +### Deep Learning Enhancements +- **New grid and random search methods**: Advanced hyperparameter optimization techniques for neural networks +- **AutoML methods Hyperband and Hyperopt**: Automated machine learning capabilities for efficient model selection and hyperparameter tuning +- **Custom loss functions and custom metrics**: Flexibility to define domain-specific loss functions and evaluation metrics +- **TensorBoard support**: Integration with TensorBoard for visualization and monitoring of training progress +- **Multi-input and output support for fit and evaluate**: Enhanced neural network architecture support for complex models + +### Clustering Algorithms +- **DBSCAN - Density based clustering (phase 1)**: Initial implementation of DBSCAN algorithm for density-based clustering + +## Improvements + +### Deep Learning Performance +- **Implement cache logic to speed performance**: Intelligent caching mechanisms to reduce computation overhead +- **Reduce GPU idle time when moving model state between workers**: Optimized GPU utilization in distributed training scenarios +- **Use Keras version from TensorFlow**: Streamlined dependency management by using TensorFlow's built-in Keras +- **Add top n to evaluate**: Enhanced model evaluation with top-n accuracy metrics + +### Graph Algorithm Enhancements +- **Support BIGINT for all graph methods**: Extended data type support for large-scale graph processing + +### Infrastructure Improvements +- **Switch to CloudBees (was Jenkins)**: Upgraded continuous integration infrastructure for better reliability and performance + +## Download and Installation + +You are invited to [download the 1.18.0 release](https://dist.apache.org/repos/dist/release/madlib/1.18.0/) and [review the release notes](https://github.com/apache/madlib/blob/master/RELEASE_NOTES). + +Also please refer to the [list of supported databases and OS](https://cwiki.apache.org/confluence/display/MADLIB/Database+and+OS+Support) for compatibility information. + +## What's New + +This release represents a major advancement in MADlib's deep learning capabilities, introducing AutoML features that make machine learning more accessible to users without extensive hyperparameter tuning expertise. The TensorBoard integration provides powerful visualization capabilities for monitoring and debugging neural network training. + +The performance improvements, particularly in GPU utilization and caching, make MADlib more suitable for production deep learning workloads at scale. + +For more details about the new deep learning features, please refer to the [Apache MADlib deep learning notes](https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning) and the [Jupyter notebook examples](https://github.com/apache/madlib-site/tree/asf-site/community-artifacts/Deep-learning). + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/blog/posts/madlib-1.19.0-release.md b/docs/blog/posts/madlib-1.19.0-release.md new file mode 100644 index 00000000..6a12d5ca --- /dev/null +++ b/docs/blog/posts/madlib-1.19.0-release.md @@ -0,0 +1,50 @@ +--- +date: 2022-03-08 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 1.19.0 Release + +On March 8, 2022, MADlib completed its ninth release as an Apache Software Foundation Top Level Project. + + + +## New Features + +### Clustering Algorithms +- **DBSCAN: Fast parallel-optimized DBSCAN**: Introduction of Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm with parallel optimization for large-scale clustering tasks + +### Neural Network Enhancements +- **MLP: Add rmsprop and Adam optimization techniques**: Enhanced Multi-Layer Perceptron (MLP) with additional optimization algorithms for better convergence and performance + +## Improvements + +### Graph Algorithm Optimizations +- **Improve WCC subtx count and catalog entry frequency**: Performance improvements for Weakly Connected Components algorithm, reducing transaction overhead and catalog access frequency + +### Neural Network Improvements +- **MLP: Set lambda value for minibatch**: Better regularization control for mini-batch training in neural networks + +### Algorithm Stability +- **GLM-multinom: Use non-temp tables in GroupIterationController**: Improved stability for multinomial GLM by using persistent tables instead of temporary ones + +### Infrastructure +- **Jenkins: Add new dockerfile for PG11**: Enhanced continuous integration with PostgreSQL 11 support +- **Build: Use dynamic_library_path for module pathname**: Improved library loading mechanism for better portability + +## Download and Installation + +You are invited to [download the 1.19.0 release](https://dist.apache.org/repos/dist/release/madlib/1.19.0/) and [review the release notes](https://github.com/apache/madlib/blob/master/RELEASE_NOTES). + +Also please refer to the [list of supported databases and OS](https://cwiki.apache.org/confluence/display/MADLIB/Database+and+OS+Support) for compatibility information. + +## What's New + +This release introduces DBSCAN, a powerful clustering algorithm that can find clusters of arbitrary shape and is robust to outliers. The parallel-optimized implementation makes it suitable for large-scale data analysis tasks. + +The neural network improvements provide more optimization options and better performance for deep learning workloads, while the various performance optimizations ensure better scalability across all algorithms. + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/blog/posts/madlib-1.20.0-release.md b/docs/blog/posts/madlib-1.20.0-release.md new file mode 100644 index 00000000..d1785f2e --- /dev/null +++ b/docs/blog/posts/madlib-1.20.0-release.md @@ -0,0 +1,44 @@ +--- +date: 2022-08-03 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 1.20.0 Release + +On August 3, 2022, MADlib completed its tenth release as an Apache Software Foundation Top Level Project. + + + +## New Features + +### XGBoost Integration +- **Python based XGBoost with single and grid search executions**: Complete integration of XGBoost algorithm with both single model training and automated hyperparameter grid search capabilities + +### Graph Algorithm Enhancements +- **Add multicolumn support for WCC and Pagerank**: Enhanced Weakly Connected Components (WCC) and PageRank algorithms to support composite identifiers, making them more suitable for complex real-world graph data + +## Improvements + +### Performance Optimizations +- **Reuse update plan in GroupIterationController**: Significant performance improvement for iterative algorithms by reusing query execution plans +- **Adjust ORCA to reduce planning time**: Optimized query planning for Elastic Net, GLM, and SVM algorithms, reducing overall execution time + +### Documentation +- **Update online examples for various modules**: Refreshed and expanded examples across multiple algorithm modules for better user experience + +## Download and Installation + +You are invited to [download the 1.20.0 release](https://dist.apache.org/repos/dist/release/madlib/1.20.0/) and [review the release notes](https://github.com/apache/madlib/blob/master/RELEASE_NOTES). + +Also please refer to the [list of supported databases and OS](https://cwiki.apache.org/confluence/display/MADLIB/Database+and+OS+Support) for compatibility information. + +## What's New + +This release marks a significant milestone with the introduction of XGBoost, one of the most popular gradient boosting frameworks. The Python-based implementation provides seamless integration with MADlib's existing ecosystem while offering both simple training and advanced hyperparameter optimization capabilities. + +The graph algorithm improvements make MADlib more suitable for complex network analysis tasks, while the performance optimizations ensure better scalability for large datasets. + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/blog/posts/madlib-1.21.0-release.md b/docs/blog/posts/madlib-1.21.0-release.md new file mode 100644 index 00000000..60352168 --- /dev/null +++ b/docs/blog/posts/madlib-1.21.0-release.md @@ -0,0 +1,40 @@ +--- +date: 2023-03-01 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 1.21.0 Release + +On March 1, 2023, MADlib completed its eleventh release as an Apache Software Foundation Top Level Project. + + + +## New Features + +### Graph Algorithms +- **Add warm start for weakly connected components**: Improved performance for iterative graph computations by allowing algorithms to resume from previous states +- **Add multicolumn identifier support for SSSP and APSP**: Enhanced Single Source Shortest Path (SSSP) and All Pairs Shortest Path (APSP) algorithms to work with composite keys + +### Platform Support +- **Add support for Photon3 OS**: Extended platform compatibility to include VMware's Photon OS 3.0 + +## Improvements + +### XGBoost Enhancements +- **Add support for bigint and varchar columns**: Expanded data type support for XGBoost algorithms, allowing for more flexible data processing +- **Enable eval_metrics parameter**: Added evaluation metrics configuration for better model assessment during training + +## Download and Installation + +You are invited to [download the 1.21.0 release](https://dist.apache.org/repos/dist/release/madlib/1.21.0/) and [review the release notes](https://github.com/apache/madlib/blob/master/RELEASE_NOTES). + +Also please refer to the [list of supported databases and OS](https://cwiki.apache.org/confluence/display/MADLIB/Database+and+OS+Support) for compatibility information. + +## What's New + +This release focuses on enhancing graph algorithms and expanding XGBoost capabilities. The warm start feature for graph algorithms significantly improves performance for large-scale graph computations, while the multicolumn support makes the algorithms more flexible for real-world data scenarios. + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/blog/posts/madlib-2.0.0-release.md b/docs/blog/posts/madlib-2.0.0-release.md new file mode 100644 index 00000000..779e3ebd --- /dev/null +++ b/docs/blog/posts/madlib-2.0.0-release.md @@ -0,0 +1,44 @@ +--- +date: 2023-06-20 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 2.0.0 Release + +On June 20, 2023, MADlib completed its second major release, marking a significant milestone in the project's evolution. + + + +## New Features + +### Platform Support +- **Add support for python3**: Full Python 3 compatibility for all MADlib components +- **Add support for GP7 Beta**: Early support for Greenplum Database 7 Beta +- **GP6 python3 extension support**: Enhanced Python 3 integration with Greenplum 6 +- **Postgres 13/14/15 support**: Extended PostgreSQL compatibility to versions 13, 14, and 15 + +## Improvements + +### Machine Learning Algorithms +- **XGBoost: Add support for version 1.7.5**: Updated to the latest XGBoost version with performance improvements and new features +- **DL: Add support for tensorflow 2.10.1 and keras 2.10.0**: Updated deep learning framework support for better performance and compatibility +- **DBScan: Add support for rtree 1.0.1**: Enhanced clustering algorithm with updated spatial indexing + +## Breaking Changes + +This major release includes some breaking changes. Please review the [migration guide](https://github.com/apache/madlib/blob/madlib2-master/RELEASE_NOTES) before upgrading from MADlib 1.x versions. + +## Download and Installation + +You are invited to [download the 2.0.0 release](https://dist.apache.org/repos/dist/release/madlib/2.0.0/) and [review the release notes](https://github.com/apache/madlib/blob/madlib2-master/RELEASE_NOTES). + +Also please refer to the [list of supported databases and OS](https://cwiki.apache.org/confluence/display/MADLIB/Installation+Guide+for+MADlib+2.X) for compatibility information. + +## What's New in 2.0 + +This major release represents a significant step forward in MADlib's evolution, with comprehensive Python 3 support and expanded database platform compatibility. The updated machine learning libraries provide better performance and access to the latest algorithmic improvements. + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/blog/posts/madlib-2.1.0-release.md b/docs/blog/posts/madlib-2.1.0-release.md new file mode 100644 index 00000000..ef895168 --- /dev/null +++ b/docs/blog/posts/madlib-2.1.0-release.md @@ -0,0 +1,39 @@ +--- +date: 2023-09-08 +categories: + - Release +authors: + - madlib-team +--- + +# MADlib 2.1.0 Release + +On September 8, 2023, MADlib completed its thirteenth release as an Apache Software Foundation Top Level Project. + + + +## Improvements + +### Build System +- **Fix PG 15 support**: Enhanced compatibility with PostgreSQL 15 +- **Add ubuntu flag for PyXB installation**: Improved installation process on Ubuntu systems +- **Add the actual path of $libdir to dynamic_library_path**: Better library path handling +- **Remove PyXB as a packaged dependency**: Replaced with external pyxb-x dependency for better maintainability +- **Use PG15 in Jenkins CI**: Updated continuous integration to test against PostgreSQL 15 + +### Algorithm Fixes +- **Assoc_rules: Fix SERIAL cache issue**: Resolved caching problems in association rules algorithm +- **DL: Remove SERIAL from load_keras_model**: Improved deep learning model loading functionality +- **CRF: Fix anyarray -> anycompatiblearray change for PG14**: Updated Conditional Random Fields for PostgreSQL 14 compatibility + +## Download and Installation + +You are invited to [download the 2.1.0 release](https://dist.apache.org/repos/dist/release/madlib/2.1.0/) and [review the release notes](https://github.com/apache/madlib/blob/madlib2-master/RELEASE_NOTES). + +Also please refer to the [list of supported databases and OS](https://cwiki.apache.org/confluence/display/MADLIB/Installation+Guide+for+MADlib+2.X) for compatibility information. + +## What's Next + +This release focuses on stability and compatibility improvements, ensuring MADlib works seamlessly with the latest PostgreSQL versions while maintaining backward compatibility with existing installations. + +For technical support and questions, please visit our [community forums](../../community/index.md) or check the [documentation](../../documentation/user-guide.md). \ No newline at end of file diff --git a/docs/community/contributing.md b/docs/community/contributing.md new file mode 100644 index 00000000..aed72cb7 --- /dev/null +++ b/docs/community/contributing.md @@ -0,0 +1,56 @@ +# Contributing to Apache MADlib + +We welcome contributions from the community! This page provides information on how to contribute to the Apache MADlib project. + +## Getting Started + +### Step-by-Step Contribution Guide + +For detailed instructions on contributing to MADlib, please visit our [Contribution Guidelines](https://cwiki.apache.org/confluence/display/MADLIB/Contribution+Guidelines) on the MADlib Wiki. + +### Quick Links + +- **Source Code**: [GitHub Repository](https://github.com/apache/madlib) +- **Issue Tracking**: [MADlib JIRA](https://issues.apache.org/jira/browse/MADLIB) +- **Developer Forum**: [Subscribe](mailto:dev-subscribe@madlib.apache.org) | [Archives](https://mail-archives.apache.org/mod_mbox/madlib-dev/) + +## Ways to Contribute + +### Code Contributions +- Bug fixes +- New algorithms and features +- Performance improvements +- Documentation updates + +### Non-Code Contributions +- Testing and bug reports +- Documentation improvements +- Community support +- Tutorials and examples + +## Development Process + +1. **Join the Community**: Subscribe to the [developer mailing list](mailto:dev-subscribe@madlib.apache.org) +2. **Find an Issue**: Browse [open issues](https://issues.apache.org/jira/browse/MADLIB) or propose new features +3. **Fork and Clone**: Fork the [GitHub repository](https://github.com/apache/madlib) +4. **Develop**: Make your changes following our coding standards +5. **Test**: Ensure all tests pass +6. **Submit**: Create a pull request + +## Developer Resources + +- [MADlib Architecture](https://cwiki.apache.org/confluence/display/MADLIB/Architecture) +- [Module Anatomy](https://cwiki.apache.org/confluence/display/MADLIB/Module+Anatomy) +- [SQL API Style Guide](https://cwiki.apache.org/confluence/display/MADLIB/SQL+API+Guide) +- [Quick Start Guide for Developers](https://cwiki.apache.org/confluence/display/MADLIB/Quick+Start+Guide+for+Developers) + +## Code of Conduct + +Apache MADlib follows the [Apache Software Foundation Code of Conduct](https://www.apache.org/foundation/policies/conduct.html). Please be respectful and inclusive in all interactions. + +## Questions? + +If you have questions about contributing, please: +- Ask on the [developer mailing list](mailto:dev-subscribe@madlib.apache.org) +- Join our community discussions +- Check the [developer documentation](https://cwiki.apache.org/confluence/display/MADLIB/) \ No newline at end of file diff --git a/docs/community/developers.md b/docs/community/developers.md new file mode 100644 index 00000000..65e1a317 --- /dev/null +++ b/docs/community/developers.md @@ -0,0 +1,118 @@ +# Developer Resources + +Resources for developers who want to contribute to Apache MADlib or integrate it into their applications. + +## Quick Start for Developers + +For developers interested in contributing to MADlib, we provide comprehensive resources to get you started quickly. + +[Developer Quick Start Guide](https://cwiki.apache.org/confluence/display/MADLIB/Quick+Start+Guide+for+Developers){ .md-button .md-button--primary } + +## Development Environment + +### Docker Environment +We provide a Docker image with all necessary dependencies to compile and test MADlib. This is the fastest way to get a development environment up and running. + +### Build from Source +Complete instructions for building MADlib from source on various platforms. + +## Architecture and Design + +### Core Architecture +- [MADlib Architecture Overview](https://cwiki.apache.org/confluence/display/MADLIB/Architecture) +- [Module Anatomy](https://cwiki.apache.org/confluence/display/MADLIB/Module+Anatomy) +- [Technical Design Document](../design.pdf) + +### API Guidelines +- [SQL API Style Guide](https://cwiki.apache.org/confluence/display/MADLIB/SQL+API+Guide) +- Best practices for algorithm implementation +- Performance optimization guidelines + +## Development Workflow + +### Source Code Management +- **Repository**: [GitHub - apache/madlib](https://github.com/apache/madlib) +- **Branching**: Feature branches and pull requests +- **Code Review**: All changes require review + +### Testing +- Unit tests for all algorithms +- Integration tests with multiple database platforms +- Performance benchmarks + +### Continuous Integration +- Automated testing on multiple platforms +- Code quality checks +- Documentation generation + +## Contributing Guidelines + +### Getting Started +1. **Join the Community**: [Developer Mailing List](mailto:dev-subscribe@madlib.apache.org) +2. **Find Issues**: [MADlib JIRA](https://issues.apache.org/jira/browse/MADLIB) +3. **Read Guidelines**: [Contribution Guidelines](https://cwiki.apache.org/confluence/display/MADLIB/Contribution+Guidelines) + +### Development Process +- Fork and clone the repository +- Create feature branches +- Follow coding standards +- Write comprehensive tests +- Submit pull requests + +## Algorithm Development + +### Adding New Algorithms +- Algorithm design principles +- Implementation patterns +- Documentation requirements +- Testing strategies + +### Performance Optimization +- Parallel processing patterns +- Memory management +- Database-specific optimizations + +## Platform Support + +### Supported Databases +- PostgreSQL (11, 12, 13, 14, 15) +- Greenplum Database (5.x, 6.x, 7.x) + +### Operating Systems +- Linux (CentOS, Ubuntu, RHEL) +- macOS +- Docker containers + +## Community and Support + +### Communication Channels +- [Developer Mailing List](mailto:dev-subscribe@madlib.apache.org) +- [Mailing List Archives](https://mail-archives.apache.org/mod_mbox/madlib-dev/) +- [GitHub Discussions](https://github.com/apache/madlib/discussions) + +### Regular Activities +- Weekly developer calls +- Quarterly planning meetings +- Annual contributor summits + +## Resources and Tools + +### Development Tools +- Recommended IDEs and editors +- Debugging tools +- Profiling utilities + +### Documentation Tools +- Doxygen for API documentation +- Sphinx for user guides +- Wiki for design documents + +## Getting Help + +If you need help with development: + +1. **Check Documentation**: Start with our [developer wiki](https://cwiki.apache.org/confluence/display/MADLIB/) +2. **Ask the Community**: Post to the [developer mailing list](mailto:dev-subscribe@madlib.apache.org) +3. **Report Issues**: Use [JIRA](https://issues.apache.org/jira/browse/MADLIB) for bugs and feature requests + +We're here to help you succeed as a MADlib contributor! \ No newline at end of file diff --git a/docs/community/index.md b/docs/community/index.md new file mode 100644 index 00000000..3bd73caa --- /dev/null +++ b/docs/community/index.md @@ -0,0 +1,100 @@ +# Community + +Welcome to the Apache MADlib community! We are an open source project dedicated to bringing advanced machine learning capabilities to SQL databases. + +--- + +## Reporting Issues + +We need your feedback, so if you find a bug, would like to suggest an improvement, or create a request then please follow the steps below to let us know. + +- Start by logging into [MADlib JIRA](https://issues.apache.org/jira/browse/MADLIB). If you don't have an account yet you can create one yourself. +- To report a bug: + 1. Create a new issue → Bug. + 2. Fill in the required (and optional) fields. +- To suggest an improvement or a new feature: + 1. Create a new issue → New Feature. + 2. Fill in the required (and optional) fields. +- Submit the issue. You should receive an email confirmation. Thanks for your feedback! + +--- + +## User Resources {#user-resources} + +### User Forum + +Our online user forum open to discuss any topics of interest to users of the product. + +- [Subscribe](mailto:user-subscribe@madlib.apache.org) to our user forum +- [Browse](https://mail-archives.apache.org/mod_mbox/madlib-user/) our user forum archives + +--- + +## Developer Resources {#developer-resources} + +### Developer Forum + +Our online developer forum open to discuss any topics of interest to open source contributors. + +- [Subscribe](mailto:dev-subscribe@madlib.apache.org) to our developer forum +- [Browse](https://mail-archives.apache.org/mod_mbox/madlib-dev/) our developer forum archives + +### Contribution Guide {#contribution} + +Step by step instructions guiding you through the MADlib contribution model + +- [Contribution Guidelines](https://cwiki.apache.org/confluence/display/MADLIB/Contribution+Guidelines) + +### Source Code Repository + +- Source code available on github, contributions welcome: [https://github.com/apache/madlib](https://github.com/apache/madlib) + +### Design Documents + +There are several resources aimed at helping new developers understand how MADlib is designed + +- [MADlib Architecture](https://cwiki.apache.org/confluence/display/MADLIB/Architecture) +- [Anatomy of a MADlib Module](https://cwiki.apache.org/confluence/display/MADLIB/Module+Anatomy) +- [MADlib SQL API Style Guide](https://cwiki.apache.org/confluence/display/MADLIB/SQL+API+Guide) +- [Technical Design Document](../design.pdf) + +--- + +## Research {#research} + +Interaction and collaboration with the open source and academic communities continues to be a core foundation of our project. We have papers published in major conferences. Including: + +- [MAD Skills – VLDB 2009](https://db.cs.berkeley.edu/papers/vldb09-madskills.pdf) +- [Hybrid In-Database Inference for Declarative Information Extraction – SIGMOD 2011](https://amplab.cs.berkeley.edu/publication/hybrid-in-database-inference-for-declarative-information-extraction/) +- [Towards a Unified Architecture for In-Database Analytics – SIGMOD 2012](https://www.cs.stanford.edu/~chrismre/papers/bismarck-full.pdf) +- [The MADlib Analytics Library or MAD Skills, the SQL – VLDB 2012](https://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-38.html) +- [Distributed Deep Learning on Data Systems: A Comparative Analysis of Approaches – 2021](https://adalabucsd.github.io/papers/TR_2021_Cerebro-DS.pdf) + +--- + +## Datasets {#datasets} + +There is a growing set of publicly available datasets. Here are some examples: + +- [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/index.php) +- [Google Dataset Search](https://datasetsearch.research.google.com/) +- [Kaggle Datasets](https://www.kaggle.com/datasets) +- [KDnuggets List of Datasets](https://www.kdnuggets.com/datasets/index.html) + +--- + +## Related Products + +- [PostgreSQL](https://postgresql.org) +- [Greenplum Database](https://greenplum.org/) +- [PivotalR](https://cran.r-project.org/web/packages/PivotalR/) + + + +## Subscribe + +To stay updated with the latest MADlib news: + +- Subscribe to our [user mailing list](mailto:user-subscribe@madlib.apache.org) +- Follow our [GitHub repository](https://github.com/apache/madlib) +- Check our [community page](../community/overview.md) for more ways to get involved \ No newline at end of file diff --git a/docs/community/research.md b/docs/community/research.md new file mode 100644 index 00000000..4c73defe --- /dev/null +++ b/docs/community/research.md @@ -0,0 +1,114 @@ +# Research Papers + +Interaction and collaboration with the open source and academic communities continues to be a core foundation of our project. We have papers published in major conferences. + +## Published Papers + +### Foundational Papers + +**MAD Skills – VLDB 2009** +The original paper that coined the term "MAD Skills" for data analysis and laid the foundation for the MADlib project. +[Read Paper](https://db.cs.berkeley.edu/papers/vldb09-madskills.pdf) + +**The MADlib Analytics Library or MAD Skills, the SQL – VLDB 2012** +Comprehensive overview of the MADlib analytics library and its SQL-based approach to machine learning. +[Read Paper](https://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-38.html) + +### Architecture and Systems + +**Towards a Unified Architecture for In-Database Analytics – SIGMOD 2012** +Discusses the architectural principles behind in-database analytics systems like MADlib. +[Read Paper](https://www.cs.stanford.edu/~chrismre/papers/bismarck-full.pdf) + +**Hybrid In-Database Inference for Declarative Information Extraction – SIGMOD 2011** +Explores hybrid approaches to information extraction using in-database processing. +[Read Paper](https://amplab.cs.berkeley.edu/publication/hybrid-in-database-inference-for-declarative-information-extraction/) + +### Recent Research + +**Distributed Deep Learning on Data Systems: A Comparative Analysis of Approaches – 2021** +Comparative analysis of different approaches to distributed deep learning, including MADlib's approach. +[Read Paper](https://adalabucsd.github.io/papers/TR_2021_Cerebro-DS.pdf) + +## Research Areas + +### In-Database Machine Learning +- Scalable algorithms for large datasets +- SQL-based machine learning interfaces +- Integration with database query optimizers + +### Distributed Computing +- Massively parallel processing (MPP) architectures +- Shared-nothing distributed systems +- Fault tolerance and reliability + +### Deep Learning Systems +- GPU acceleration in database systems +- Distributed neural network training +- Model management and versioning + +### Graph Analytics +- Large-scale graph processing +- Parallel graph algorithms +- Social network analysis + +## Academic Collaborations + +### University Partners + +**UC Berkeley** +Key research and development of scalable estimators and foundational algorithms. + +**Stanford University** +Research in convex optimization and statistical learning theory. + +**University of Florida** +Text analytics and natural language processing research. + +**UC San Diego** +Artificial neural networks on distributed systems and deep learning infrastructure. + +## Research Impact + +MADlib research has influenced: +- Database system design for analytics workloads +- SQL extensions for machine learning +- Distributed machine learning frameworks +- In-database processing paradigms + +## Citing MADlib + +If you use MADlib in your research, please cite the appropriate papers: + +```bibtex +@article{hellerstein2012madlib, + title={The MADlib analytics library: or MAD skills, the SQL}, + author={Hellerstein, Joseph M and R{\'e}, Christopher and Schoppmann, Florian and Wang, Daisy Zhe and Fratkin, Eugene and Gorajek, Aleksander and Ng, Kee Siong and Welton, Caleb and Feng, Xixuan and Li, Kun and others}, + journal={Proceedings of the VLDB Endowment}, + volume={5}, + number={12}, + pages={1700--1711}, + year={2012}, + publisher={VLDB Endowment} +} +``` + +## Future Research Directions + +Areas of active research and development: +- AutoML and automated model selection +- Federated learning capabilities +- Real-time streaming analytics +- Advanced deep learning architectures +- Quantum machine learning algorithms + +## Get Involved in Research + +Interested in collaborating on MADlib research? + +- Join our [developer community](developers.md) +- Participate in academic conferences +- Contribute to research publications +- Propose new research directions + +For research collaborations and academic partnerships, please contact us through the [developer mailing list](mailto:dev-subscribe@madlib.apache.org). \ No newline at end of file diff --git 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+ + + +
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+ + + +
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+
+ + + +
+
+ + + + +

Contributing to MathJax

+

You are interested in giving us a hand? That's awesome! We've put together some brief guidelines that should help you get started quickly and easily.

+

There are lots and lots of ways to get involved, this document covers:

+ +

Reporting An Issue

+

If you're about to raise an issue because you think you've found a +problem with MathJax, or you'd like to make a request for a new +feature in the codebase, or any other reason… please read this first.

+

The GitHub issue tracker is the preferred channel for bug reports, +feature requests, change requests and submitting pull +requests, but please respect the following restrictions:

+
    +
  • +

    Please search for existing issues. Help us keep duplicate issues + to a minimum by checking to see if someone has already reported your + problem or requested your idea.

    +
    • +
  • +

    Please do not use the issue tracker for personal support + requests (use the MathJax User Group).

    +
    • +
  • +

    Please be civil. Keep the discussion on topic and respect the + opinions of others. See also our Conduct Guidelines

    +
    • +
+

Bug Reports

+

A bug is a demonstrable problem that is caused by the code in the repository. +Good bug reports are extremely helpful - thank you!

+

Guidelines for bug reports:

+
    +
  1. +

    Use the GitHub issue search — check if the issue has already been + reported.

    +
    2. +
  2. +

    Check if the issue has been fixed — look for closed issues in the + current milestone or try to reproduce it + using the latest develop branch. Please note that we only pack MathJax for releases, so on the develop branch you have to use /unpacked/MathJax.js etc. to test.

    +
    3. +
  3. +

    Share a live sample of the problem — without a live page it is usually impossible to debug problems; see also the Bug Report Template below.

    +
    4. +
  4. +

    Isolate the problem — a live sample is a starting point but if you want to speed things up create a reduced test + case. Be specific about your setup (browser, OS versions etc). Use services like jsbin, CodePen, JSfiddle to make collaboration on minimal test cases easier for everyone. Use the unpacked copy of MathJax ([...]/unpacked/MathJax.js etc.) for better debugging.

    +
    5. +
  5. +

    Include a screenshot/cast as a last resort — Is your issue about a layout + or design feature / bug but hard to reproduce or isolate? Then please provide a screenshot or screencast. Tools like LICEcap or SauceLabs allow you to quickly and easily record a screencasts. Make it an animated gif, embed it directly into your GitHub issue -- kapow!

    +
    6. +
  6. +

    Use the Bug Report template below or click this + link + to start creating a bug report with the template automatically.

    +
    7. +
+

A good bug report shouldn't leave others needing to chase you up for +more information. Be sure to include the details of your environment.

+

Here is a real example

+

Template Example (click to use): +

Short and descriptive example bug report title
+
+### Issue Summary
+
+A summary of the issue and the browser/OS environment in which it occurs. If
+suitable, include the steps required to reproduce the bug.
+
+### Steps to Reproduce
+
+1. This is the first step
+2. This is the second step
+3. Further steps, etc.
+
+Any other information you want to share that is relevant to the issue
+being reported. Especially, why do you consider this to be a bug? What
+do you expect to happen instead?
+
+### Technical details:
+
+* MathJax Version: 2.3 (latest commit: f3aaf3a2a3e964df2770dc4aaaa9c87ce5f47e2c)
+* Client OS: Mac OS X 10.8.4
+* Browser: Chrome 29.0.1547.57
+

+

Feature Requests

+

Feature requests are welcome. Before you submit one be sure to have:

+
    +
  1. Read the + Roadmaps, + use the GitHub search and check the feature hasn't already been + requested.
    2. +
  2. Take a moment to think about whether your idea fits with the scope + and aims of the project, or if it might better fit being a custom + extension.
    3. +
  3. Remember, it's up to you to make a strong case to convince the + project's leaders of the merits of this feature. Please provide as + much detail and context as possible, this means explaining the use + case and why it is likely to be common.
    4. +
  4. Clearly indicate whether this is a feature request for MathJax + core, input & output jax, or extensions.
    5. +
+

Change Requests

+

Change requests cover both architectural and functional changes to how +MathJax works. If you have an idea for a new or different dependency, +a refactor, or an improvement to a feature, etc - please be sure to:

+
    +
  1. Use the GitHub search and check someone else didn't get there first
    2. +
  2. Take a moment to think about the best way to make a case for, and + explain what you're thinking. Are you sure this shouldn't really be + a bug report or a feature + request? Is it really one idea or is it many? + What's the context? What problem are you solving? Why is what you + are suggesting better than what's already there? Does it fit with + the Roadmap?
    3. +
+

Working on MathJax core

+

You want to contribute code? Fantastic! Let's get you started.

+

Key Branches & Tags

+

To get it out of the way:

+
    +
  • develop is + the development branch. All work on the next release happens here so + you should generally branch off develop. Do NOT use this branch + for a production site.
    • +
  • master contains the latest + release of MathJax. This branch may be used in production. Do + NOT use this branch to work on MathJax's source.
    • +
+

Submitting Pull Requests

+

Pull requests are awesome. If you're looking to raise a PR for +something which doesn't have an open issue, please think carefully +about raising an issue which your PR can close, +especially if you're fixing a bug. This makes it more likely that +there will be enough information available for your PR to be properly +tested and merged.

+
Need Help?
+

If you're not completely clear on how to submit / update / do Pull +Requests, please check out our source control +policies. For +more insights, chech the excellent in depth Git Workflow +guide from +Ghost, in particular

+ +

Testing and Quality Assurance

+

Never underestimate just how useful quality assurance is. If you're +looking to get involved with the code base and don't know where to +start, checking out and testing a pull request is one of the most +useful things you could do.

+

If you want to get involved with testing MathJax, there is a set of QA +Documentation in our testing +framework.

+

Essentially though, check out the latest develop +branch, take it for a spin, and if you find +anything odd, please follow the bug report guidelines +and let us know!

+

Checking out a Pull Request

+

These are some excellent +instructions on +configuring your GitHub repository to allow you to checkout pull +requests in the same way as branches: +https://gist.github.com/piscisaureus/3342247.

+

Writing documentation

+

MathJax's main documentation can be found at docs.mathjax.org. +The source of the docs is hosted in the +mathjax/mathjax-docs repo here on GitHub.

+

The documentation is generated using Sphinx-doc and hosted on +Read the docs. +You can clone the repo and submit pull requests following the +pull-request guidelines.

+

Translation

+

If you wish to add or update translations of MathJax, please do it on +TranslateWiki.net +(and while you're there you can help other open source projects, +too, because you're awesome!).

+

For bug reports and other questions that don't fit on +TranslateWiki.net, head over to the +mathjax/mathjax-i18n +repository.

+

Conduct

+

We are committed to providing a friendly, safe and welcoming environment for +all, regardless of gender, sexual orientation, disability, ethnicity, religion, +or similar personal characteristic.

+

Please be kind and courteous. There's no need to be mean or rude. +Respect that people have differences of opinion and that every design or +implementation choice carries a trade-off and numerous costs. There is seldom +a right answer, merely an optimal answer given a set of values and +circumstances.

+

Please keep unstructured critique to a minimum. If you have solid ideas you +want to experiment with, make a fork and see how it works.

+

We will exclude you from interaction if you insult, demean or harass anyone. +That is not welcome behaviour. We interpret the term "harassment" as +including the definition in the +Citizen Code of Conduct; +if you have any lack of clarity about what might be included in that concept, +please read their definition. In particular, we don't tolerate behavior that +excludes people in socially marginalized groups.

+

Private harassment is also unacceptable. No matter who you are, if you feel +you have been or are being harassed or made uncomfortable by a community +member, please contact one of the channel ops or any of the +MathJax core team +immediately. Whether you're a regular contributor or a newcomer, we care about +making this community a safe place for you and we've got your back.

+

Likewise any spamming, trolling, flaming, baiting or other attention-stealing +behaviour is not welcome.

+

We also suggest to read discourse's +rules

+

References

+
    +
  • We heavily borrowed from Mozilla and Ghost -- thank you!
    • +
  • https://github.com/TryGhost/Ghost/blob/master/CONTRIBUTING.md
    • +
  • https://github.com/mozilla/rust/wiki/Note-development-policy
    • +
  • https://github.com/jden/CONTRIBUTING.md/blob/master/CONTRIBUTING.md
    • +
  • http://blog.discourse.org/2013/03/the-universal-rules-of-civilized-discourse/
    • +
+ + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + +
+ + + +
+ + + +
+
+
+
+ + + + + + + + + + + + \ No newline at end of file diff --git a/docs/mathjax/LICENSE b/docs/docs/mathjax/LICENSE similarity index 100% rename from docs/mathjax/LICENSE rename to docs/docs/mathjax/LICENSE diff --git a/docs/mathjax/MathJax.js b/docs/docs/mathjax/MathJax.js similarity index 100% rename from docs/mathjax/MathJax.js rename to docs/docs/mathjax/MathJax.js diff --git a/docs/mathjax/bower.json b/docs/docs/mathjax/bower.json similarity index 100% rename from docs/mathjax/bower.json rename to docs/docs/mathjax/bower.json diff --git a/docs/mathjax/composer.json b/docs/docs/mathjax/composer.json similarity index 100% rename from docs/mathjax/composer.json rename to docs/docs/mathjax/composer.json diff --git a/docs/mathjax/config/AM_CHTML-full.js b/docs/docs/mathjax/config/AM_CHTML-full.js similarity index 100% rename from docs/mathjax/config/AM_CHTML-full.js rename to docs/docs/mathjax/config/AM_CHTML-full.js diff --git a/docs/mathjax/config/AM_CHTML.js 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MathJax

+

Beautiful math in all browsers

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MathJax is an open-source JavaScript display engine for LaTeX, MathML, and +AsciiMath notation that works in all modern browsers. It was designed with +the goal of consolidating the recent advances in web technologies into a +single, definitive, math-on-the-web platform supporting the major browsers +and operating systems. It requires no setup on the part of the user (no +plugins to download or software to install), so the page author can write +web documents that include mathematics and be confident that users will be +able to view it naturally and easily. Simply include MathJax and some +mathematics in a web page, and MathJax does the rest.

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Some of the main features of MathJax include:

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    High-quality display of LaTeX, MathML, and AsciiMath notation in HTML pages

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    Supported in most browsers with no plug-ins, extra fonts, or special + setup for the reader

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    Easy for authors, flexible for publishers, extensible for developers

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    Supports math accessibility, cut-and-paste interoperability, and other + advanced functionality

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    Powerful API for integration with other web applications

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See http://www.mathjax.org/ for additional details.

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Installation and Usage

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The MathJax installation and usage documentation is available in a +separate GitHub repository at

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  https://github.com/mathjax/mathjax-docs
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The HTML versions are now available at

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  http://docs.mathjax.org/
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where it is possible for you to submit corrections and modifications +directly to the documentation on line.

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Community

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The main MathJax website is http://www.mathjax.org, and it includes +announcements and other important information. MathJax is maintained and +distributed on GitHub at http://github.com/mathjax/MathJax. A user forum +for asking questions and getting assistance is hosted at Google, and the +bug tracker is hosted at GitHub:

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Bug tracker: https://github.com/mathjax/MathJax/issues
+MathJax-Users Group: http://groups.google.com/group/mathjax-users

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Before reporting a bug, please check that it has not already been reported. +Also, please use the bug tracker for reporting bugs rather than the help forum.

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+++ b/docs/docs/v2.1.0/apsp_8sql__in.html @@ -0,0 +1,361 @@ + + + + + + + + +MADlib: apsp.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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+Functions
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+
apsp.sql_in File Reference
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+
+ +

SQL functions for graph analytics. +More...

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+Functions

void graph_apsp (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, text grouping_cols)
 
void graph_apsp (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table)
 
void graph_apsp_get_path (text apsp_table, bigint source_vertex, bigint dest_vertex, text path_table)
 
void graph_apsp_get_path (text apsp_table, bigint[] source_vertex, bigint[] dest_vertex, text path_table)
 
varchar graph_apsp (varchar message)
 
varchar graph_apsp ()
 
+

Detailed Description

+

Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

+

http://www.apache.org/licenses/LICENSE-2.0

+

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

+
Date
Nov 2016
+
See also
Provides all pairs shortest path algorithm.
+

Function Documentation

+ +

◆ graph_apsp() [1/4]

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void graph_apsp (text vertex_table,
text vertex_id,
text edge_table,
text edge_args,
text out_table,
text grouping_cols 
)
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◆ graph_apsp() [2/4]

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void graph_apsp (text vertex_table,
text vertex_id,
text edge_table,
text edge_args,
text out_table 
)
+
+ +
+
+ +

◆ graph_apsp() [3/4]

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varchar graph_apsp (varchar message)
+
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+ +

◆ graph_apsp() [4/4]

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varchar graph_apsp ()
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◆ graph_apsp_get_path() [1/2]

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void graph_apsp_get_path (text apsp_table,
bigint source_vertex,
bigint dest_vertex,
text path_table 
)
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+ +
+
+ +

◆ graph_apsp_get_path() [2/2]

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void graph_apsp_get_path (text apsp_table,
bigint [] source_vertex,
bigint [] dest_vertex,
text path_table 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/arima_8sql__in.html b/docs/docs/v2.1.0/arima_8sql__in.html new file mode 100644 index 00000000..843ffa75 --- /dev/null +++ b/docs/docs/v2.1.0/arima_8sql__in.html @@ -0,0 +1,1054 @@ + + + + + + + + +MADlib: arima.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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+Functions
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+
arima.sql_in File Reference
+
+
+ +

Arima function for forecasting of timeseries data. +More...

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+Functions

void arima_train (text input_table, text output_table, text timestamp_column, text timeseries_column, text grouping_columns, boolean include_mean, integer[] non_seasonal_orders, text optimizer_params)
 
void arima_train (text input_table, text output_table, text timestamp_column, text timeseries_column, text grouping_columns, boolean include_mean, integer[] non_seasonal_orders)
 
void arima_train (text input_table, text output_table, text timestamp_column, text timeseries_column, text grouping_columns, boolean include_mean)
 
void arima_train (text input_table, text output_table, text timestamp_column, text timeseries_column, text grouping_columns)
 
void arima_train (text input_table, text output_table, text timestamp_column, text timeseries_column)
 
void arima_forecast (text model_table, text output_table, integer steps_ahead)
 
text arima_train (text message)
 
text arima_train ()
 
text arima_forecast (text message)
 
text arima_forecast ()
 
float8 [] __arima_residual (integer distid, float8[] tvals, integer p, integer d, integer q, float8[] phi, float8[] theta, float8 mean, float8[] prez)
 
float8 [] __arima_diff (float8[] tvals, integer d)
 
float8 [] __arima_adjust (integer distid, float8[] curr_tvals, float8[] prev_tvals, integer p)
 
float8 [] __arima_lm_delta (float8[] jj, float8[] jz, float8 u)
 
__arima_lm_result __arima_lm (integer distid, float8[] tvals, integer p, integer q, float8[] phi, float8[] theta, float8 mean, float8[] prez, float8[] prej)
 
float8 [] __arima_lm_result_sfunc (float8[] state_data, float8[] jj, float8[] jz, float8 z2)
 
float8 [] __arima_lm_result_pfunc (float8[] state1, float8[] state2)
 
__arima_lm_sum_result __arima_lm_result_ffunc (float8[] state_data)
 
aggregate __arima_lm_sum_result __arima_lm_result_agg (float8[], float8[], float8)
 
float8 [] __arima_lm_stat_sfunc (float8[] state_data, integer distid, float8[] tvals, integer p, integer q, float8[] phi, float8[] theta, float8 mean, float8 delta)
 
__arima_lm_stat_result __arima_lm_stat_ffunc (float8[] state_data)
 
aggregate __arima_lm_stat_result __arima_lm_stat_agg (integer, float8[], integer, integer, float8[], float8[], float8, float8)
 
+

Detailed Description

+
Date
August 2013
+

Function Documentation

+ +

◆ __arima_adjust()

+ +
+
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float8 [] __arima_adjust (integer distid,
float8 [] curr_tvals,
float8 [] prev_tvals,
integer p 
)
+
+ +
+
+ +

◆ __arima_diff()

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float8 [] __arima_diff (float8 [] tvals,
integer d 
)
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+ +
+
+ +

◆ __arima_lm()

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__arima_lm_result __arima_lm (integer distid,
float8 [] tvals,
integer p,
integer q,
float8 [] phi,
float8 [] theta,
float8 mean,
float8 [] prez,
float8 [] prej 
)
+
+ +
+
+ +

◆ __arima_lm_delta()

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float8 [] __arima_lm_delta (float8 [] jj,
float8 [] jz,
float8 u 
)
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+ +
+
+ +

◆ __arima_lm_result_agg()

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aggregate __arima_lm_sum_result __arima_lm_result_agg (float8 [],
float8 [],
float8  
)
+
+ +
+
+ +

◆ __arima_lm_result_ffunc()

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+
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__arima_lm_sum_result __arima_lm_result_ffunc (float8 [] state_data)
+
+ +
+
+ +

◆ __arima_lm_result_pfunc()

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float8 [] __arima_lm_result_pfunc (float8 [] state1,
float8 [] state2 
)
+
+ +
+
+ +

◆ __arima_lm_result_sfunc()

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float8 [] __arima_lm_result_sfunc (float8 [] state_data,
float8 [] jj,
float8 [] jz,
float8 z2 
)
+
+ +
+
+ +

◆ __arima_lm_stat_agg()

+ +
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aggregate __arima_lm_stat_result __arima_lm_stat_agg (integer ,
float8 [],
integer ,
integer ,
float8 [],
float8 [],
float8 ,
float8  
)
+
+ +
+
+ +

◆ __arima_lm_stat_ffunc()

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+ + + + + + + + +
__arima_lm_stat_result __arima_lm_stat_ffunc (float8 [] state_data)
+
+ +
+
+ +

◆ __arima_lm_stat_sfunc()

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float8 [] __arima_lm_stat_sfunc (float8 [] state_data,
integer distid,
float8 [] tvals,
integer p,
integer q,
float8 [] phi,
float8 [] theta,
float8 mean,
float8 delta 
)
+
+ +
+
+ +

◆ __arima_residual()

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float8 [] __arima_residual (integer distid,
float8 [] tvals,
integer p,
integer d,
integer q,
float8 [] phi,
float8 [] theta,
float8 mean,
float8 [] prez 
)
+
+ +
+
+ +

◆ arima_forecast() [1/3]

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void arima_forecast (text model_table,
text output_table,
integer steps_ahead 
)
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+ +
+
+ +

◆ arima_forecast() [2/3]

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text arima_forecast (text message)
+
+ +
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◆ arima_forecast() [3/3]

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text arima_forecast ()
+
+ +
+
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◆ arima_train() [1/7]

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void arima_train (text input_table,
text output_table,
text timestamp_column,
text timeseries_column,
text grouping_columns,
boolean include_mean,
integer [] non_seasonal_orders,
text optimizer_params 
)
+
+ +
+
+ +

◆ arima_train() [2/7]

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void arima_train (text input_table,
text output_table,
text timestamp_column,
text timeseries_column,
text grouping_columns,
boolean include_mean,
integer [] non_seasonal_orders 
)
+
+ +
+
+ +

◆ arima_train() [3/7]

+ +
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void arima_train (text input_table,
text output_table,
text timestamp_column,
text timeseries_column,
text grouping_columns,
boolean include_mean 
)
+
+ +
+
+ +

◆ arima_train() [4/7]

+ +
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void arima_train (text input_table,
text output_table,
text timestamp_column,
text timeseries_column,
text grouping_columns 
)
+
+ +
+
+ +

◆ arima_train() [5/7]

+ +
+
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void arima_train (text input_table,
text output_table,
text timestamp_column,
text timeseries_column 
)
+
+ +
+
+ +

◆ arima_train() [6/7]

+ +
+
+ + + + + + + + +
text arima_train (text message)
+
+ +
+
+ +

◆ arima_train() [7/7]

+ +
+
+ + + + + + + +
text arima_train ()
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/array__ops_8sql__in.html b/docs/docs/v2.1.0/array__ops_8sql__in.html new file mode 100644 index 00000000..1f8926e7 --- /dev/null +++ b/docs/docs/v2.1.0/array__ops_8sql__in.html @@ -0,0 +1,1350 @@ + + + + + + + + +MADlib: array_ops.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
array_ops.sql_in File Reference
+
+
+ +

implementation of array operations in SQL +More...

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+Functions

anyarray array_add (anyarray x, anyarray y)
 Adds two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
aggregate anyarray sum (anyarray)
 Aggregate, element-wise sum of arrays. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_sub (anyarray x, anyarray y)
 Subtracts two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_mult (anyarray x, anyarray y)
 Element-wise product of two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_div (anyarray x, anyarray y)
 Element-wise division of two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
float8 array_dot (anyarray x, anyarray y)
 Dot-product of two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
bool array_contains (anyarray x, anyarray y)
 Checks whether one array contains the other. This function returns TRUE if each non-zero element in the right array equals to the element with the same index in the left array. More...
 
anyelement array_max (anyarray x)
 This function finds the maximum value in the array. NULLs are ignored. Return type is the same as the input type. More...
 
float8 [] array_max_index (anyarray x)
 This function finds the maximum value and corresponding index in the array. NULLs are ignored. Return type is the same as the input type. More...
 
anyelement array_min (anyarray x)
 This function finds the minimum value in the array. NULLs are ignored. Return type is the same as the input type. More...
 
float8 [] array_min_index (anyarray x)
 This function finds the minimum value and corresponding index in the array. NULLs are ignored. Return type is the same as the input type. More...
 
anyelement array_sum (anyarray x)
 This function finds the sum of the values in the array. NULLs are ignored. Return type is the same as the input type. More...
 
float8 array_sum_big (anyarray x)
 This function finds the sum of the values in the array. NULLs are ignored. Return type is always FLOAT8 regardless of input. This function is meant to replace array_sum() in the cases when sum may overflow the element type. More...
 
anyelement array_abs_sum (anyarray x)
 This function finds the sum of abs of the values in the array. NULLs are ignored. Return type is the same as the input type. More...
 
anyarray array_abs (anyarray x)
 This function takes an array as the input and finds absolute value of each element in the array, returning the resulting array. It requires that all the values are NON-NULL. More...
 
float8 array_mean (anyarray x)
 This function finds the mean of the values in the array. NULLs are ignored. More...
 
float8 array_stddev (anyarray x)
 This function finds the standard deviation of the values in the array. NULLs are ignored. More...
 
float8 [] array_of_float (integer k)
 This function creates an array of set size (the argument value) of FLOAT8, initializing the values to 0.0;. More...
 
bigint [] array_of_bigint (integer k)
 This function creates an array of set size (the argument value) of BIGINT, initializing the values to 0;. More...
 
anyarray array_fill (anyarray x, anyelement k)
 This functions set every values in the array to some desired value (provided as the argument). More...
 
anyarray array_cos (anyarray x)
 This function takes an array as the input and apply cos function element-wise, returning the resulting array. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_scalar_mult (anyarray x, anyelement k)
 This function takes an array as the input and executes element-wise multiplication by the scalar provided as the second argument, returning the resulting array. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_scalar_add (anyarray x, anyelement k)
 This function takes an array as the input and executes element-wise addition by the scalar provided as the second argument, returning the resulting array. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_filter (anyarray x, anyelement k, text op)
 This function takes an array as the input and keep only elements that satisfy the operator on specified scalar. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_filter (anyarray x, anyelement k)
 This function takes an array as the input and removes elements that equal to specified scalar. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
anyarray array_filter (anyarray x)
 This function takes an array as the input and removes elements that equal to 0. It requires that all the values are NON-NULL. Return type is the same as the input type. More...
 
float8 [] array_sqrt (anyarray x)
 This function takes an array as the input and finds square root of each element in the array, returning the resulting array. It requires that all the values are NON-NULL. More...
 
anyarray array_pow (anyarray x, anyelement y)
 This function takes an array and a float8 as the input and finds power of each element in the array, returning the resulting array. It requires that all the values are NON-NULL. More...
 
float8 [] array_square (anyarray x)
 This function takes an array as the input and finds square of each element in the array, returning the resulting array. It requires that all the values are NON-NULL. More...
 
float8 [] normalize (anyarray x)
 This function normalizes an array as sum of squares to be 1. More...
 
boolean array_contains_null (anyarray x)
 Function to check if array contains NULL. More...
 
anyarray array_cum_sum (anyarray x)
 This function takes an array as the input and computes the cumulative sum with the first element being the same. It requires that all the values are NON-NULL. More...
 
anyarray array_cum_prod (anyarray x)
 This function takes an array as the input and computes the cumulative product with the first element being the same. It requires that all the values are NON-NULL. More...
 
set< record > array_unnest_2d_to_1d (bigint[] x, int unnest_row_id, bigint[] unnest_result)
 This function takes a 2-D array as the input and unnests it by one level. It returns a set of 1-D arrays that correspond to rows of the input array as well as an ID column containing row positions occupied by those 1-D arrays within the 2-D array (the ID column values start with 1 and not 0) More...
 
set< record > array_unnest_2d_to_1d (float8[] x, int unnest_row_id, float8[] unnest_result)
 
set< record > array_unnest_2d_to_1d (anyarray x, int unnest_row_id, anyarray unnest_result)
 
text array_unnest_2d_to_1d ()
 
bytea array_to_bytea (anyarray)
 
+

Detailed Description

+
Date
April 2011
+

Function Documentation

+ +

◆ array_abs()

+ +
+
+ + + + + + + + +
anyarray array_abs (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Absolute value of all elements of x.
+ +
+
+ +

◆ array_abs_sum()

+ +
+
+ + + + + + + + +
anyelement array_abs_sum (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Sum of absolute value of x
+ +
+
+ +

◆ array_add()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_add (anyarray x,
anyarray y 
)
+
+
Parameters
+ + + +
xArray x
yArray y
+
+
+
Returns
Sum of x and y.
+ +
+
+ +

◆ array_contains()

+ +
+
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bool array_contains (anyarray x,
anyarray y 
)
+
+
Parameters
+ + + +
xArray x
yArray y
+
+
+
Returns
Returns true if x contains y.
+ +
+
+ +

◆ array_contains_null()

+ +
+
+ + + + + + + + +
boolean array_contains_null (anyarray x)
+
+
Parameters
+ + +
xArray x.
+
+
+
Returns
True if x has NULL value else False.
+ +
+
+ +

◆ array_cos()

+ +
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anyarray array_cos (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Array with each element of cos(x).
+ +
+
+ +

◆ array_cum_prod()

+ +
+
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anyarray array_cum_prod (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Cumulative product of the elements in x.
+ +
+
+ +

◆ array_cum_sum()

+ +
+
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anyarray array_cum_sum (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Cumulative sum of the elements in x.
+ +
+
+ +

◆ array_div()

+ +
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anyarray array_div (anyarray x,
anyarray y 
)
+
+
Parameters
+ + + +
xArray x
yArray y
+
+
+
Returns
Element-wise division of x and y.
+ +
+
+ +

◆ array_dot()

+ +
+
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float8 array_dot (anyarray x,
anyarray y 
)
+
+
Parameters
+ + + +
xArray x
yArray y
+
+
+
Returns
Dot-product of x and y.
+ +
+
+ +

◆ array_fill()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_fill (anyarray x,
anyelement k 
)
+
+
Parameters
+ + + +
xSome array
kDesired value
+
+
+
Returns
Fills array with desired value.
+ +
+
+ +

◆ array_filter() [1/3]

+ +
+
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anyarray array_filter (anyarray x,
anyelement k,
text op 
)
+
+
Parameters
+ + + + +
xArray x
kScalar
opOperator
+
+
+
Returns
Filtered array.
+ +
+
+ +

◆ array_filter() [2/3]

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_filter (anyarray x,
anyelement k 
)
+
+
Parameters
+ + + +
xArray x
kScalar
+
+
+
Returns
Filtered array.
+ +
+
+ +

◆ array_filter() [3/3]

+ +
+
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anyarray array_filter (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Filtered array.
+ +
+
+ +

◆ array_max()

+ +
+
+ + + + + + + + +
anyelement array_max (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Max of x.
+ +
+
+ +

◆ array_max_index()

+ +
+
+ + + + + + + + +
float8 [] array_max_index (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Array as [max, index].
+ +
+
+ +

◆ array_mean()

+ +
+
+ + + + + + + + +
float8 array_mean (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Mean of x.
+ +
+
+ +

◆ array_min()

+ +
+
+ + + + + + + + +
anyelement array_min (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Min of x.
+ +
+
+ +

◆ array_min_index()

+ +
+
+ + + + + + + + +
float8 [] array_min_index (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Array as [min, index].
+ +
+
+ +

◆ array_mult()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_mult (anyarray x,
anyarray y 
)
+
+
Parameters
+ + + +
xArray x
yArray y
+
+
+
Returns
Element-wise product of x and y.
+ +
+
+ +

◆ array_of_bigint()

+ +
+
+ + + + + + + + +
bigint [] array_of_bigint (integer k)
+
+
Parameters
+ + +
kArray size.
+
+
+
Returns
Array of size k.
+ +
+
+ +

◆ array_of_float()

+ +
+
+ + + + + + + + +
float8 [] array_of_float (integer k)
+
+
Parameters
+ + +
kArray size
+
+
+
Returns
Array of size k.
+ +
+
+ +

◆ array_pow()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_pow (anyarray x,
anyelement y 
)
+
+
Parameters
+ + + +
xArray x
yDesired power
+
+
+
Returns
Power of y for all elements of x.
+ +
+
+ +

◆ array_scalar_add()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_scalar_add (anyarray x,
anyelement k 
)
+
+
Parameters
+ + + +
xArray x
kScalar
+
+
+
Returns
Array with each element of x added by scalar.
+ +
+
+ +

◆ array_scalar_mult()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_scalar_mult (anyarray x,
anyelement k 
)
+
+
Parameters
+ + + +
xArray x
kScalar
+
+
+
Returns
Array with each element of x multiplied by scalar.
+ +
+
+ +

◆ array_sqrt()

+ +
+
+ + + + + + + + +
float8 [] array_sqrt (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Square root of all elements of x.
+ +
+
+ +

◆ array_square()

+ +
+
+ + + + + + + + +
float8 [] array_square (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Square of all elements of x.
+ +
+
+ +

◆ array_stddev()

+ +
+
+ + + + + + + + +
float8 array_stddev (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Standard deviation of x.
+ +
+
+ +

◆ array_sub()

+ +
+
+ + + + + + + + + + + + + + + + + + +
anyarray array_sub (anyarray x,
anyarray y 
)
+
+
Parameters
+ + + +
xArray x
yArray y
+
+
+
Returns
x-y.
+ +
+
+ +

◆ array_sum()

+ +
+
+ + + + + + + + +
anyelement array_sum (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Sum of x.
+ +
+
+ +

◆ array_sum_big()

+ +
+
+ + + + + + + + +
float8 array_sum_big (anyarray x)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Sum of x.
+ +
+
+ +

◆ array_to_bytea()

+ +
+
+ + + + + + + + +
bytea array_to_bytea (anyarray )
+
+ +
+
+ +

◆ array_unnest_2d_to_1d() [1/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
set<record> array_unnest_2d_to_1d (bigint [] x,
int unnest_row_id,
bigint [] unnest_result 
)
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Set of 1-D arrays that corrspond to rows of x and an ID column.
+ +
+
+ +

◆ array_unnest_2d_to_1d() [2/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
set<record> array_unnest_2d_to_1d (float8 [] x,
int unnest_row_id,
float8 [] unnest_result 
)
+
+ +
+
+ +

◆ array_unnest_2d_to_1d() [3/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
set<record> array_unnest_2d_to_1d (anyarray x,
int unnest_row_id,
anyarray unnest_result 
)
+
+ +
+
+ +

◆ array_unnest_2d_to_1d() [4/4]

+ +
+
+ + + + + + + +
text array_unnest_2d_to_1d ()
+
+ +
+
+ +

◆ normalize()

+ +
+
+ + + + + + + + +
float8 [] normalize (anyarray x)
+
+
Parameters
+ + +
xArray x.
+
+
+
Returns
Array normalized by its 2-norm.
+ +
+
+ +

◆ sum()

+ +
+
+ + + + + + + + +
aggregate anyarray sum (anyarray )
+
+
Parameters
+ + +
xArray x
+
+
+
Returns
Sum of x
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/assoc__rules_8sql__in.html b/docs/docs/v2.1.0/assoc__rules_8sql__in.html new file mode 100644 index 00000000..1daf4c7f --- /dev/null +++ b/docs/docs/v2.1.0/assoc__rules_8sql__in.html @@ -0,0 +1,561 @@ + + + + + + + + +MADlib: assoc_rules.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
assoc_rules.sql_in File Reference
+
+
+ +

The assoc_rules function computes association rules for a given set of data. The data is assumed to have two dimensions; items (between which we are trying to discover associations), and a transaction id. This tranaction id groups the items by event and could also be a user id, date, etc. depending on the context of the data. This function assumes the data is stored in two columns with one transaction id and one item per row. +More...

+ + + + + + + + + + + + + + + + + + + +

+Functions

set< text[]> gen_rules_from_cfp (text, int, int, int)
 
assoc_rules_results assoc_rules (float8 support, float8 confidence, text tid_col, text item_col, text input_table, text output_schema, boolean verbose, integer max_itemset_size, integer max_lhs_size, integer max_rhs_size)
 
assoc_rules_results assoc_rules (float8 support, float8 confidence, text tid_col, text item_col, text input_table, text output_schema, boolean verbose, integer max_itemset_size, integer max_lhs_size)
 
assoc_rules_results assoc_rules (float8 support, float8 confidence, text tid_col, text item_col, text input_table, text output_schema, boolean verbose, integer max_itemset_size)
 
assoc_rules_results assoc_rules (float8 support, float8 confidence, text tid_col, text item_col, text input_table, text output_schema)
 The short form of the above function with vobose removed. More...
 
assoc_rules_results assoc_rules (float8 support, float8 confidence, text tid_col, text item_col, text input_table, text output_schema, boolean verbose)
 
text assoc_rules (text message)
 
text assoc_rules ()
 
+

Detailed Description

+
Date
June 2011
+
+August 2012
+
See also
For a brief introduction to the association rules implementation, see the module description Apriori Algorithm.
+

Function Documentation

+ +

◆ assoc_rules() [1/7]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
assoc_rules_results assoc_rules (float8 support,
float8 confidence,
text tid_col,
text item_col,
text input_table,
text output_schema,
boolean verbose,
integer max_itemset_size,
integer max_lhs_size,
integer max_rhs_size 
)
+
+
Parameters
+ + + + + + + + +
supportminimum level of support needed for each itemset to be included in result
confidenceminimum level of confidence needed for each rule to be included in result
tid_colname of the column storing the transaction ids
item_colname of the column storing the products
input_tablename of the table where the data is stored
output_schemaname of the schema where the final results will be stored
verbosedetermining if output contains comments
+
+
+
Returns
The schema and table name containing association rules, and total number of rules found.
+

This function computes the association rules between products in a data set. It reads the name of the table, the column names of the product and ids, and computes ssociation rules using the Apriori algorithm, and subject to the support and confidence constraints as input by the user. This version of association rules has verbose functionality. When verbose is true, output of function includes iteration steps and comments on Apriori algorithm steps.

+ +
+
+ +

◆ assoc_rules() [2/7]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
assoc_rules_results assoc_rules (float8 support,
float8 confidence,
text tid_col,
text item_col,
text input_table,
text output_schema,
boolean verbose,
integer max_itemset_size,
integer max_lhs_size 
)
+
+ +
+
+ +

◆ assoc_rules() [3/7]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
assoc_rules_results assoc_rules (float8 support,
float8 confidence,
text tid_col,
text item_col,
text input_table,
text output_schema,
boolean verbose,
integer max_itemset_size 
)
+
+ +
+
+ +

◆ assoc_rules() [4/7]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
assoc_rules_results assoc_rules (float8 support,
float8 confidence,
text tid_col,
text item_col,
text input_table,
text output_schema 
)
+
+ +
+
+ +

◆ assoc_rules() [5/7]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
assoc_rules_results assoc_rules (float8 support,
float8 confidence,
text tid_col,
text item_col,
text input_table,
text output_schema,
boolean verbose 
)
+
+ +
+
+ +

◆ assoc_rules() [6/7]

+ +
+
+ + + + + + + + +
text assoc_rules (text message)
+
+ +
+
+ +

◆ assoc_rules() [7/7]

+ +
+
+ + + + + + + +
text assoc_rules ()
+
+ +
+
+ +

◆ gen_rules_from_cfp()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
set<text[]> gen_rules_from_cfp (text ,
int ,
int ,
int  
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/balance__sample_8sql__in.html b/docs/docs/v2.1.0/balance__sample_8sql__in.html new file mode 100644 index 00000000..adc9ac08 --- /dev/null +++ b/docs/docs/v2.1.0/balance__sample_8sql__in.html @@ -0,0 +1,481 @@ + + + + + + + + +MADlib: balance_sample.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
balance_sample.sql_in File Reference
+
+
+ +

SQL functions for balanced data sets sampling. +More...

+ + + + + + + + + + + + + + + + + + +

+Functions

void balance_sample (text source_table, text output_table, text class_col, varchar class_sizes, integer output_table_size, text grouping_cols, boolean with_replacement, boolean keep_null)
 
void balance_sample (text source_table, text output_table, text class_col, varchar class_sizes, integer output_table_size, text grouping_cols, boolean with_replacement)
 
void balance_sample (text source_table, text output_table, text class_col, varchar class_sizes, integer output_table_size, text grouping_cols)
 
void balance_sample (text source_table, text output_table, text class_col, varchar class_sizes, integer output_table_size)
 
void balance_sample (text source_table, text output_table, text class_col, varchar class_sizes)
 
void balance_sample (text source_table, text output_table, text class_col)
 
varchar balance_sample (varchar message)
 
varchar balance_sample ()
 
+

Detailed Description

+

Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

+

http://www.apache.org/licenses/LICENSE-2.0

+

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

+
Date
12/14/2017
+
See also
Given a table, balanced sampling returns a sampled data set with specified proportions for each class (defaults to uniform sampling).
+

Function Documentation

+ +

◆ balance_sample() [1/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void balance_sample (text source_table,
text output_table,
text class_col,
varchar class_sizes,
integer output_table_size,
text grouping_cols,
boolean with_replacement,
boolean keep_null 
)
+
+ +
+
+ +

◆ balance_sample() [2/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void balance_sample (text source_table,
text output_table,
text class_col,
varchar class_sizes,
integer output_table_size,
text grouping_cols,
boolean with_replacement 
)
+
+ +
+
+ +

◆ balance_sample() [3/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void balance_sample (text source_table,
text output_table,
text class_col,
varchar class_sizes,
integer output_table_size,
text grouping_cols 
)
+
+ +
+
+ +

◆ balance_sample() [4/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void balance_sample (text source_table,
text output_table,
text class_col,
varchar class_sizes,
integer output_table_size 
)
+
+ +
+
+ +

◆ balance_sample() [5/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void balance_sample (text source_table,
text output_table,
text class_col,
varchar class_sizes 
)
+
+ +
+
+ +

◆ balance_sample() [6/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
void balance_sample (text source_table,
text output_table,
text class_col 
)
+
+ +
+
+ +

◆ balance_sample() [7/8]

+ +
+
+ + + + + + + + +
varchar balance_sample (varchar message)
+
+ +
+
+ +

◆ balance_sample() [8/8]

+ +
+
+ + + + + + + +
varchar balance_sample ()
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/bayes_8sql__in.html b/docs/docs/v2.1.0/bayes_8sql__in.html new file mode 100644 index 00000000..d2768db2 --- /dev/null +++ b/docs/docs/v2.1.0/bayes_8sql__in.html @@ -0,0 +1,978 @@ + + + + + + + + +MADlib: bayes.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
bayes.sql_in File Reference
+
+
+ +

SQL functions for naive Bayes. +More...

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+Functions

args_and_value_double argmax_transition (args_and_value_double oldmax, integer newkey, float8 newvalue)
 
args_and_value_double argmax_combine (args_and_value_double max1, args_and_value_double max2)
 
integer [] argmax_final (args_and_value_double finalstate)
 
aggregate integer [] argmax (integer key, float8 value)
 
void create_nb_prepared_data_tables (varchar trainingSource, varchar trainingClassColumn, varchar trainingAttrColumn, integer numAttrs, varchar featureProbsDestName, varchar classPriorsDestName)
 Precompute all class priors and feature probabilities. More...
 
void create_nb_prepared_data_tables (varchar trainingSource, varchar trainingClassColumn, varchar trainingAttrColumn, varchar numericAttrsColumnIndices, integer numAttrs, varchar featureProbsDestName, varchar numericFeatureStatsDestName, varchar classPriorsDestName)
 
void create_nb_classify_view (varchar featureProbsSource, varchar classPriorsSource, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar destName)
 Create a view with columns (key, nb_classification) More...
 
void create_nb_classify_view (varchar featureProbsSource, varchar classPriorsSource, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar numericFeatureStatsSource, varchar destName)
 
void create_nb_classify_view (varchar trainingSource, varchar trainingClassColumn, varchar trainingAttrColumn, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar destName)
 
void create_nb_classify_view (varchar trainingSource, varchar trainingClassColumn, varchar trainingAttrColumn, varchar numericAttrsColumnIndices, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar destName)
 
void create_nb_probs_view (varchar featureProbsSource, varchar classPriorsSource, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar destName)
 Create view with columns (key, class, nb_prob) More...
 
void create_nb_probs_view (varchar featureProbsSource, varchar classPriorsSource, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar numericFeatureStatsSource, varchar destName)
 
void create_nb_probs_view (varchar trainingSource, varchar trainingClassColumn, varchar trainingAttrColumn, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar destName)
 
void create_nb_probs_view (varchar trainingSource, varchar trainingClassColumn, varchar trainingAttrColumn, varchar numericAttrsColumnIndices, varchar classifySource, varchar classifyKeyColumn, varchar classifyAttrColumn, integer numAttrs, varchar destName)
 
+

Detailed Description

+
Date
January 2011
+
See also
For a brief introduction to Naive Bayes Classification, see the module description Naive Bayes Classification.
+

Function Documentation

+ +

◆ argmax()

+ +
+
+ + + + + + + + + + + + + + + + + + +
aggregate integer [] argmax (integer key,
float8 value 
)
+
+ +
+
+ +

◆ argmax_combine()

+ +
+
+ + + + + + + + + + + + + + + + + + +
args_and_value_double argmax_combine (args_and_value_double max1,
args_and_value_double max2 
)
+
+ +
+
+ +

◆ argmax_final()

+ +
+
+ + + + + + + + +
integer [] argmax_final (args_and_value_double finalstate)
+
+ +
+
+ +

◆ argmax_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
args_and_value_double argmax_transition (args_and_value_double oldmax,
integer newkey,
float8 newvalue 
)
+
+ +
+
+ +

◆ create_nb_classify_view() [1/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_classify_view (varchar featureProbsSource,
varchar classPriorsSource,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar destName 
)
+
+

The created relation will be

+

{TABLE|VIEW} destName (key, nb_classification)

+

where nb_classification is an array containing the most likely class(es) of the record in classifySource identified by key.

+
Parameters
+ + + + + + + + +
featureProbsSourceName of table with precomputed feature probabilities, as created with create_nb_prepared_data_tables()
classPriorsSourceName of table with precomputed class priors, as created with create_nb_prepared_data_tables()
classifySourceName of the relation that contains data to be classified
classifyKeyColumnName of column in classifySource that can serve as unique identifier (the key of the source relation)
classifyAttrColumnName of attributes-array column in classifySource
numAttrsNumber of attributes to use for classification
destNameName of the view to create
+
+
+
Note
create_nb_classify_view can be called in an ad-hoc fashion. See Naive Bayes Classification for instructions.
+
Usage
    +
  1. Create Naive Bayes classifications view: 
    SELECT create_nb_classify_view(
+    'featureProbsName', 'classPriorsName',
+    'classifySource', 'classifyKeyColumn', 'classifyAttrColumn',
+    numAttrs, 'destName'
+);
    2. +
  2. Show Naive Bayes classifications: 
    SELECT * FROM destName;
    3. +
+
+ +
+
+ +

◆ create_nb_classify_view() [2/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_classify_view (varchar featureProbsSource,
varchar classPriorsSource,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar numericFeatureStatsSource,
varchar destName 
)
+
+ +
+
+ +

◆ create_nb_classify_view() [3/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_classify_view (varchar trainingSource,
varchar trainingClassColumn,
varchar trainingAttrColumn,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar destName 
)
+
+ +
+
+ +

◆ create_nb_classify_view() [4/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_classify_view (varchar trainingSource,
varchar trainingClassColumn,
varchar trainingAttrColumn,
varchar numericAttrsColumnIndices,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar destName 
)
+
+ +
+
+ +

◆ create_nb_prepared_data_tables() [1/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_prepared_data_tables (varchar trainingSource,
varchar trainingClassColumn,
varchar trainingAttrColumn,
integer numAttrs,
varchar featureProbsDestName,
varchar classPriorsDestName 
)
+
+

Feature probabilities are stored in a table of format 

TABLE featureProbsDestName (
+    class INTEGER,
+    attr INTEGER,
+    value INTEGER,
+    cnt INTEGER,
+    attr_cnt INTEGER
+)

Class priors are stored in a table of format 

TABLE classPriorsDestName (
+    class INTEGER,
+    class_cnt INTEGER,
+    all_cnt INTEGER
+)
Parameters
+ + + + + + + +
trainingSourceName of relation containing the training data
trainingClassColumnName of class column in training data
trainingAttrColumnName of attributes-array column in training data
numAttrsNumber of attributes to use for classification
featureProbsDestNameName of feature-probabilities table to create
classPriorsDestNameName of class-priors table to create
+
+
+
Usage
Precompute feature probabilities and class priors: 
SELECT create_nb_prepared_data_tables(
+    'trainingSource', 'trainingClassColumn', 'trainingAttrColumn',
+    numAttrs, 'featureProbsName', 'classPriorsName'
+);
+ +
+
+ +

◆ create_nb_prepared_data_tables() [2/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_prepared_data_tables (varchar trainingSource,
varchar trainingClassColumn,
varchar trainingAttrColumn,
varchar numericAttrsColumnIndices,
integer numAttrs,
varchar featureProbsDestName,
varchar numericFeatureStatsDestName,
varchar classPriorsDestName 
)
+
+ +
+
+ +

◆ create_nb_probs_view() [1/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_probs_view (varchar featureProbsSource,
varchar classPriorsSource,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar destName 
)
+
+

The created view will be of the following form:

+
VIEW destName (
+    key ANYTYPE,
+    class INTEGER,
+    nb_prob FLOAT8
+)

where nb_prob is the Naive-Bayes probability that class is the true class of the record in classifySource identified by key.

+
Parameters
+ + + + + + + + +
featureProbsSourceName of table with precomputed feature probabilities, as created with create_nb_prepared_data_tables()
classPriorsSourceName of table with precomputed class priors, as created with create_nb_prepared_data_tables()
classifySourceName of the relation that contains data to be classified
classifyKeyColumnName of column in classifySource that can serve as unique identifier (the key of the source relation)
classifyAttrColumnName of attributes-array column in classifySource
numAttrsNumber of attributes to use for classification
destNameName of the view to create
+
+
+
Note
create_nb_probs_view can be called in an ad-hoc fashion. See Naive Bayes Classification for instructions.
+
Usage
    +
  1. Create Naive Bayes probabilities view: 
    SELECT create_nb_probs_view(
+    'featureProbsName', 'classPriorsName',
+    'classifySource', 'classifyKeyColumn', 'classifyAttrColumn',
+    numAttrs, 'destName'
+);
    2. +
  2. Show Naive Bayes probabilities: 
    SELECT * FROM destName;
    3. +
+
+ +
+
+ +

◆ create_nb_probs_view() [2/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_probs_view (varchar featureProbsSource,
varchar classPriorsSource,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar numericFeatureStatsSource,
varchar destName 
)
+
+ +
+
+ +

◆ create_nb_probs_view() [3/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_probs_view (varchar trainingSource,
varchar trainingClassColumn,
varchar trainingAttrColumn,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar destName 
)
+
+ +
+
+ +

◆ create_nb_probs_view() [4/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_nb_probs_view (varchar trainingSource,
varchar trainingClassColumn,
varchar trainingAttrColumn,
varchar numericAttrsColumnIndices,
varchar classifySource,
varchar classifyKeyColumn,
varchar classifyAttrColumn,
integer numAttrs,
varchar destName 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/bc_s.png b/docs/docs/v2.1.0/bc_s.png new file mode 100644 index 0000000000000000000000000000000000000000..224b29aa9847d5a4b3902efd602b7ddf7d33e6c2 GIT binary patch literal 676 zcmV;V0$crwP)y__>=_9%My z{n931IS})GlGUF8K#6VIbs%684A^L3@%PlP2>_sk`UWPq@f;rU*V%rPy_ekbhXT&s z(GN{DxFv}*vZp`F>S!r||M`I*nOwwKX+BC~3P5N3-)Y{65c;ywYiAh-1*hZcToLHK ztpl1xomJ+Yb}K(cfbJr2=GNOnT!UFA7Vy~fBz8?J>XHsbZoDad^8PxfSa0GDgENZS zuLCEqzb*xWX2CG*b&5IiO#NzrW*;`VC9455M`o1NBh+(k8~`XCEEoC1Ybwf;vr4K3 zg|EB<07?SOqHp9DhLpS&bzgo70I+ghB_#)K7H%AMU3v}xuyQq9&Bm~++VYhF09a+U zl7>n7Jjm$K#b*FONz~fj;I->Bf;ule1prFN9FovcDGBkpg>)O*-}eLnC{6oZHZ$o% zXKW$;0_{8hxHQ>l;_*HATI(`7t#^{$(zLe}h*mqwOc*nRY9=?Sx4OOeVIfI|0V(V2 zBrW#G7Ss9wvzr@>H*`r>zE z+e8bOBgqIgldUJlG(YUDviMB`9+DH8n-s9SXRLyJHO1!=wY^79WYZMTa(wiZ!zP66 zA~!21vmF3H2{ngD;+`6j#~6j;$*f*G_2ZD1E;9(yaw7d-QnSCpK(cR1zU3qU0000< KMNUMnLSTYoA~SLT literal 0 HcmV?d00001 diff --git a/docs/docs/v2.1.0/bdwn.png b/docs/docs/v2.1.0/bdwn.png new file mode 100644 index 0000000000000000000000000000000000000000..940a0b950443a0bb1b216ac03c45b8a16c955452 GIT binary patch literal 147 zcmeAS@N?(olHy`uVBq!ia0vp^>_E)H!3HEvS)PKZC{Gv1kP61Pb5HX&C2wk~_T + + + + + + + +MADlib: bfs.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
bfs.sql_in File Reference
+
+
+ +

SQL functions for graph analytics. +More...

+ + + + + + + + + + + + + + +

+Functions

void graph_bfs (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint source_vertex, text out_table, int max_distance, boolean directed, text grouping_cols)
 
void graph_bfs (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint source_vertex, text out_table, int max_distance, boolean directed)
 
void graph_bfs (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint source_vertex, text out_table, int max_distance)
 
void graph_bfs (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint source_vertex, text out_table)
 
varchar graph_bfs (varchar message)
 
varchar graph_bfs ()
 
+

Detailed Description

+

Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

+

http://www.apache.org/licenses/LICENSE-2.0

+

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

+
Date
Jun 2017
+
See also
Provides a breadth first search graph algorithm.
+

Function Documentation

+ +

◆ graph_bfs() [1/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void graph_bfs (text vertex_table,
text vertex_id,
text edge_table,
text edge_args,
bigint source_vertex,
text out_table,
int max_distance,
boolean directed,
text grouping_cols 
)
+
+ +
+
+ +

◆ graph_bfs() [2/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void graph_bfs (text vertex_table,
text vertex_id,
text edge_table,
text edge_args,
bigint source_vertex,
text out_table,
int max_distance,
boolean directed 
)
+
+ +
+
+ +

◆ graph_bfs() [3/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void graph_bfs (text vertex_table,
text vertex_id,
text edge_table,
text edge_args,
bigint source_vertex,
text out_table,
int max_distance 
)
+
+ +
+
+ +

◆ graph_bfs() [4/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void graph_bfs (text vertex_table,
text vertex_id,
text edge_table,
text edge_args,
bigint source_vertex,
text out_table 
)
+
+ +
+
+ +

◆ graph_bfs() [5/6]

+ +
+
+ + + + + + + + +
varchar graph_bfs (varchar message)
+
+ +
+
+ +

◆ graph_bfs() [6/6]

+ +
+
+ + + + + + + +
varchar graph_bfs ()
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/closed.png b/docs/docs/v2.1.0/closed.png new file mode 100644 index 0000000000000000000000000000000000000000..98cc2c909da37a6df914fbf67780eebd99c597f5 GIT binary patch literal 132 zcmeAS@N?(olHy`uVBq!ia0vp^oFL4>1|%O$WD@{V-kvUwAr*{o@8{^CZMh(5KoB^r_<4^zF@3)Cp&&t3hdujKf f*?bjBoY!V+E))@{xMcbjXe@)LtDnm{r-UW|*e5JT literal 0 HcmV?d00001 diff --git a/docs/docs/v2.1.0/clustered__variance_8sql__in.html b/docs/docs/v2.1.0/clustered__variance_8sql__in.html new file mode 100644 index 00000000..4339449d --- /dev/null +++ b/docs/docs/v2.1.0/clustered__variance_8sql__in.html @@ -0,0 +1,1938 @@ + + + + + + + + +MADlib: clustered_variance.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
clustered_variance.sql_in File Reference
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+Functions

void clustered_variance_linregr (text source_table, text out_table, text depvar, text indvar, text clustervar, text grouping_col)
 Compute the clustered errors. More...
 
void clustered_variance_linregr (text source_table, text out_table, text depvar, text indvar, text clustervar)
 
text clustered_variance_linregr ()
 
text clustered_variance_linregr (text msg)
 
bytea8 __clustered_err_lin_transition (bytea8 state, float8 y, float8[] x, float8[] coef)
 
bytea8 __clustered_err_lin_merge (bytea8 state1, bytea8 state2)
 
__clustered_agg_result __clustered_err_lin_final (bytea8 state)
 
aggregate __clustered_agg_result __clustered_err_lin_step (float8, float8[], float8[])
 
__clustered_lin_result __clustered_lin_compute_stats (float8[] coef, float8[] meatvec, float8[] breadvec, integer mcluster, integer numrows)
 
float8 [] __array_add (float8[] x, float8[] y)
 
aggregate float8 [] __array_sum (float8[])
 
void clustered_variance_logregr (text source_table, text out_table, text depvar, text indvar, text clustervar, text grouping_col, integer max_iter, text optimizer, float8 tolerance, boolean verbose_mode)
 
void clustered_variance_logregr (text source_table, text out_table, text depvar, text indvar, text clustervar)
 
void clustered_variance_logregr (text source_table, text out_table, text depvar, text indvar, text clustervar, text grouping_col)
 
void clustered_variance_logregr (text source_table, text out_table, text depvar, text indvar, text clustervar, text grouping_col, integer max_iter)
 
void clustered_variance_logregr (text source_table, text out_table, text depvar, text indvar, text clustervar, text grouping_col, integer max_iter, text optimizer)
 
void clustered_variance_logregr (text source_table, text out_table, text depvar, text indvar, text clustervar, text grouping_col, integer max_iter, text optimizer, float8 tolerance)
 
text clustered_variance_logregr ()
 
text clustered_variance_logregr (text msg)
 
bytea8 __clustered_err_log_transition (bytea8 state, boolean y, float8[] x, float8[] coef)
 
bytea8 __clustered_err_log_merge (bytea8 state1, bytea8 state2)
 
__clustered_agg_result __clustered_err_log_final (bytea8 state)
 
aggregate __clustered_agg_result __clustered_err_log_step (boolean, float8[], float8[])
 
__clustered_log_result __clustered_log_compute_stats (float8[] coef, float8[] meatvec, float8[] breadvec, integer mcluster, integer numrows)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols, text optimizer_params, boolean verbose_mode)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols, text optimizer_params)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname)
 
text clustered_variance_mlogregr ()
 
text clustered_variance_mlogregr (text msg)
 
bytea8 __clustered_err_mlog_transition (bytea8 state, integer y, float8[] x, float8[] coef, integer num_cat, integer ref_cat)
 
bytea8 __clustered_err_mlog_merge (bytea8 state1, bytea8 state2)
 
__clustered_agg_result __clustered_err_mlog_final (bytea8 state)
 
aggregate __clustered_agg_result __clustered_err_mlog_step (integer, float8[], float8[], integer, integer)
 
__clustered_mlog_result __clustered_mlog_compute_stats (float8[] coef, float8[] meatvec, float8[] breadvec, integer mcluster, integer numrows)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose_mode)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols, integer max_iter, varchar optimizer, float8 tolerance)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols, integer max_iter, varchar optimizer)
 
void clustered_variance_mlogregr (text source_table, text out_table, text dependent_varname, text independent_varname, text cluster_varname, integer ref_category, text grouping_cols, integer max_iter)
 
+

Function Documentation

+ +

◆ __array_add()

+ +
+
+ + + + + + + + + + + + + + + + + + +
float8 [] __array_add (float8 [] x,
float8 [] y 
)
+
+ +
+
+ +

◆ __array_sum()

+ +
+
+ + + + + + + + +
aggregate float8 [] __array_sum (float8 [])
+
+ +
+
+ +

◆ __clustered_err_lin_final()

+ +
+
+ + + + + + + + +
__clustered_agg_result __clustered_err_lin_final (bytea8 state)
+
+ +
+
+ +

◆ __clustered_err_lin_merge()

+ +
+
+ + + + + + + + + + + + + + + + + + +
bytea8 __clustered_err_lin_merge (bytea8 state1,
bytea8 state2 
)
+
+ +
+
+ +

◆ __clustered_err_lin_step()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
aggregate __clustered_agg_result __clustered_err_lin_step (float8 ,
float8 [],
float8 [] 
)
+
+ +
+
+ +

◆ __clustered_err_lin_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
bytea8 __clustered_err_lin_transition (bytea8 state,
float8 y,
float8 [] x,
float8 [] coef 
)
+
+ +
+
+ +

◆ __clustered_err_log_final()

+ +
+
+ + + + + + + + +
__clustered_agg_result __clustered_err_log_final (bytea8 state)
+
+ +
+
+ +

◆ __clustered_err_log_merge()

+ +
+
+ + + + + + + + + + + + + + + + + + +
bytea8 __clustered_err_log_merge (bytea8 state1,
bytea8 state2 
)
+
+ +
+
+ +

◆ __clustered_err_log_step()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
aggregate __clustered_agg_result __clustered_err_log_step (boolean ,
float8 [],
float8 [] 
)
+
+ +
+
+ +

◆ __clustered_err_log_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
bytea8 __clustered_err_log_transition (bytea8 state,
boolean y,
float8 [] x,
float8 [] coef 
)
+
+ +
+
+ +

◆ __clustered_err_mlog_final()

+ +
+
+ + + + + + + + +
__clustered_agg_result __clustered_err_mlog_final (bytea8 state)
+
+ +
+
+ +

◆ __clustered_err_mlog_merge()

+ +
+
+ + + + + + + + + + + + + + + + + + +
bytea8 __clustered_err_mlog_merge (bytea8 state1,
bytea8 state2 
)
+
+ +
+
+ +

◆ __clustered_err_mlog_step()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
aggregate __clustered_agg_result __clustered_err_mlog_step (integer ,
float8 [],
float8 [],
integer ,
integer  
)
+
+ +
+
+ +

◆ __clustered_err_mlog_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
bytea8 __clustered_err_mlog_transition (bytea8 state,
integer y,
float8 [] x,
float8 [] coef,
integer num_cat,
integer ref_cat 
)
+
+ +
+
+ +

◆ __clustered_lin_compute_stats()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
__clustered_lin_result __clustered_lin_compute_stats (float8 [] coef,
float8 [] meatvec,
float8 [] breadvec,
integer mcluster,
integer numrows 
)
+
+ +
+
+ +

◆ __clustered_log_compute_stats()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
__clustered_log_result __clustered_log_compute_stats (float8 [] coef,
float8 [] meatvec,
float8 [] breadvec,
integer mcluster,
integer numrows 
)
+
+ +
+
+ +

◆ __clustered_mlog_compute_stats()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
__clustered_mlog_result __clustered_mlog_compute_stats (float8 [] coef,
float8 [] meatvec,
float8 [] breadvec,
integer mcluster,
integer numrows 
)
+
+ +
+
+ +

◆ clustered_variance_linregr() [1/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_linregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar,
text grouping_col 
)
+
+
Parameters
+ + + + + + + +
source_tableData table name
out_tableThe result table
depvarDependent variable expression
indvarIndependent variable expression
clustervarThe expressions used to clustering
grouping_colThe names of grouping columns
+
+
+ +
+
+ +

◆ clustered_variance_linregr() [2/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_linregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar 
)
+
+ +
+
+ +

◆ clustered_variance_linregr() [3/4]

+ +
+
+ + + + + + + +
text clustered_variance_linregr ()
+
+ +
+
+ +

◆ clustered_variance_linregr() [4/4]

+ +
+
+ + + + + + + + +
text clustered_variance_linregr (text msg)
+
+ +
+
+ +

◆ clustered_variance_logregr() [1/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_logregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar,
text grouping_col,
integer max_iter,
text optimizer,
float8 tolerance,
boolean verbose_mode 
)
+
+ +
+
+ +

◆ clustered_variance_logregr() [2/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_logregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar 
)
+
+ +
+
+ +

◆ clustered_variance_logregr() [3/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_logregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar,
text grouping_col 
)
+
+ +
+
+ +

◆ clustered_variance_logregr() [4/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_logregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar,
text grouping_col,
integer max_iter 
)
+
+ +
+
+ +

◆ clustered_variance_logregr() [5/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_logregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar,
text grouping_col,
integer max_iter,
text optimizer 
)
+
+ +
+
+ +

◆ clustered_variance_logregr() [6/8]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_logregr (text source_table,
text out_table,
text depvar,
text indvar,
text clustervar,
text grouping_col,
integer max_iter,
text optimizer,
float8 tolerance 
)
+
+ +
+
+ +

◆ clustered_variance_logregr() [7/8]

+ +
+
+ + + + + + + +
text clustered_variance_logregr ()
+
+ +
+
+ +

◆ clustered_variance_logregr() [8/8]

+ +
+
+ + + + + + + + +
text clustered_variance_logregr (text msg)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [1/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols,
text optimizer_params,
boolean verbose_mode 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [2/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols,
text optimizer_params 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [3/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [4/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [5/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [6/11]

+ +
+
+ + + + + + + +
text clustered_variance_mlogregr ()
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [7/11]

+ +
+
+ + + + + + + + +
text clustered_variance_mlogregr (text msg)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [8/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols,
integer max_iter,
varchar optimizer,
float8 tolerance,
boolean verbose_mode 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [9/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols,
integer max_iter,
varchar optimizer,
float8 tolerance 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [10/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols,
integer max_iter,
varchar optimizer 
)
+
+ +
+
+ +

◆ clustered_variance_mlogregr() [11/11]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_mlogregr (text source_table,
text out_table,
text dependent_varname,
text independent_varname,
text cluster_varname,
integer ref_category,
text grouping_cols,
integer max_iter 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/clustered__variance__coxph_8sql__in.html b/docs/docs/v2.1.0/clustered__variance__coxph_8sql__in.html new file mode 100644 index 00000000..fba2409a --- /dev/null +++ b/docs/docs/v2.1.0/clustered__variance__coxph_8sql__in.html @@ -0,0 +1,480 @@ + + + + + + + + +MADlib: clustered_variance_coxph.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
clustered_variance_coxph.sql_in File Reference
+
+
+ +

SQL functions for clustered robust cox proportional hazards regression. +More...

+ + + + + + + + + + + + + + + + + + + + + + +

+Functions

varchar clustered_variance_coxph ()
 
varchar clustered_variance_coxph (varchar message)
 
void clustered_variance_coxph (text model_table, text output_table, text clustervar)
 
float8 [] coxph_a_b_transition (float8[], integer, boolean, float8[], float8)
 
float8 [] coxph_a_b_merge (float8[], float8[])
 
__coxph_a_b_result coxph_a_b_final (float8[])
 
aggregate __coxph_a_b_result coxph_a_b (integer, boolean, float8[], float8)
 
float8 [] coxph_compute_w (float8[] x, boolean status, float8[] coef, float8[] h, float8 s, float8 a, float8[] b)
 
__coxph_cl_var_result coxph_compute_clustered_stats (float8[] coef, float8[] hessian, float8[] a)
 
void robust_variance_coxph (varchar model_table, varchar output_table, varchar clustervar)
 
+

Detailed Description

+
Date
Oct 2013
+
See also
For a brief introduction to clustered robust cox regression, see the module description Clustered Variance
+

Function Documentation

+ +

◆ clustered_variance_coxph() [1/3]

+ +
+
+ + + + + + + +
varchar clustered_variance_coxph ()
+
+ +
+
+ +

◆ clustered_variance_coxph() [2/3]

+ +
+
+ + + + + + + + +
varchar clustered_variance_coxph (varchar message)
+
+ +
+
+ +

◆ clustered_variance_coxph() [3/3]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
void clustered_variance_coxph (text model_table,
text output_table,
text clustervar 
)
+
+ +
+
+ +

◆ coxph_a_b()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
aggregate __coxph_a_b_result coxph_a_b (integer ,
boolean ,
float8 [],
float8  
)
+
+ +
+
+ +

◆ coxph_a_b_final()

+ +
+
+ + + + + + + + +
__coxph_a_b_result coxph_a_b_final (float8 [])
+
+ +
+
+ +

◆ coxph_a_b_merge()

+ +
+
+ + + + + + + + + + + + + + + + + + +
float8 [] coxph_a_b_merge (float8 [],
float8 [] 
)
+
+ +
+
+ +

◆ coxph_a_b_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float8 [] coxph_a_b_transition (float8 [],
integer ,
boolean ,
float8 [],
float8  
)
+
+ +
+
+ +

◆ coxph_compute_clustered_stats()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
__coxph_cl_var_result coxph_compute_clustered_stats (float8 [] coef,
float8 [] hessian,
float8 [] a 
)
+
+ +
+
+ +

◆ coxph_compute_w()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float8 [] coxph_compute_w (float8 [] x,
boolean status,
float8 [] coef,
float8 [] h,
float8 s,
float8 a,
float8 [] b 
)
+
+ +
+
+ +

◆ robust_variance_coxph()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
void robust_variance_coxph (varchar model_table,
varchar output_table,
varchar clustervar 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/cols2vec_8sql__in.html b/docs/docs/v2.1.0/cols2vec_8sql__in.html new file mode 100644 index 00000000..6a549414 --- /dev/null +++ b/docs/docs/v2.1.0/cols2vec_8sql__in.html @@ -0,0 +1,300 @@ + + + + + + + + +MADlib: cols2vec.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
cols2vec.sql_in File Reference
+
+
+ +

A set of utilities to ease basic table transformations (such as *aggregating multiple columns in an array) +More...

+ + + + + + + + + + + + +

+Functions

void cols2vec (varchar source_table, varchar output_table, varchar list_of_features, varchar list_of_features_to_exclude, varchar cols_to_output)
 
void cols2vec (varchar source_table, varchar output_table, varchar list_of_features, varchar list_of_features_to_exclude)
 
void cols2vec (varchar source_table, varchar output_table, varchar list_of_features)
 
text cols2vec (text message)
 
text cols2vec ()
 
+

Detailed Description

+

Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

+

http://www.apache.org/licenses/LICENSE-2.0

+

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

+
Date
July 2018
+

Function Documentation

+ +

◆ cols2vec() [1/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cols2vec (varchar source_table,
varchar output_table,
varchar list_of_features,
varchar list_of_features_to_exclude,
varchar cols_to_output 
)
+
+ +
+
+ +

◆ cols2vec() [2/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cols2vec (varchar source_table,
varchar output_table,
varchar list_of_features,
varchar list_of_features_to_exclude 
)
+
+ +
+
+ +

◆ cols2vec() [3/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
void cols2vec (varchar source_table,
varchar output_table,
varchar list_of_features 
)
+
+ +
+
+ +

◆ cols2vec() [4/5]

+ +
+
+ + + + + + + + +
text cols2vec (text message)
+
+ +
+
+ +

◆ cols2vec() [5/5]

+ +
+
+ + + + + + + +
text cols2vec ()
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/conjugate__gradient_8sql__in.html b/docs/docs/v2.1.0/conjugate__gradient_8sql__in.html new file mode 100644 index 00000000..6167581c --- /dev/null +++ b/docs/docs/v2.1.0/conjugate__gradient_8sql__in.html @@ -0,0 +1,247 @@ + + + + + + + + +MADlib: conjugate_gradient.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
conjugate_gradient.sql_in File Reference
+
+
+ +

SQL function computing Conjugate Gradient. +More...

+ + + + + + + +

+Functions

float [] conjugate_gradient (text matrix, text val_id, text row_id, float[] b, float precision_limit, int verbosity)
 Compute conjugate gradient. More...
 
float [] conjugate_gradient (text matrix, text val_id, text row_id, float[] b, float precision_limit)
 
+

Detailed Description

+
Date
March 2011
+

Function Documentation

+ +

◆ conjugate_gradient() [1/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float [] conjugate_gradient (text matrix,
text val_id,
text row_id,
float [] b,
float precision_limit,
int verbosity 
)
+
+
Parameters
+ + + + + + + +
matrixName of the table containing argument matrix A
val_idName of the column contains row values
row_idName of the column contains row number
bArray containing values of b
precision_limitPrecision threshold after which process will terminate
verbosityVerbose flag (0 = false, 1 = true)
+
+
+
Returns
Array containing values of x
+ +
+
+ +

◆ conjugate_gradient() [2/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float [] conjugate_gradient (text matrix,
text val_id,
text row_id,
float [] b,
float precision_limit 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/correlation_8sql__in.html b/docs/docs/v2.1.0/correlation_8sql__in.html new file mode 100644 index 00000000..23ca3b7e --- /dev/null +++ b/docs/docs/v2.1.0/correlation_8sql__in.html @@ -0,0 +1,777 @@ + + + + + + + + +MADlib: correlation.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
correlation.sql_in File Reference
+
+
+ +

SQL functions for correlation computation. +More...

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+Functions

float8 [] correlation_transition (float8[] state, float8[] x, float8[] mean)
 
float8 [] correlation_merge (float8[] left_state, float8[] right_state)
 
float8 [] correlation_final (float8[] state)
 
aggregate float8 [] correlation_agg (float8[], float8[])
 
aggregate float8 [] covariance_agg (float8[], float8[])
 
text correlation (varchar source_table, varchar output_table, varchar target_cols, boolean verbose, varchar grouping_cols, integer n_groups_per_run)
 
text correlation (varchar source_table, varchar output_table, varchar target_cols, boolean verbose, varchar grouping_cols)
 
text correlation (varchar source_table, varchar output_table, varchar target_cols, boolean verbose)
 
text correlation (varchar source_table, varchar output_table, varchar target_cols)
 
text correlation (varchar source_table, varchar output_table)
 
text correlation (text input_message)
 
text correlation ()
 
text covariance (varchar source_table, varchar output_table, varchar target_cols, boolean verbose, varchar grouping_cols, integer n_groups_per_run)
 
text covariance (varchar source_table, varchar output_table, varchar target_cols, boolean verbose, varchar grouping_cols)
 
text covariance (varchar source_table, varchar output_table, varchar target_cols, boolean verbose)
 
text covariance (varchar source_table, varchar output_table, varchar target_cols)
 
text covariance (varchar source_table, varchar output_table)
 
text covariance (text input_message)
 
text covariance ()
 
+

Detailed Description

+
Date
April 2013
+
See also
For a brief introduction to correlation, see the module description Covariance and Correlation
+

Function Documentation

+ +

◆ correlation() [1/7]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
text correlation (varchar source_table,
varchar output_table,
varchar target_cols,
boolean verbose,
varchar grouping_cols,
integer n_groups_per_run 
)
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◆ correlation() [2/7]

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text correlation (varchar source_table,
varchar output_table,
varchar target_cols,
boolean verbose,
varchar grouping_cols 
)
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◆ correlation() [3/7]

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text correlation (varchar source_table,
varchar output_table,
varchar target_cols,
boolean verbose 
)
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◆ correlation() [4/7]

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text correlation (varchar source_table,
varchar output_table,
varchar target_cols 
)
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◆ correlation() [5/7]

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text correlation (varchar source_table,
varchar output_table 
)
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◆ correlation() [6/7]

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text correlation (text input_message)
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◆ correlation() [7/7]

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text correlation ()
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◆ correlation_agg()

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aggregate float8 [] correlation_agg (float8 [],
float8 [] 
)
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◆ correlation_final()

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float8 [] correlation_final (float8 [] state)
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◆ correlation_merge()

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float8 [] correlation_merge (float8 [] left_state,
float8 [] right_state 
)
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◆ correlation_transition()

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float8 [] correlation_transition (float8 [] state,
float8 [] x,
float8 [] mean 
)
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◆ covariance() [1/7]

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text covariance (varchar source_table,
varchar output_table,
varchar target_cols,
boolean verbose,
varchar grouping_cols,
integer n_groups_per_run 
)
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◆ covariance() [2/7]

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text covariance (varchar source_table,
varchar output_table,
varchar target_cols,
boolean verbose,
varchar grouping_cols 
)
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◆ covariance() [3/7]

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text covariance (varchar source_table,
varchar output_table,
varchar target_cols,
boolean verbose 
)
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◆ covariance() [4/7]

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text covariance (varchar source_table,
varchar output_table,
varchar target_cols 
)
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◆ covariance() [5/7]

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text covariance (varchar source_table,
varchar output_table 
)
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◆ covariance() [6/7]

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text covariance (text input_message)
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◆ covariance() [7/7]

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text covariance ()
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◆ covariance_agg()

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aggregate float8 [] covariance_agg (float8 [],
float8 [] 
)
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+ + + + diff --git a/docs/docs/v2.1.0/cox__prop__hazards_8sql__in.html b/docs/docs/v2.1.0/cox__prop__hazards_8sql__in.html new file mode 100644 index 00000000..a56f1521 --- /dev/null +++ b/docs/docs/v2.1.0/cox__prop__hazards_8sql__in.html @@ -0,0 +1,2134 @@ + + + + + + + + +MADlib: cox_prop_hazards.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
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User Documentation for Apache MADlib
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+Functions
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cox_prop_hazards.sql_in File Reference
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SQL functions for cox proportional hazards. +More...

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+Functions

float8 [] array_avg_transition (float8[] state, float8[] x, boolean use_abs)
 
float8 [] array_avg_merge (float8[] left, float8[] right)
 
float8 [] array_avg_final (float8[] state)
 
aggregate float8 [] array_avg (float8[], boolean)
 
void coxph_train (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, varchar right_censoring_status, varchar strata, varchar optimizer_params)
 Compute cox-regression coefficients and diagnostic statistics. More...
 
varchar coxph_train ()
 
varchar coxph_train (varchar message)
 
void coxph_train (varchar source_table, varchar output_table, varchar dependent_variable, varchar independent_variable, varchar right_censoring_status, varchar strata)
 Cox regression training function. More...
 
void coxph_train (varchar source_table, varchar output_table, varchar dependent_variable, varchar independent_variable, varchar right_censoring_status)
 Cox regression training function. More...
 
void coxph_train (varchar source_table, varchar output_table, varchar dependent_variable, varchar independent_variable)
 Cox regression training function. More...
 
void coxph_predict (text model_table, text source_table, text id_col_name, text output_table, text pred_type, text reference)
 Predict the linear Predictor or the risk for the given data. More...
 
void coxph_predict (text model_table, text source_table, text id_col_name, text output_table, text pred_type)
 
void coxph_predict (text model_table, text source_table, text id_col_name, text output_table)
 
float8 _coxph_predict_resp (float8[] coef, float8[] col_ind_var, float8[] mean_ind_var, text pred_type)
 
float8 [] _coxph_predict_terms (float8[] coef, float8[] col_ind_var, float8[] mean_ind_var)
 
varchar coxph_predict (varchar message)
 
varchar coxph_predict ()
 
float8 [] _split_transition (float8[], float8, integer, integer)
 
float8 [] _split_merge (float8[], float8[])
 
float8 [] _split_final (float8[])
 
aggregate float8 [] _compute_splits (float8, integer, integer)
 
integer _compute_grpid (float8[] splits, float8 split_col, boolean reverse)
 
integer _compute_grpid (float8[] splits, float8 split_col)
 
coxph_result compute_coxph_result (float8[] coef, float8 l, float8[] d2l, integer niter, float8[] stds)
 
coxph_step_result coxph_improved_step_final (float8[] state)
 
float8 [] coxph_improved_step_transition (float8[] state, float8[] x, float8[] y, integer[] status, float8[] coef, float8[] max_coef)
 
float8 [] coxph_step_inner_final (float8[] state)
 
float8 [] coxph_step_outer_transition (float8[] state1, float8[] state2)
 
coxph_step_result coxph_improved_strata_step_final (float8[] state)
 
aggregate float8 [] coxph_improved_strata_step_outer (float8[] state)
 
void cox_zph (varchar coxph_model_table, varchar output_table)
 Test the proportional hazards assumption for a Cox regression model fit (coxph_train) More...
 
varchar cox_zph ()
 
varchar cox_zph (varchar message)
 
float8 [] __zph_transition (float8[] state, float8[] x, float8[] coef)
 
float8 [] __zph_merge (float8[] left_state, float8[] right_state)
 
float8 [] __zph_final (float8[] left_state)
 
aggregate float8 [] zph_agg (float8[] x, float8[] coef)
 
float8 [] __coxph_scale_resid (integer m, float8[] hessian, float8[] resid)
 
float8 [] __array_elem_corr_transition (float8[] state, float8[] x, float8 y)
 
float8 [] __array_elem_corr_merge (float8[] left_state, float8[] right_state)
 
float8 [] __array_elem_corr_final (float8[] state)
 
aggregate float8 [] array_elem_corr_agg (float8[] array_input, float8 common_elem)
 
float8 [] __coxph_resid_stat_transition (float8[] state, float8 w, float8[] residual, float8[] hessian, integer m)
 
float8 [] __coxph_resid_stat_merge (float8[] state1, float8[] state2)
 
__cox_resid_stat_result __coxph_resid_stat_final (float8[] state)
 
aggregate float8 [] __coxph_resid_stat_agg (float8 w, float8[] residual, float8[] hessian, integer m)
 
void cox_prop_hazards (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar status)
 Cox regression training function. More...
 
void cox_prop_hazards (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable)
 Cox regression training function. More...
 
varchar cox_prop_hazards (varchar usage_string)
 
varchar cox_prop_hazards ()
 
cox_prop_hazards_result cox_prop_hazards_regr (varchar source, varchar indepColumn, varchar depColumn, varchar status, integer maxNumIterations=20, varchar optimizer="newton", float8 precision=0.0001)
 
cox_prop_hazards_result cox_prop_hazards_regr (varchar source, varchar indepColumn, varchar depColumn, varchar status)
 
cox_prop_hazards_result cox_prop_hazards_regr (varchar source, varchar indepColumn, varchar depColumn, varchar status, integer maxNumIterations)
 
cox_prop_hazards_result cox_prop_hazards_regr (varchar source, varchar indepColumn, varchar depColumn, varchar status, integer maxNumIterations, varchar optimizer)
 
float8 [] __array_element_min (float8[], float8[])
 
aggregate float8 [] array_element_min (float8[])
 
float8 [] __array_element_max (float8[], float8[])
 
aggregate float8 [] array_element_max (float8[])
 
+

Detailed Description

+
Date
July 2012
+
See also
For a brief introduction to cox regression, see the module description Cox-Proportional Hazards Regression
+

Function Documentation

+ +

◆ __array_elem_corr_final()

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float8 [] __array_elem_corr_final (float8 [] state)
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◆ __array_elem_corr_merge()

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float8 [] __array_elem_corr_merge (float8 [] left_state,
float8 [] right_state 
)
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◆ __array_elem_corr_transition()

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float8 [] __array_elem_corr_transition (float8 [] state,
float8 [] x,
float8 y 
)
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◆ __array_element_max()

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float8 [] __array_element_max (float8 [],
float8 [] 
)
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◆ __array_element_min()

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float8 [] __array_element_min (float8 [],
float8 [] 
)
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◆ __coxph_resid_stat_agg()

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aggregate float8 [] __coxph_resid_stat_agg (float8 w,
float8 [] residual,
float8 [] hessian,
integer m 
)
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◆ __coxph_resid_stat_final()

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__cox_resid_stat_result __coxph_resid_stat_final (float8 [] state)
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◆ __coxph_resid_stat_merge()

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float8 [] __coxph_resid_stat_merge (float8 [] state1,
float8 [] state2 
)
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◆ __coxph_resid_stat_transition()

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float8 [] __coxph_resid_stat_transition (float8 [] state,
float8 w,
float8 [] residual,
float8 [] hessian,
integer m 
)
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◆ __coxph_scale_resid()

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float8 [] __coxph_scale_resid (integer m,
float8 [] hessian,
float8 [] resid 
)
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◆ __zph_final()

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float8 [] __zph_final (float8 [] left_state)
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◆ __zph_merge()

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float8 [] __zph_merge (float8 [] left_state,
float8 [] right_state 
)
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◆ __zph_transition()

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float8 [] __zph_transition (float8 [] state,
float8 [] x,
float8 [] coef 
)
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◆ _compute_grpid() [1/2]

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integer _compute_grpid (float8 [] splits,
float8 split_col,
boolean reverse 
)
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◆ _compute_grpid() [2/2]

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integer _compute_grpid (float8 [] splits,
float8 split_col 
)
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◆ _compute_splits()

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aggregate float8 [] _compute_splits (float8 ,
integer ,
integer  
)
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◆ _coxph_predict_resp()

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float8 _coxph_predict_resp (float8 [] coef,
float8 [] col_ind_var,
float8 [] mean_ind_var,
text pred_type 
)
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◆ _coxph_predict_terms()

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float8 [] _coxph_predict_terms (float8 [] coef,
float8 [] col_ind_var,
float8 [] mean_ind_var 
)
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◆ _split_final()

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float8 [] _split_final (float8 [])
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◆ _split_merge()

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float8 [] _split_merge (float8 [],
float8 [] 
)
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◆ _split_transition()

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float8 [] _split_transition (float8 [],
float8 ,
integer ,
integer  
)
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◆ array_avg()

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aggregate float8 [] array_avg (float8 [],
boolean  
)
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◆ array_avg_final()

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float8 [] array_avg_final (float8 [] state)
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◆ array_avg_merge()

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float8 [] array_avg_merge (float8 [] left,
float8 [] right 
)
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◆ array_avg_transition()

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float8 [] array_avg_transition (float8 [] state,
float8 [] x,
boolean use_abs 
)
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◆ array_elem_corr_agg()

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aggregate float8 [] array_elem_corr_agg (float8 [] array_input,
float8 common_elem 
)
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◆ array_element_max()

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aggregate float8 [] array_element_max (float8 [])
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◆ array_element_min()

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aggregate float8 [] array_element_min (float8 [])
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◆ compute_coxph_result()

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coxph_result compute_coxph_result (float8 [] coef,
float8 l,
float8 [] d2l,
integer niter,
float8 [] stds 
)
+
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+
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◆ cox_prop_hazards() [1/4]

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void cox_prop_hazards (varchar source_table,
varchar out_table,
varchar dependent_varname,
varchar independent_varname,
varchar status 
)
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+ +
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◆ cox_prop_hazards() [2/4]

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void cox_prop_hazards (varchar source_table,
varchar out_table,
varchar dependent_variable,
varchar independent_variable 
)
+
+ +
+
+ +

◆ cox_prop_hazards() [3/4]

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varchar cox_prop_hazards (varchar usage_string)
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◆ cox_prop_hazards() [4/4]

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varchar cox_prop_hazards ()
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◆ cox_prop_hazards_regr() [1/4]

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cox_prop_hazards_result cox_prop_hazards_regr (varchar source,
varchar indepColumn,
varchar depColumn,
varchar status,
integer maxNumIterations = 20,
varchar optimizer = "newton",
float8 precision = 0.0001 
)
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◆ cox_prop_hazards_regr() [2/4]

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cox_prop_hazards_result cox_prop_hazards_regr (varchar source,
varchar indepColumn,
varchar depColumn,
varchar status 
)
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◆ cox_prop_hazards_regr() [3/4]

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cox_prop_hazards_result cox_prop_hazards_regr (varchar source,
varchar indepColumn,
varchar depColumn,
varchar status,
integer maxNumIterations 
)
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◆ cox_prop_hazards_regr() [4/4]

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cox_prop_hazards_result cox_prop_hazards_regr (varchar source,
varchar indepColumn,
varchar depColumn,
varchar status,
integer maxNumIterations,
varchar optimizer 
)
+
+ +
+
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◆ cox_zph() [1/3]

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void cox_zph (varchar coxph_model_table,
varchar output_table 
)
+
+
Parameters
+ + + +
coxph_model_tableName of the table that contains the Cox Proportional Hazards model
output_tableName of the output table to contain the statistics to test the proportional hazards assumption
+
+
+
Returns
An output table with following columns: Columns of the matrix contain the correlation coefficient between transformed , a chi-square, and the two-sided p-value.
    +
  • rho FLOAT8[] - Array of correlation coefficient between survival time and the scaled Schoenfeld residuals
    • +
  • chi_square FLOAT8[] - Chi-square test statistic for the
    • +
  • p_value FLOAT8[] - Two-side p-value for the chi-square test
    • +
+
+ +
+
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◆ cox_zph() [2/3]

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varchar cox_zph ()
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◆ cox_zph() [3/3]

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varchar cox_zph (varchar message)
+
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+
+ +

◆ coxph_improved_step_final()

+ +
+
+ + + + + + + + +
coxph_step_result coxph_improved_step_final (float8 [] state)
+
+ +
+
+ +

◆ coxph_improved_step_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float8 [] coxph_improved_step_transition (float8 [] state,
float8 [] x,
float8 [] y,
integer [] status,
float8 [] coef,
float8 [] max_coef 
)
+
+ +
+
+ +

◆ coxph_improved_strata_step_final()

+ +
+
+ + + + + + + + +
coxph_step_result coxph_improved_strata_step_final (float8 [] state)
+
+ +
+
+ +

◆ coxph_improved_strata_step_outer()

+ +
+
+ + + + + + + + +
aggregate float8 [] coxph_improved_strata_step_outer (float8 [] state)
+
+ +
+
+ +

◆ coxph_predict() [1/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_predict (text model_table,
text source_table,
text id_col_name,
text output_table,
text pred_type,
text reference 
)
+
+
Parameters
+ + + + + + +
model_tableName of the table containing the cox model.
source_tableName of the table containing the prediction data.
output_tableName of the table to store the prediction results into.
pred_typeType of prediction. Can be one of 'linear_predictors', 'risk' or 'terms'.
referenceReference level to use for centering predictions. Can be one of 'overall' or 'strata'.
+
+
+ +
+
+ +

◆ coxph_predict() [2/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_predict (text model_table,
text source_table,
text id_col_name,
text output_table,
text pred_type 
)
+
+ +
+
+ +

◆ coxph_predict() [3/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_predict (text model_table,
text source_table,
text id_col_name,
text output_table 
)
+
+ +
+
+ +

◆ coxph_predict() [4/5]

+ +
+
+ + + + + + + + +
varchar coxph_predict (varchar message)
+
+ +
+
+ +

◆ coxph_predict() [5/5]

+ +
+
+ + + + + + + +
varchar coxph_predict ()
+
+ +
+
+ +

◆ coxph_step_inner_final()

+ +
+
+ + + + + + + + +
float8 [] coxph_step_inner_final (float8 [] state)
+
+ +
+
+ +

◆ coxph_step_outer_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + +
float8 [] coxph_step_outer_transition (float8 [] state1,
float8 [] state2 
)
+
+ +
+
+ +

◆ coxph_train() [1/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_train (varchar source_table,
varchar output_table,
varchar dependent_varname,
varchar independent_varname,
varchar right_censoring_status,
varchar strata,
varchar optimizer_params 
)
+
+

To include an intercept in the model, set one coordinate in the independentVariables array to 1.

+
Parameters
+ + + + + + + + +
source_tableName of the source relation containing the training data
output_tableName of the output relation to contain the coxph_train model
independent_varnameName of the independent column
dependent_varnameName of the dependent column measuring time of death
right_censoring_statusName of the column that determines right censoring support
strataComma-separated list of column names on which to stratify the data
optimizer_paramsComma-separated list of parameters for the optimizer function
+
+
+
Returns
An output table with following columns:
    +
  • coef FLOAT8[] - Array of coefficients, \( \boldsymbol \beta \)
    • +
  • log_likelihood FLOAT8 - Log-likelihood \(l(\boldsymbol \beta)\)
    • +
  • std_err FLOAT8[] - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
    • +
  • z_stats FLOAT8[] - Array of Wald z-statistics, \( \boldsymbol z \)
    • +
  • p_values FLOAT8[] - Array of Wald p-values, \( \boldsymbol p \)
    • +
  • hessian FLOAT8[] - Hessian Matrix
    • +
  • num_iterations INTEGER - The number of iterations before the algorithm terminated
    • +
+
+
    +
  • Get vector of coefficients \( \boldsymbol \beta \) and all diagnostic statistics:
    + 
    SELECT coxph_train(
+   'source_table', 'output_table',
+   'dependent_varname', 'independent_varname'
+   'right_censoring_status', 'strata'
+);
    • +
  • Get vector of coefficients \( \boldsymbol \beta \):
    + 
    SELECT coef from output_table
    • +
+

See Cox-Proportional Hazards Regression for more details.

+ +
+
+ +

◆ coxph_train() [2/6]

+ +
+
+ + + + + + + +
varchar coxph_train ()
+
+ +
+
+ +

◆ coxph_train() [3/6]

+ +
+
+ + + + + + + + +
varchar coxph_train (varchar message)
+
+ +
+
+ +

◆ coxph_train() [4/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_train (varchar source_table,
varchar output_table,
varchar dependent_variable,
varchar independent_variable,
varchar right_censoring_status,
varchar strata 
)
+
+ +
+
+ +

◆ coxph_train() [5/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_train (varchar source_table,
varchar output_table,
varchar dependent_variable,
varchar independent_variable,
varchar right_censoring_status 
)
+
+ +
+
+ +

◆ coxph_train() [6/6]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void coxph_train (varchar source_table,
varchar output_table,
varchar dependent_variable,
varchar independent_variable 
)
+
+ +
+
+ +

◆ zph_agg()

+ +
+
+ + + + + + + + + + + + + + + + + + +
aggregate float8 [] zph_agg (float8 [] x,
float8 [] coef 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/create__indicators_8sql__in.html b/docs/docs/v2.1.0/create__indicators_8sql__in.html new file mode 100644 index 00000000..bf782d0b --- /dev/null +++ b/docs/docs/v2.1.0/create__indicators_8sql__in.html @@ -0,0 +1,324 @@ + + + + + + + + +MADlib: create_indicators.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
create_indicators.sql_in File Reference
+
+
+ +

SQL functions for dummy coding categorical variables. +More...

+ + + + + + + + + + + + + + +

+Functions

void create_indicator_variables (text source_table, text out_table, text categorical_cols, boolean keep_null, text distributed_by)
 Create new table containing dummy coded variables for categorical variables. More...
 
void create_indicator_variables (text source_table, text out_table, text categorical_cols, boolean keep_null)
 Create new table containing dummy coded variables for categorical variables. More...
 
void create_indicator_variables (text source_table, text out_table, text categorical_cols)
 
varchar create_indicator_variables (varchar message)
 
varchar create_indicator_variables ()
 
+

Detailed Description

+

Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

+

http://www.apache.org/licenses/LICENSE-2.0

+

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

+
Date
June 2014
+
See also
Calculates dummy-coded indicator variables for categorical variables
+

Function Documentation

+ +

◆ create_indicator_variables() [1/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_indicator_variables (text source_table,
text out_table,
text categorical_cols,
boolean keep_null,
text distributed_by 
)
+
+
Parameters
+ + + + + + +
source_tableName of table containing categorical variable
out_tableName of table to output dummy variables
categorical_colsComma-separated list of column names to dummy code
keep_nullBoolean to determine the behavior for rows with NULL value
distributed_byComma-separated list of column names to use for distribution of output
+
+
+
Returns
Void
+ +
+
+ +

◆ create_indicator_variables() [2/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void create_indicator_variables (text source_table,
text out_table,
text categorical_cols,
boolean keep_null 
)
+
+
Parameters
+ + + + + +
source_tableName of table containing categorical variable
out_tableName of table to output dummy variables
categorical_colsComma-separated list of column names to dummy code
keep_nullBoolean to determine the behavior for rows with NULL value
+
+
+
Returns
Void
+ +
+
+ +

◆ create_indicator_variables() [3/5]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
void create_indicator_variables (text source_table,
text out_table,
text categorical_cols 
)
+
+ +
+
+ +

◆ create_indicator_variables() [4/5]

+ +
+
+ + + + + + + + +
varchar create_indicator_variables (varchar message)
+
+ +
+
+ +

◆ create_indicator_variables() [5/5]

+ +
+
+ + + + + + + +
varchar create_indicator_variables ()
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/crf_8sql__in.html b/docs/docs/v2.1.0/crf_8sql__in.html new file mode 100644 index 00000000..6d4c75ff --- /dev/null +++ b/docs/docs/v2.1.0/crf_8sql__in.html @@ -0,0 +1,543 @@ + + + + + + + + +MADlib: crf.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
crf.sql_in File Reference
+
+
+ +

SQL functions for conditional random field. +More...

+ + + + + + + + + + + + + + + + + + + + + + + +

+Functions

float8 [] lincrf_lbfgs_step_transition (float8[], float8[], float8[], float8[], float8, float8, float8[])
 
float8 [] lincrf_lbfgs_step_merge_states (float8[] state1, float8[] state2)
 
float8 [] lincrf_lbfgs_step_final (float8[] state)
 
float8 internal_lincrf_lbfgs_converge (float8[] state)
 
lincrf_result internal_lincrf_lbfgs_result (float8[] state)
 
aggregate float8 [] lincrf_lbfgs_step (float8[], float8[], float8[], float8, float8, float8[])
 
aggregate anyarray array_union (anyarray)
 
integer compute_lincrf (text source, text sparse_R, text dense_M, text sparse_M, text featureSize, integer tagSize, integer maxNumIterations)
 
text lincrf_train (text train_feature_tbl, text train_featureset_tbl, text label_tbl, text crf_stats_tbl, text crf_weights_tbl, integer max_iterations)
 Compute linear-chain crf coefficients and diagnostic statistics. More...
 
text lincrf_train (text train_feature_tbl, text train_featureset_tbl, text label_tbl, text crf_stats_tbl, text crf_weights_tbl)
 
+

Detailed Description

+
Date
July 2012
+
See also
For a brief introduction to conditional random field, see the module description Conditional Random Field.
+

Function Documentation

+ +

◆ array_union()

+ +
+
+ + + + + + + + +
aggregate anyarray array_union (anyarray )
+
+ +
+
+ +

◆ compute_lincrf()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
integer compute_lincrf (text source,
text sparse_R,
text dense_M,
text sparse_M,
text featureSize,
integer tagSize,
integer maxNumIterations 
)
+
+ +
+
+ +

◆ internal_lincrf_lbfgs_converge()

+ +
+
+ + + + + + + + +
float8 internal_lincrf_lbfgs_converge (float8 [] state)
+
+ +
+
+ +

◆ internal_lincrf_lbfgs_result()

+ +
+
+ + + + + + + + +
lincrf_result internal_lincrf_lbfgs_result (float8 [] state)
+
+ +
+
+ +

◆ lincrf_lbfgs_step()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
aggregate float8 [] lincrf_lbfgs_step (float8 [],
float8 [],
float8 [],
float8 ,
float8 ,
float8 [] 
)
+
+ +
+
+ +

◆ lincrf_lbfgs_step_final()

+ +
+
+ + + + + + + + +
float8 [] lincrf_lbfgs_step_final (float8 [] state)
+
+ +
+
+ +

◆ lincrf_lbfgs_step_merge_states()

+ +
+
+ + + + + + + + + + + + + + + + + + +
float8 [] lincrf_lbfgs_step_merge_states (float8 [] state1,
float8 [] state2 
)
+
+ +
+
+ +

◆ lincrf_lbfgs_step_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float8 [] lincrf_lbfgs_step_transition (float8 [],
float8 [],
float8 [],
float8 [],
float8 ,
float8 ,
float8 [] 
)
+
+ +
+
+ +

◆ lincrf_train() [1/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
text lincrf_train (text train_feature_tbl,
text train_featureset_tbl,
text label_tbl,
text crf_stats_tbl,
text crf_weights_tbl,
integer max_iterations 
)
+
+
Parameters
+ + + + + + + + + + +
sourceName of the source relation containing the training data
sparse_RName of the sparse single state feature column (of type DOUBLE PRECISION[])
dense_MName of the dense two state feature column (of type DOUBLE PRECISION[])
sparse_MName of the sparse two state feature column (of type DOUBLE PRECISION[])
featureSizeName of feature size column (of type DOUBLE PRECISION)
tagSizeThe number of tags in the tag set
featuresetThe unique feature set
crf_featureThe Name of output feature table
maxNumIterationsThe maximum number of iterations
+
+
+
Returns
a composite value:
    +
  • coef FLOAT8[] - Array of coefficients, \( \boldsymbol c \)
    • +
  • log_likelihood FLOAT8 - Log-likelihood \( l(\boldsymbol c) \)
    • +
  • num_iterations INTEGER - The number of iterations before the algorithm terminated
    +
    +A 'crf_feature' table is used to store all the features and corresponding weights
    • +
+
+
Note
This function starts an iterative algorithm. It is not an aggregate function. Source and column names have to be passed as strings (due to limitations of the SQL syntax).
+ +
+
+ +

◆ lincrf_train() [2/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
text lincrf_train (text train_feature_tbl,
text train_featureset_tbl,
text label_tbl,
text crf_stats_tbl,
text crf_weights_tbl 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/crf__data__loader_8sql__in.html b/docs/docs/v2.1.0/crf__data__loader_8sql__in.html new file mode 100644 index 00000000..cec5a623 --- /dev/null +++ b/docs/docs/v2.1.0/crf__data__loader_8sql__in.html @@ -0,0 +1,326 @@ + + + + + + + + +MADlib: crf_data_loader.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
crf_data_loader.sql_in File Reference
+
+
+ +

Create database tables and import POS/NER training/testing data to the database. +More...

+ + + + + + +

+Functions

void crf_train_data (text datapath)
 
void crf_test_data (text datapath)
 
+

Detailed Description

+
Date
Feb. 2012
+

Function Documentation

+ +

◆ crf_test_data()

+ +
+
+ + + + + + + + +
void crf_test_data (text datapath)
+
+
Input
+
    +
  1. Prepare an input test data segment table, e.g.:
    2. +
+
    +
  • CREATE TABLE test_segmenttbl (start_pos integer,doc_id integer,seg_text text, max_pos integer) 
    sql> select * from test_segmenttbl order by doc_id, start_pos;
+start_pos | doc_id |   seg_text    | max_pos
+----------+---------+--------------+-------------
+     0    |    1   |          the  |    26
+     1    |    1   |       madlib  |    26
+     2    |    1   |      mission  |    26
+     3    |    1   |            :  |    26
+     4    |    1   |           to  |    26
+     5    |    1   |       foster  |    26
+     6    |    1   |   widespread  |    26
+     7    |    1   |  development  |    26
+     8    |    1   |           of  |    26
+     9    |    1   |     scalable  |    26
+     10   |    1   |     analytic  |    26
+     11   |    1   |       skills  |    26
+     12   |    1   |            ,  |    26
+     13   |    1   |           by  |    26
+     ...
+     24   |    1   |  open-source  |    26
+     25   |    1   |   development |    26
+     26   |    1   |             . |    26
+
    • +
+
Usage
    +
  • create tables and import data to the database SELECT madlib.crf_test_data('/path/to/modeldata')
    • +
+
+ +
+
+ +

◆ crf_train_data()

+ +
+
+ + + + + + + + +
void crf_train_data (text datapath)
+
+
Input
+
    +
  1. Prepare an input train data segment table, e.g.:
    2. +
+
    +
  • CREATE TABLE train_segmenttbl (start_pos integer,doc_id integer,seg_text text, max_pos integer) 
    sql> select * from train_segmenttbl order by doc_id, start_pos;
+start_pos | doc_id | seg_text      | max_pos
+----------+---------+--------------+-------------
+     0    |    1   |       madlib  |    9
+     1    |    1   |           is  |    9
+     2    |    1   |           an  |    9
+     3    |    1   |  open-source  |    9
+     4    |    1   |      library  |    9
+     5    |    1   |          for  |    9
+     6    |    1   |     scalable  |    9
+     7    |    1   |  in-database  |    9
+     8    |    1   |    analytics  |    9
+     9    |    1   |            .  |    9
+     0    |    2   |           it  |   16
+     1    |    2   |     provides  |   16
+     2    |    2   |data-parallel  |   16
+     3    |    2   |implementations|   16
+     ...
+     14   |    2   |  unstructured |   16
+     15   |    2   |          data |   16
+     16   |    2   |             . |   16
+
    • +
+
    +
  1. Prepare an input dictionary table, e.g.,:
    2. +
+
    +
  • CREATE TABLE crf_dictionary (token text,token_id integer,label text,count integer,total integer) 
    sql> select * from crf_dictionary;
+token       | label  | count | total
+------------+--------+--------------
+   freefall |   11   |   1   |  1
+     policy |   11   |   2   |  2
+   measures |   12   |   1   |  1
+ commitment |   11   |   1   |  1
+        new |    6   |   1   |  1
+     speech |   11   |   1   |  1
+         's |   16   |   2   |  2
+     reckon |   30   |   1   |  1
+ underlying |   28   |   1   |  1
+ ...
+
    • +
+
    +
  1. Prepare an input label table, e.g.,:
    2. +
+
    +
  • CREATE TABLE labeltbl (id integer,label character varying) 
    sql> select * from labeltbl order by id;
+id          | label
+------------+--------
+      0     |   CC
+      1     |   CD
+      2     |   DT
+      3     |   EX
+      4     |   FW
+      5     |   IN
+      6     |   JJ
+...
+     42     |    ,
+     43     |    .
+     44     |    :
+
    • +
+
    +
  1. Prepare an input regex table, e.g.,:
    2. +
+
    +
  • CREATE TABLE crf_regex (pattern text,name text) 
    sql> select * from crf_regex;
+pattern       |   name
+------------- +---------------
+^[A-Z][a-z]+$ |  InitCapital%
+     ^[A-Z]+$ |  isAllCapital%
+ ^.*[0-9]+.*$ |  containsDigit%
+      ^.+[.]$ |  endsWithDot%
+      ^.+[,]$ |  endsWithComma%
+       ^.+er$ |  endsWithER%
+      ^.+est$ |  endsWithEst%
+       ^.+ed$ |  endsWithED%
+...
+
    • +
+
    +
  1. Prepare an input feature table, e.g.,:
    2. +
+
    +
  • CREATE TABLE featuretbl (id integer,name text,prev_label_id integer,label_id integer,weight float) 
    sql> select * from featuretbl order by id;
+id   |     name     | prev_label_id | label_id | weight
+-------------------------------------------------------
+1    | W_chancellor |       -1      |    13     | 2.2322
+2    |         E.13 |       13      |     5     | 2.3995
+3    |            U |       -1      |     5     | 1.2164
+4    |         W_of |       -1      |     5     | 2.8744
+5    |          E.5 |        5      |     2     | 3.7716
+6    |        W_the |       -1      |     2     | 4.1790
+7    |          E.2 |        2      |    13     | 0.8957
+...
+
    • +
+
    +
  1. Prepare an crf feature set table, e.g.,:
    2. +
+
    +
  • CREATE TABLE madlib.crf_feature_dic(f_index integer, f_name text, feature integer[]) 
    sql> select * from crf_feature_dic order by id;
+f_index|     f_name   | feature
+--------------------------------
+0      | W_chancellor |       -1
+1      |         E.13 |       13
+2      |            U |       -1
+3      |         W_of |       -1
+4      |          E.5 |        5
+5      |        W_the |       -1
+...
+
    • +
+
Usage
    +
  • create tables and import data to the database SELECT madlib.crf_train_data('/path/to/modeldata')
    • +
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/crf__feature__gen_8sql__in.html b/docs/docs/v2.1.0/crf__feature__gen_8sql__in.html new file mode 100644 index 00000000..5879d05a --- /dev/null +++ b/docs/docs/v2.1.0/crf__feature__gen_8sql__in.html @@ -0,0 +1,289 @@ + + + + + + + + +MADlib: crf_feature_gen.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
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+Functions
+
+
crf_feature_gen.sql_in File Reference
+
+
+ +

SQL function for POS/NER feature extraction. +More...

+ + + + + + + + +

+Functions

void crf_train_fgen (text train_segment_tbl, text regex_tbl, text label_tbl, text dictionary_tbl, text train_feature_tbl, text train_featureset_tbl)
 This function extracts POS/NER features from the training data. More...
 
void crf_test_fgen (text test_segment_tbl, text dictionary_tbl, text label_tbl, text regex_tbl, text crf_weights_tbl, text viterbi_mtbl, text viterbi_rtbl)
 This function extracts POS/NER features from the testing data. More...
 
+

Detailed Description

+
Date
February 2012
+
See also
For an introduction to POS/NER feature extraction, see the module description Conditional Random Field
+

Function Documentation

+ +

◆ crf_test_fgen()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void crf_test_fgen (text test_segment_tbl,
text dictionary_tbl,
text label_tbl,
text regex_tbl,
text crf_weights_tbl,
text viterbi_mtbl,
text viterbi_rtbl 
)
+
+

This feature extraction function will produce two factor tables, "m table" (viterbi_mtbl) and "r table" (viterbi_rtbl). The viterbi_mtbl table and viterbi_rtbl table are used to calculate the best label sequence for each sentence.

+
    +
  • viterbi_mtbl table encodes the edge features which are solely dependent on upon current label and previous y value. The m table has three columns which are prev_label, label, and value respectively. If the number of labels in \( n \), then the m factor table will \( n^2 \) rows. Each row encodes the transition feature weight value from the previous label to the current label.
    • +
+

startFeature is considered as a special edge feature which is from the beginning to the first token. Likewise, endFeature can be considered as a special edge feature which is from the last token to the very end. So m table encodes the edgeFeature, startFeature, and endFeature. If the total number of labels in the label space is 45 from 0 to 44, then the m factor array is as follows: 

+                 0  1  2  3  4  5...44
+startFeature -1  a  a  a  a  a  a...a
+edgeFeature   0  a  a  a  a  a  a...a
+edgeFeature   1  a  a  a  a  a  a...a
+...
+edgeFeature  44  a  a  a  a  a  a...a
+endFeature   45  a  a  a  a  a  a...a
    +
  • viterbi_r table is related to specific tokens. It encodes the single state features, e.g., wordFeature, RegexFeature for all tokens. The r table is represented in the following way. 
    +       0  1  2  3  4...44
+token1 a  a  a  a  a...a
+token2 a  a  a  a  a...a
    • +
+
Parameters
+ + + + + + + + +
test_segment_tblName of table containing all the tokenized testing sentences.
dictionary_tblName of table containing the dictionary_tbl.
label_tblName of table containing the the label space used in POS or other NLP tasks.
regex_tblName of table containing all the regular expressions to capture regex features.
crf_weights_tblName of the table containing featureset weights.
viterbi_mtblName of table to store the m factors.
viterbi_rtblName of table to store the r factors.
+
+
+ +
+
+ +

◆ crf_train_fgen()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void crf_train_fgen (text train_segment_tbl,
text regex_tbl,
text label_tbl,
text dictionary_tbl,
text train_feature_tbl,
text train_featureset_tbl 
)
+
+
Parameters
+ + + + + + + +
train_segment_tblName of table containing all the tokenized training sentences.
regex_tblName of table containing all the regular expressions to capture regex features.
label_tblName of the label table containing unique ids and label names.
dictionary_tblName of table containing the dictionary_tbl.
train_feature_tblfeatures generated from the traning dataset
train_featureset_tblunique feature set generated from the training dataset
+
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/cross__validation_8sql__in.html b/docs/docs/v2.1.0/cross__validation_8sql__in.html new file mode 100644 index 00000000..df24b51a --- /dev/null +++ b/docs/docs/v2.1.0/cross__validation_8sql__in.html @@ -0,0 +1,701 @@ + + + + + + + + +MADlib: cross_validation.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
cross_validation.sql_in File Reference
+
+
+ +

SQL functions for cross validation. +More...

+ + + + + + + + + + + + + + + + + + + + + + + + + +

+Functions

void cross_validation_general (varchar modelling_func, varchar[] modelling_params, varchar[] modelling_params_type, varchar param_explored, varchar[] explore_values, varchar predict_func, varchar[] predict_params, varchar[] predict_params_type, varchar metric_func, varchar[] metric_params, varchar[] metric_params_type, varchar data_tbl, varchar data_id, boolean id_is_random, varchar validation_result, varchar[] data_cols, integer n_folds)
 
void cross_validation_general (varchar modelling_func, varchar[] modelling_params, varchar[] modelling_params_type, varchar param_explored, varchar[] explore_values, varchar predict_func, varchar[] predict_params, varchar[] predict_params_type, varchar metric_func, varchar[] metric_params, varchar[] metric_params_type, varchar data_tbl, varchar data_id, boolean id_is_random, varchar validation_result, varchar[] data_cols)
 
void cv_linregr_train (varchar tbl_source, varchar col_ind_var, varchar col_dep_var, varchar tbl_result)
 A wrapper for linear regression. More...
 
void cv_linregr_predict (varchar tbl_model, varchar tbl_newdata, varchar col_ind_var, varchar col_id, varchar tbl_predict)
 A wrapper for linear regression prediction. More...
 
void mse_error (varchar tbl_prediction, varchar tbl_actual, varchar id_actual, varchar values_actual, varchar tbl_error)
 
void misclassification_avg (varchar tbl_prediction, varchar tbl_actual, varchar id_actual, varchar values_actual, varchar tbl_error)
 
void cv_logregr_predict (varchar tbl_model, varchar tbl_newdata, varchar col_ind_var, varchar col_id, varchar tbl_predict)
 A prediction function for logistic regression The result is stored in the table of tbl_predict. More...
 
integer logregr_accuracy (float8[] coef, float8[] col_ind, boolean col_dep)
 Metric function for logistic regression. More...
 
void cv_logregr_accuracy (varchar tbl_predict, varchar tbl_source, varchar col_id, varchar col_dep_var, varchar tbl_accuracy)
 Metric function for logistic regression. More...
 
+

Detailed Description

+
Date
January 2011
+
See also
For a brief introduction to the usage of cross validation, see the module description Cross Validation.
+

Function Documentation

+ +

◆ cross_validation_general() [1/2]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cross_validation_general (varchar modelling_func,
varchar [] modelling_params,
varchar [] modelling_params_type,
varchar param_explored,
varchar [] explore_values,
varchar predict_func,
varchar [] predict_params,
varchar [] predict_params_type,
varchar metric_func,
varchar [] metric_params,
varchar [] metric_params_type,
varchar data_tbl,
varchar data_id,
boolean id_is_random,
varchar validation_result,
varchar [] data_cols,
integer n_folds 
)
+
+ +
+
+ +

◆ cross_validation_general() [2/2]

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+
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void cross_validation_general (varchar modelling_func,
varchar [] modelling_params,
varchar [] modelling_params_type,
varchar param_explored,
varchar [] explore_values,
varchar predict_func,
varchar [] predict_params,
varchar [] predict_params_type,
varchar metric_func,
varchar [] metric_params,
varchar [] metric_params_type,
varchar data_tbl,
varchar data_id,
boolean id_is_random,
varchar validation_result,
varchar [] data_cols 
)
+
+ +
+
+ +

◆ cv_linregr_predict()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cv_linregr_predict (varchar tbl_model,
varchar tbl_newdata,
varchar col_ind_var,
varchar col_id,
varchar tbl_predict 
)
+
+ +
+
+ +

◆ cv_linregr_train()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cv_linregr_train (varchar tbl_source,
varchar col_ind_var,
varchar col_dep_var,
varchar tbl_result 
)
+
+ +
+
+ +

◆ cv_logregr_accuracy()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cv_logregr_accuracy (varchar tbl_predict,
varchar tbl_source,
varchar col_id,
varchar col_dep_var,
varchar tbl_accuracy 
)
+
+

It computes the percentage of correct predictions. The result is stored in the table of tbl_accuracy

+ +
+
+ +

◆ cv_logregr_predict()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void cv_logregr_predict (varchar tbl_model,
varchar tbl_newdata,
varchar col_ind_var,
varchar col_id,
varchar tbl_predict 
)
+
+

This function can be used together with cross-validation

+ +
+
+ +

◆ logregr_accuracy()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
integer logregr_accuracy (float8 [] coef,
float8 [] col_ind,
boolean col_dep 
)
+
+
Parameters
+ + + + +
coefLogistic fitting coefficients. Note: MADlib logregr_train function, unlike elastic_net, does not produce a separate intercept term.
col_indIndependent variable, an array
col_depDependent variable
+
+
+

returns 1 if the prediction is the same as col_dep, otherwise 0

+ +
+
+ +

◆ misclassification_avg()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void misclassification_avg (varchar tbl_prediction,
varchar tbl_actual,
varchar id_actual,
varchar values_actual,
varchar tbl_error 
)
+
+ +
+
+ +

◆ mse_error()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void mse_error (varchar tbl_prediction,
varchar tbl_actual,
varchar id_actual,
varchar values_actual,
varchar tbl_error 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dbscan_8sql__in.html b/docs/docs/v2.1.0/dbscan_8sql__in.html new file mode 100644 index 00000000..845268c8 --- /dev/null +++ b/docs/docs/v2.1.0/dbscan_8sql__in.html @@ -0,0 +1,1069 @@ + + + + + + + + +MADlib: dbscan.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
dbscan.sql_in File Reference
+
+
+ +

Partitions a set of observations into clusters of arbitrary shape based on the density of nearby neighbors. +More...

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+Functions

void dbscan (varchar source_table, varchar output_table, varchar id_column, varchar expr_point, float8 eps, integer min_samples, varchar metric, varchar algorithm, integer max_segmentation_depth)
 
void dbscan (varchar source_table, varchar output_table, varchar id_column, varchar expr_point, float8 eps, integer min_samples, varchar metric, varchar algorithm)
 
void dbscan (varchar source_table, varchar output_table, varchar id_column, varchar expr_point, float8 eps, integer min_samples, varchar metric)
 
void dbscan (varchar source_table, varchar output_table, varchar id_column, varchar point, float8 eps, integer min_samples)
 
void dbscan (varchar source_table, varchar output_table, varchar id_column, varchar expr_point, float8 eps)
 
void dbscan_predict (varchar dbscan_table, varchar source_table, varchar id_column, varchar expr_point, varchar output_table)
 
varchar dbscan (varchar message)
 
varchar dbscan ()
 
varchar dbscan_predict (varchar message)
 
varchar dbscan_predict ()
 
bigint [][] sf_merge (bigint[][] state1, bigint[][] state2)
 
bigint [][] sf_final (bigint[][] state)
 
bigint [][] sf_transition (bigint[] state, bigint src, bigint dest, integer[] n_rows, integer gp_segment_id)
 
aggregate bigint [][] build_snowflake_table (bigint, bigint, integer[], integer)
 
set< __dbscan_edge > __dbscan_unpack_edge (bigint[][] packed)
 
float8 __dbscan_safe_ln (float8 x)
 
float8 __dbscan_safe_exp (float8 x)
 
aggregate float8 prod (float8)
 
float8 __dbscan_split_volume (float8 v, float8 eps_bin, float8 eps_bins)
 
float8 __dbscan_estimate_neighbors (float8 internal_points, float8 v, float8 eps, bigint d)
 
float8 __dbscan_range_query_penalty (bigint internal_points, float8 neighbors)
 
bigint __dbscan_allocate_segs (bigint avail_segs, float8 left_points, float8 right_points, float8 rqp_left, float8 rqp_right)
 
__dbscan_losses __dbscan_segmentation_loss (bigint left_internal, bigint right_internal, bigint left_external, bigint right_external, bigint avail_segs, float8 v, float8 eps, bigint d, float8 eps_bin, float8 eps_bins)
 
set< __dbscan_record > __dbscan_leaf (__dbscan_record db_rec, real eps, int min_samples, text metric, bigint num_internal_points, bigint num_external_points)
 
+

Detailed Description

+

Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

+

http://www.apache.org/licenses/LICENSE-2.0

+

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

+
Date
May 2020
+

Function Documentation

+ +

◆ __dbscan_allocate_segs()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
bigint __dbscan_allocate_segs (bigint avail_segs,
float8 left_points,
float8 right_points,
float8 rqp_left,
float8 rqp_right 
)
+
+ +
+
+ +

◆ __dbscan_estimate_neighbors()

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float8 __dbscan_estimate_neighbors (float8 internal_points,
float8 v,
float8 eps,
bigint d 
)
+
+ +
+
+ +

◆ __dbscan_leaf()

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set<__dbscan_record> __dbscan_leaf (__dbscan_record db_rec,
real eps,
int min_samples,
text metric,
bigint num_internal_points,
bigint num_external_points 
)
+
+ +
+
+ +

◆ __dbscan_range_query_penalty()

+ +
+
+ + + + + + + + + + + + + + + + + + +
float8 __dbscan_range_query_penalty (bigint internal_points,
float8 neighbors 
)
+
+ +
+
+ +

◆ __dbscan_safe_exp()

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float8 __dbscan_safe_exp (float8 x)
+
+ +
+
+ +

◆ __dbscan_safe_ln()

+ +
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float8 __dbscan_safe_ln (float8 x)
+
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+
+ +

◆ __dbscan_segmentation_loss()

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__dbscan_losses __dbscan_segmentation_loss (bigint left_internal,
bigint right_internal,
bigint left_external,
bigint right_external,
bigint avail_segs,
float8 v,
float8 eps,
bigint d,
float8 eps_bin,
float8 eps_bins 
)
+
+ +
+
+ +

◆ __dbscan_split_volume()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
float8 __dbscan_split_volume (float8 v,
float8 eps_bin,
float8 eps_bins 
)
+
+ +
+
+ +

◆ __dbscan_unpack_edge()

+ +
+
+ + + + + + + + +
set<__dbscan_edge> __dbscan_unpack_edge (bigint packed[][])
+
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+ +

◆ build_snowflake_table()

+ +
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aggregate bigint [][] build_snowflake_table (bigint ,
bigint ,
integer [],
integer  
)
+
+ +
+
+ +

◆ dbscan() [1/7]

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void dbscan (varchar source_table,
varchar output_table,
varchar id_column,
varchar expr_point,
float8 eps,
integer min_samples,
varchar metric,
varchar algorithm,
integer max_segmentation_depth 
)
+
+ +
+
+ +

◆ dbscan() [2/7]

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void dbscan (varchar source_table,
varchar output_table,
varchar id_column,
varchar expr_point,
float8 eps,
integer min_samples,
varchar metric,
varchar algorithm 
)
+
+ +
+
+ +

◆ dbscan() [3/7]

+ +
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void dbscan (varchar source_table,
varchar output_table,
varchar id_column,
varchar expr_point,
float8 eps,
integer min_samples,
varchar metric 
)
+
+ +
+
+ +

◆ dbscan() [4/7]

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void dbscan (varchar source_table,
varchar output_table,
varchar id_column,
varchar point,
float8 eps,
integer min_samples 
)
+
+ +
+
+ +

◆ dbscan() [5/7]

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void dbscan (varchar source_table,
varchar output_table,
varchar id_column,
varchar expr_point,
float8 eps 
)
+
+ +
+
+ +

◆ dbscan() [6/7]

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varchar dbscan (varchar message)
+
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◆ dbscan() [7/7]

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varchar dbscan ()
+
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◆ dbscan_predict() [1/3]

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void dbscan_predict (varchar dbscan_table,
varchar source_table,
varchar id_column,
varchar expr_point,
varchar output_table 
)
+
+ +
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◆ dbscan_predict() [2/3]

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varchar dbscan_predict (varchar message)
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◆ dbscan_predict() [3/3]

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varchar dbscan_predict ()
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◆ prod()

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aggregate float8 prod (float8 )
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◆ sf_final()

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bigint [][] sf_final (bigint state[][])
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◆ sf_merge()

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bigint [][] sf_merge (bigint state1[][],
bigint state2[][] 
)
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◆ sf_transition()

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bigint [][] sf_transition (bigint [] state,
bigint src,
bigint dest,
integer [] n_rows,
integer gp_segment_id 
)
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+ + + + diff --git a/docs/docs/v2.1.0/decision__tree_8sql__in.html b/docs/docs/v2.1.0/decision__tree_8sql__in.html new file mode 100644 index 00000000..2914d804 --- /dev/null +++ b/docs/docs/v2.1.0/decision__tree_8sql__in.html @@ -0,0 +1,2748 @@ + + + + + + + + +MADlib: decision_tree.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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decision_tree.sql_in File Reference
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+Functions

void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth, integer min_split, integer min_bucket, integer n_bins, text pruning_params, text null_handling_params, boolean verbose_mode)
 Training of decision tree. More...
 
void __build_tree (boolean is_classification, text split_criterion, text training_table_name, text output_table_name, text id_col_name, text dependent_variable, boolean dep_is_bool, text list_of_features, varchar[] cat_features, varchar[] ordered_cat_features, varchar[] boolean_cats, varchar[] con_features, text grouping_cols, text weights, integer max_depth, integer min_split, integer min_bucket, integer n_bins, text cp_table, smallint max_n_surr, text msg_level, text null_proxy, integer n_folds)
 
text tree_train (text message)
 
text tree_train ()
 
bytea8 _dst_compute_con_splits_transition (bytea8 state, float8[] con_features, integer n_per_seg, smallint num_splits)
 
bytea8 _dst_compute_con_splits_final (bytea8 state)
 
aggregate bytea8 _dst_compute_con_splits (float8[], integer, smallint)
 
integer [] _dst_compute_entropy_transition (integer[] state, integer encoded_dep_var, integer num_dep_var)
 
integer [] _dst_compute_entropy_merge (integer[] state1, integer[] state2)
 
float8 _dst_compute_entropy_final (integer[] state)
 
aggregate float8 _dst_compute_entropy (integer, integer)
 
integer [] _map_catlevel_to_int (text[] cat_values_in_text, text[] cat_levels_in_text, integer[] cat_n_levels, boolean null_as_category)
 
bytea8 _initialize_decision_tree (boolean is_regression_tree, text impurity_function, smallint num_response_labels, smallint max_n_surr)
 
bytea8 _compute_leaf_stats_transition (bytea8 state, bytea8 tree_state, integer[] cat_features, float8[] con_features, float8 response, float8 weight, integer[] cat_levels, bytea8 con_splits, smallint n_response_labels, boolean weights_as_rows)
 
bytea8 _compute_leaf_stats_merge (bytea8 state1, bytea8 state2)
 
aggregate bytea8 _compute_leaf_stats (bytea8, integer[], float8[], float8, float8, integer[], bytea8, smallint, boolean)
 
_tree_result_type _dt_apply (bytea8 tree, bytea8 state, bytea8 con_splits, smallint min_split, smallint min_bucket, smallint max_depth, boolean subsample, integer num_random_features)
 
bytea8 _compute_surr_stats_transition (bytea8 state, bytea8 tree_state, integer[] cat_features, float8[] con_features, integer[] cat_levels, bytea8 con_splits, integer dup_count)
 
aggregate bytea8 _compute_surr_stats (bytea8, integer[], float8[], integer[], bytea8, integer)
 
bytea8 _dt_surr_apply (bytea8 tree, bytea8 state, bytea8 con_splits)
 
_flattened_tree _print_decision_tree (bytea8 tree)
 
float8 [] _compute_var_importance (bytea8 tree, integer n_cat_features, integer n_con_features)
 
float8 _predict_dt_response (bytea8 tree, integer[] cat_features, float8[] con_features)
 
float8 [] _predict_dt_prob (bytea8 tree, integer[] cat_features, float8[] con_features)
 
void tree_predict (text model, text source, text output, text pred_type)
 Use decision tree model to make predictions. More...
 
void __tree_predict (text model, text source, text output, text pred_type, boolean use_existing_tables, integer k)
 
void tree_predict (text model, text source, text output)
 
text tree_predict (text message)
 
text tree_predict ()
 
varchar tree_surr_display (text model_table)
 Display decision tree in dot or text format. More...
 
varchar tree_surr_display ()
 
varchar tree_display (text model_table, boolean dot_format, boolean verbose)
 Display decision tree in dot or text format. More...
 
varchar tree_display (text model_table, boolean dot_format)
 
varchar tree_display (text model_table)
 
varchar tree_display ()
 
text _display_decision_tree (bytea8 tree, text[] cat_features, text[] con_features, text[] cat_levels_in_text, integer[] cat_n_levels, text[] dependent_levels, text id_prefix, boolean verbose)
 
text _display_decision_tree (bytea8 tree, text[] cat_features, text[] con_features, text[] cat_levels_in_text, integer[] cat_n_levels, text[] dependent_levels, text id_prefix)
 
text _display_decision_tree_surrogate (bytea8 tree, text[] cat_features, text[] con_features, text[] cat_levels_in_text, integer[] cat_n_levels)
 
text _display_text_decision_tree (bytea8 tree, text[] cat_features, text[] con_features, text[] cat_levels_in_text, integer[] cat_n_levels, text[] dependent_levels)
 
set< _cat_levels_type > _gen_cat_levels_set (text[] grp_keys, integer[] cat_n_levels, integer n_cat, text[] cat_sorted_origin)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth, integer min_split, integer min_bucket, integer n_bins, text pruning_params, text null_handling_params)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth, integer min_split, integer min_bucket, integer n_bins, text pruning_params)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth, integer min_split, integer min_bucket, integer n_bins)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth, integer min_split, integer min_bucket)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth, integer min_split)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights, integer max_depth)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols, text weights)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion, text grouping_cols)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text split_criterion)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude)
 
void tree_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features)
 
+

Function Documentation

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◆ __build_tree()

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void __build_tree (boolean is_classification,
text split_criterion,
text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
boolean dep_is_bool,
text list_of_features,
varchar [] cat_features,
varchar [] ordered_cat_features,
varchar [] boolean_cats,
varchar [] con_features,
text grouping_cols,
text weights,
integer max_depth,
integer min_split,
integer min_bucket,
integer n_bins,
text cp_table,
smallint max_n_surr,
text msg_level,
text null_proxy,
integer n_folds 
)
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◆ __tree_predict()

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void __tree_predict (text model,
text source,
text output,
text pred_type,
boolean use_existing_tables,
integer k 
)
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◆ _compute_leaf_stats()

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+
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aggregate bytea8 _compute_leaf_stats (bytea8 ,
integer [],
float8 [],
float8 ,
float8 ,
integer [],
bytea8 ,
smallint ,
boolean  
)
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+ +
+
+ +

◆ _compute_leaf_stats_merge()

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bytea8 _compute_leaf_stats_merge (bytea8 state1,
bytea8 state2 
)
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◆ _compute_leaf_stats_transition()

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bytea8 _compute_leaf_stats_transition (bytea8 state,
bytea8 tree_state,
integer [] cat_features,
float8 [] con_features,
float8 response,
float8 weight,
integer [] cat_levels,
bytea8 con_splits,
smallint n_response_labels,
boolean weights_as_rows 
)
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◆ _compute_surr_stats()

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aggregate bytea8 _compute_surr_stats (bytea8 ,
integer [],
float8 [],
integer [],
bytea8 ,
integer  
)
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◆ _compute_surr_stats_transition()

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bytea8 _compute_surr_stats_transition (bytea8 state,
bytea8 tree_state,
integer [] cat_features,
float8 [] con_features,
integer [] cat_levels,
bytea8 con_splits,
integer dup_count 
)
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◆ _compute_var_importance()

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float8 [] _compute_var_importance (bytea8 tree,
integer n_cat_features,
integer n_con_features 
)
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◆ _display_decision_tree() [1/2]

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text _display_decision_tree (bytea8 tree,
text [] cat_features,
text [] con_features,
text [] cat_levels_in_text,
integer [] cat_n_levels,
text [] dependent_levels,
text id_prefix,
boolean verbose 
)
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◆ _display_decision_tree() [2/2]

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text _display_decision_tree (bytea8 tree,
text [] cat_features,
text [] con_features,
text [] cat_levels_in_text,
integer [] cat_n_levels,
text [] dependent_levels,
text id_prefix 
)
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◆ _display_decision_tree_surrogate()

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text _display_decision_tree_surrogate (bytea8 tree,
text [] cat_features,
text [] con_features,
text [] cat_levels_in_text,
integer [] cat_n_levels 
)
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◆ _display_text_decision_tree()

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text _display_text_decision_tree (bytea8 tree,
text [] cat_features,
text [] con_features,
text [] cat_levels_in_text,
integer [] cat_n_levels,
text [] dependent_levels 
)
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◆ _dst_compute_con_splits()

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aggregate bytea8 _dst_compute_con_splits (float8 [],
integer ,
smallint  
)
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◆ _dst_compute_con_splits_final()

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bytea8 _dst_compute_con_splits_final (bytea8 state)
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◆ _dst_compute_con_splits_transition()

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bytea8 _dst_compute_con_splits_transition (bytea8 state,
float8 [] con_features,
integer n_per_seg,
smallint num_splits 
)
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◆ _dst_compute_entropy()

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aggregate float8 _dst_compute_entropy (integer ,
integer  
)
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◆ _dst_compute_entropy_final()

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float8 _dst_compute_entropy_final (integer [] state)
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◆ _dst_compute_entropy_merge()

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integer [] _dst_compute_entropy_merge (integer [] state1,
integer [] state2 
)
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◆ _dst_compute_entropy_transition()

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integer [] _dst_compute_entropy_transition (integer [] state,
integer encoded_dep_var,
integer num_dep_var 
)
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◆ _dt_apply()

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_tree_result_type _dt_apply (bytea8 tree,
bytea8 state,
bytea8 con_splits,
smallint min_split,
smallint min_bucket,
smallint max_depth,
boolean subsample,
integer num_random_features 
)
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◆ _dt_surr_apply()

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bytea8 _dt_surr_apply (bytea8 tree,
bytea8 state,
bytea8 con_splits 
)
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◆ _gen_cat_levels_set()

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set<_cat_levels_type> _gen_cat_levels_set (text [] grp_keys,
integer [] cat_n_levels,
integer n_cat,
text [] cat_sorted_origin 
)
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◆ _initialize_decision_tree()

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bytea8 _initialize_decision_tree (boolean is_regression_tree,
text impurity_function,
smallint num_response_labels,
smallint max_n_surr 
)
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◆ _map_catlevel_to_int()

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integer [] _map_catlevel_to_int (text [] cat_values_in_text,
text [] cat_levels_in_text,
integer [] cat_n_levels,
boolean null_as_category 
)
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◆ _predict_dt_prob()

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float8 [] _predict_dt_prob (bytea8 tree,
integer [] cat_features,
float8 [] con_features 
)
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◆ _predict_dt_response()

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float8 _predict_dt_response (bytea8 tree,
integer [] cat_features,
float8 [] con_features 
)
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◆ _print_decision_tree()

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_flattened_tree _print_decision_tree (bytea8 tree)
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◆ tree_display() [1/4]

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varchar tree_display (text model_table,
boolean dot_format,
boolean verbose 
)
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Parameters
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tree_modelName of the table containing the decision tree model
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◆ tree_display() [2/4]

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varchar tree_display (text model_table,
boolean dot_format 
)
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◆ tree_display() [3/4]

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varchar tree_display (text model_table)
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◆ tree_display() [4/4]

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varchar tree_display ()
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◆ tree_predict() [1/4]

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void tree_predict (text model,
text source,
text output,
text pred_type 
)
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Parameters
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modelName of the table containing the decision tree model
sourceName of table containing prediction data
outputName of table to output prediction results
pred_typeOPTIONAL (Default = 'response'). For regression trees, 'response', implies output is the predicted value. For classification trees, this can be 'response', giving the classification prediction as output, or ‘prob’, giving the class probabilities as output (for two classes, only a single probability value is output that corresponds to the first class when the two classes are sorted by name; in case of more than two classes, an array of class probabilities (a probability of each class) is output).
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See Decision Tree for more details.

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◆ tree_predict() [2/4]

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void tree_predict (text model,
text source,
text output 
)
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◆ tree_predict() [3/4]

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text tree_predict (text message)
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◆ tree_predict() [4/4]

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text tree_predict ()
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◆ tree_surr_display() [1/2]

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varchar tree_surr_display (text model_table)
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Parameters
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tree_modelName of the table containing the decision tree model
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◆ tree_surr_display() [2/2]

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varchar tree_surr_display ()
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◆ tree_train() [1/14]

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void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth,
integer min_split,
integer min_bucket,
integer n_bins,
text pruning_params,
text null_handling_params,
boolean verbose_mode 
)
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Parameters
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split_criterionVarious options to compute the feature to split a node. Available options are 'gini', 'cross-entropy', and 'misclassification'. The "cart" algorithm provides an additional option of 'mse'.
training_table_nameName of the table containing data.
output_table_nameName of the table to output the model.
id_col_nameName of column containing the id information in training data.
dependent_variableName of the column that contains the output for training. Boolean, integer and text are considered classification outputs, while float values are considered regression outputs.
list_of_featuresList of column names (comma-separated string) to use as predictors. Can also be a ‘*’ implying all columns are to be used as predictors (except the ones included in the next argument). Boolean, integer, and text columns are considered categorical columns.
list_of_features_to_excludeOPTIONAL. List of column names (comma-separated string) to exlude from the predictors list.
grouping_colsOPTIONAL. List of column names (comma-separated string) to group the data by. This will lead to creating multiple decision trees, one for each group.
weightsOPTIONAL. Column name containing weights for each observation.
max_depthOPTIONAL (Default = 7). Set the maximum depth of any node of the final tree, with the root node counted as depth 0. A deeper tree can lead to better prediction but will also result in longer processing time and higher memory usage.
min_splitOPTIONAL (Default = 20). Minimum number of observations that must exist in a node for a split to be attempted.
min_bucketOPTIONAL (Default = minsplit/3). Minimum number of observations in any terminal node. If only one of minbucket or minsplit is specified, minsplit is set to minbucket*3 or minbucket to minsplit/3, as appropriate.
n_binsoptional (default = 20) number of bins to use during binning. continuous-valued features are binned into discrete bins (per the quartile values) to compute split bound- aries. this global parameter is used to compute the resolution of the bins. higher number of bins will lead to higher processing time.
pruning_params(default: cp=0) pruning parameter string containing key-value pairs. the keys can be: cp (default = 0.01) a complexity parameter that determines that a split is attempted only if it decreases the overall lack of fit by a factor of ‘cp’. n_folds (default = 0) number of cross-validation folds
verbose_modeoptional (default = false) prints status information on the splits performed and any other information useful for debugging.
+
+
+

see Decision Tree for more details.

+ +
+
+ +

◆ tree_train() [2/14]

+ +
+
+ + + + + + + + +
text tree_train (text message)
+
+ +
+
+ +

◆ tree_train() [3/14]

+ +
+
+ + + + + + + +
text tree_train ()
+
+ +
+
+ +

◆ tree_train() [4/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth,
integer min_split,
integer min_bucket,
integer n_bins,
text pruning_params,
text null_handling_params 
)
+
+ +
+
+ +

◆ tree_train() [5/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth,
integer min_split,
integer min_bucket,
integer n_bins,
text pruning_params 
)
+
+ +
+
+ +

◆ tree_train() [6/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth,
integer min_split,
integer min_bucket,
integer n_bins 
)
+
+ +
+
+ +

◆ tree_train() [7/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth,
integer min_split,
integer min_bucket 
)
+
+ +
+
+ +

◆ tree_train() [8/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth,
integer min_split 
)
+
+ +
+
+ +

◆ tree_train() [9/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights,
integer max_depth 
)
+
+ +
+
+ +

◆ tree_train() [10/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols,
text weights 
)
+
+ +
+
+ +

◆ tree_train() [11/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion,
text grouping_cols 
)
+
+ +
+
+ +

◆ tree_train() [12/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude,
text split_criterion 
)
+
+ +
+
+ +

◆ tree_train() [13/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features,
text list_of_features_to_exclude 
)
+
+ +
+
+ +

◆ tree_train() [14/14]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void tree_train (text training_table_name,
text output_table_name,
text id_col_name,
text dependent_variable,
text list_of_features 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dense__linear__systems_8sql__in.html b/docs/docs/v2.1.0/dense__linear__systems_8sql__in.html new file mode 100644 index 00000000..4e3f06a5 --- /dev/null +++ b/docs/docs/v2.1.0/dense__linear__systems_8sql__in.html @@ -0,0 +1,631 @@ + + + + + + + + +MADlib: dense_linear_systems.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+Functions
+
+
dense_linear_systems.sql_in File Reference
+
+
+ +

SQL functions for linear systems. +More...

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+Functions

bytea8 dense_residual_norm_transition (bytea8 state, float8[] a, float8 b, float8[] x)
 
bytea8 dense_residual_norm_merge_states (bytea8 state1, bytea8 state2)
 
residual_norm_result dense_residual_norm_final (bytea8 state)
 
aggregate residual_norm_result dense_residual_norm (float8[] left_hand_side, float8 right_hand_side, float8[] solution)
 Compute the residual after solving the dense linear systems. More...
 
float8 [] dense_direct_linear_system_transition (float8[] state, integer row_id, float8[] a, float8 b, integer num_rows, integer algorithm)
 
float8 [] dense_direct_linear_system_merge_states (float8[] state1, float8[] state2)
 
dense_linear_solver_result dense_direct_linear_system_final (float8[] state)
 
aggregate dense_linear_solver_result dense_direct_linear_system (integer row_id, float8[] left_hand_side, float8 right_hand_side, integer numEquations, integer algorithm)
 Solve a system of linear equations using the direct method. More...
 
varchar linear_solver_dense (varchar input_string)
 Help function, to print out the supported families. More...
 
varchar linear_solver_dense ()
 
void linear_solver_dense (varchar source_table, varchar out_table, varchar row_id, varchar left_hand_side, varchar right_hand_side, varchar grouping_cols, varchar optimizer, varchar optimizer_options)
 A wrapper function for the various marginal linear_systemsion analyzes. More...
 
void linear_solver_dense (varchar source_table, varchar out_table, varchar row_id, varchar left_hand_side, varchar right_hand_side)
 Marginal effects with default variables. More...
 
+

Detailed Description

+
Date
July 2013
+
See also
Computes the solution of a consistent linear system, for more details see the module description at Dense Linear Systems
+

Function Documentation

+ +

◆ dense_direct_linear_system()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
aggregate dense_linear_solver_result dense_direct_linear_system (integer row_id,
float8 [] left_hand_side,
float8 right_hand_side,
integer numEquations,
integer algorithm 
)
+
+
Parameters
+ + + + + + +
row_idColumn containing the row_id
left_hand_sideColumn containing the left hand side of the system
right_hand_sideColumn containing the right hand side of the system
numEquationsNumber of equations
algorithmAlgorithm used for the dense linear solver
+
+
+
Returns
A composite value:
    +
  • solution FLOAT8[] - Array of marginal effects
    • +
  • residual_norm FLOAT8 - Norm of the residual
    • +
  • iters INTEGER - Iterations taken
    • +
+
+
Usage
    +
  • Get all the diagnostic statistics:
    + 
     SELECT linear_system_dense(row_id,
+                                  left_hand_side,
+                                   right_hand_side ,
+                                   numEquations )
+ FROM dataTable;
+
    • +
+
+ +
+
+ +

◆ dense_direct_linear_system_final()

+ +
+
+ + + + + + + + +
dense_linear_solver_result dense_direct_linear_system_final (float8 [] state)
+
+ +
+
+ +

◆ dense_direct_linear_system_merge_states()

+ +
+
+ + + + + + + + + + + + + + + + + + +
float8 [] dense_direct_linear_system_merge_states (float8 [] state1,
float8 [] state2 
)
+
+ +
+
+ +

◆ dense_direct_linear_system_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float8 [] dense_direct_linear_system_transition (float8 [] state,
integer row_id,
float8 [] a,
float8 b,
integer num_rows,
integer algorithm 
)
+
+ +
+
+ +

◆ dense_residual_norm()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
aggregate residual_norm_result dense_residual_norm (float8 [] left_hand_side,
float8 right_hand_side,
float8 [] solution 
)
+
+
Parameters
+ + + + +
left_hand_sideColumn containing the left hand side of the system
right_hand_sideColumn containing the right hand side of the system
solutionSolution of the linear system
+
+
+
Returns
residual_norm FLOAT8:
+
Usage
    +
  • Get all the diagnostic statistics:
    + 
     SELECT dense_residual_norm(row_id,
+                                  left_hand_side,
+                                   right_hand_side ,
+                                   solution )
+ FROM dataTable;
+
    • +
+
+ +
+
+ +

◆ dense_residual_norm_final()

+ +
+
+ + + + + + + + +
residual_norm_result dense_residual_norm_final (bytea8 state)
+
+ +
+
+ +

◆ dense_residual_norm_merge_states()

+ +
+
+ + + + + + + + + + + + + + + + + + +
bytea8 dense_residual_norm_merge_states (bytea8 state1,
bytea8 state2 
)
+
+ +
+
+ +

◆ dense_residual_norm_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
bytea8 dense_residual_norm_transition (bytea8 state,
float8 [] a,
float8 b,
float8 [] x 
)
+
+ +
+
+ +

◆ linear_solver_dense() [1/4]

+ +
+
+ + + + + + + + +
varchar linear_solver_dense (varchar input_string)
+
+ +
+
+ +

◆ linear_solver_dense() [2/4]

+ +
+
+ + + + + + + +
varchar linear_solver_dense ()
+
+ +
+
+ +

◆ linear_solver_dense() [3/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void linear_solver_dense (varchar source_table,
varchar out_table,
varchar row_id,
varchar left_hand_side,
varchar right_hand_side,
varchar grouping_cols,
varchar optimizer,
varchar optimizer_options 
)
+
+
Parameters
+ + + + + + + + + +
source_tableString identifying the input table
out_tableString identifying the output table to be created
row_idColumn containing the row_id
left_hand_sideColumn containing the left hand side of the system
right_hand_sideColumn containing the right hand side of the system
grouping_colsColumns to group by
optimizerOptimizer to be used
optimizer_optionsOptimal parameters for the algorithms
+
+
+
Returns
void
+
Usage
For function summary information. Run sql> select linear_solver_dense('help'); OR sql> select linear_solver_dense(); OR sql> select linear_solver_dense('?'); For function usage information. Run sql> select linear_solver_dense('usage');
+ +
+
+ +

◆ linear_solver_dense() [4/4]

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
void linear_solver_dense (varchar source_table,
varchar out_table,
varchar row_id,
varchar left_hand_side,
varchar right_hand_side 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_097d0c47873b413f914e0be0fb8e0c70.html b/docs/docs/v2.1.0/dir_097d0c47873b413f914e0be0fb8e0c70.html new file mode 100644 index 00000000..7506838f --- /dev/null +++ b/docs/docs/v2.1.0/dir_097d0c47873b413f914e0be0fb8e0c70.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: svec_util Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+
svec_util Directory Reference
+
+
+ + + + +

+Directories

directory  src
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_16b90e9a6c080d7fc2617cfecd7f223b.html b/docs/docs/v2.1.0/dir_16b90e9a6c080d7fc2617cfecd7f223b.html new file mode 100644 index 00000000..d366a67d --- /dev/null +++ b/docs/docs/v2.1.0/dir_16b90e9a6c080d7fc2617cfecd7f223b.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: pg_gp Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
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+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
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+
pg_gp Directory Reference
+
+
+ + + + + +

+Files

file  svec.sql_in
 SQL type definitions and functions for sparse vector data type svec
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_1960c8c5a7f1e7616d29e5a0c180bcf2.html b/docs/docs/v2.1.0/dir_1960c8c5a7f1e7616d29e5a0c180bcf2.html new file mode 100644 index 00000000..03370cad --- /dev/null +++ b/docs/docs/v2.1.0/dir_1960c8c5a7f1e7616d29e5a0c180bcf2.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: src Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+
src Directory Reference
+
+
+ + + + +

+Directories

directory  pg_gp
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_1c3de670490e30b2adf792227ef51e32.html b/docs/docs/v2.1.0/dir_1c3de670490e30b2adf792227ef51e32.html new file mode 100644 index 00000000..21aa02f9 --- /dev/null +++ b/docs/docs/v2.1.0/dir_1c3de670490e30b2adf792227ef51e32.html @@ -0,0 +1,141 @@ + + + + + + + + +MADlib: graph Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
+
+ + +
+ +
+ +
+
+
graph Directory Reference
+
+
+ + + + + + + + + + + + + + + + + + + +

+Files

file  apsp.sql_in
 SQL functions for graph analytics.
 
file  bfs.sql_in
 SQL functions for graph analytics.
 
file  hits.sql_in
 
file  measures.sql_in
 
file  pagerank.sql_in
 
file  sssp.sql_in
 SQL functions for graph analytics.
 
file  wcc.sql_in
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_2e2767a73e2d710192c730fd426a8c90.html b/docs/docs/v2.1.0/dir_2e2767a73e2d710192c730fd426a8c90.html new file mode 100644 index 00000000..5b70eec3 --- /dev/null +++ b/docs/docs/v2.1.0/dir_2e2767a73e2d710192c730fd426a8c90.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: pg_gp Directory Reference + + + + + + + + + + + + + + + + + + + +
+
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+
+ 2.1.0 +
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User Documentation for Apache MADlib
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+
+ +
+
+
+ +
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+
+ + +
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+
+
pg_gp Directory Reference
+
+
+ + + + + +

+Files

file  svec_util.sql_in
 SQL utility functions for sparse vector data type svec
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_3749b33f41e0a82f4dfb20be7f91dfa3.html b/docs/docs/v2.1.0/dir_3749b33f41e0a82f4dfb20be7f91dfa3.html new file mode 100644 index 00000000..1f0a089a --- /dev/null +++ b/docs/docs/v2.1.0/dir_3749b33f41e0a82f4dfb20be7f91dfa3.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: pg_gp Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
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+
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+
+
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+
+ + +
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+
+
pg_gp Directory Reference
+
+
+ + + + + +

+Files

file  porter_stemmer.sql_in
 implementation of porter stemmer operations in SQL
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_3ee26ceeadb429f807bd6cd822eca1b9.html b/docs/docs/v2.1.0/dir_3ee26ceeadb429f807bd6cd822eca1b9.html new file mode 100644 index 00000000..1e99f869 --- /dev/null +++ b/docs/docs/v2.1.0/dir_3ee26ceeadb429f807bd6cd822eca1b9.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: bayes Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
+
+ + + + + + +
+
+
+ + + +
+
+ +
+
+
+ +
+ +
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+ + +
+ +
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bayes Directory Reference
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+Files

file  bayes.sql_in
 SQL functions for naive Bayes.
 
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+ + + + diff --git a/docs/docs/v2.1.0/dir_42e4eb27424bda9fbbfa95509de09bad.html b/docs/docs/v2.1.0/dir_42e4eb27424bda9fbbfa95509de09bad.html new file mode 100644 index 00000000..e03d9473 --- /dev/null +++ b/docs/docs/v2.1.0/dir_42e4eb27424bda9fbbfa95509de09bad.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: conjugate_gradient Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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conjugate_gradient Directory Reference
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+Files

file  conjugate_gradient.sql_in
 SQL function computing Conjugate Gradient.
 
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User Documentation for Apache MADlib
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dbscan Directory Reference
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+Files

file  dbscan.sql_in
 Partitions a set of observations into clusters of arbitrary shape based on the density of nearby neighbors.
 
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User Documentation for Apache MADlib
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+ +
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src Directory Reference
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+
+ + + + +

+Directories

directory  pg_gp
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_505cd743a8a717435eca324f49291a46.html b/docs/docs/v2.1.0/dir_505cd743a8a717435eca324f49291a46.html new file mode 100644 index 00000000..2df57e42 --- /dev/null +++ b/docs/docs/v2.1.0/dir_505cd743a8a717435eca324f49291a46.html @@ -0,0 +1,145 @@ + + + + + + + + +MADlib: stats Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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stats Directory Reference
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+Files

file  clustered_variance_coxph.sql_in
 SQL functions for clustered robust cox proportional hazards regression.
 
file  correlation.sql_in
 SQL functions for correlation computation.
 
file  cox_prop_hazards.sql_in
 SQL functions for cox proportional hazards.
 
file  distribution.sql_in
 SQL functions for collecting distributions.
 
file  hypothesis_tests.sql_in
 SQL functions for statistical hypothesis tests.
 
file  pred_metrics.sql_in
 A collection of summary statistics to gauge model accuracy based on predicted values vs. ground-truth values.
 
file  robust_variance_coxph.sql_in
 SQL functions for robust cox proportional hazards regression.
 
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User Documentation for Apache MADlib
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recursive_partitioning Directory Reference
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+Files

file  decision_tree.sql_in
 
file  random_forest.sql_in
 
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+ + + + diff --git a/docs/docs/v2.1.0/dir_5cd13365c66443c54a8f3b4c82c03aee.html b/docs/docs/v2.1.0/dir_5cd13365c66443c54a8f3b4c82c03aee.html new file mode 100644 index 00000000..06538b7d --- /dev/null +++ b/docs/docs/v2.1.0/dir_5cd13365c66443c54a8f3b4c82c03aee.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: svm Directory Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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svm Directory Reference
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+Files

file  svm.sql_in
 SQL functions for SVM (Poisson)
 
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+ + + + diff --git a/docs/docs/v2.1.0/dir_5ff04c1d4b766f0a4dd68c6f19ed2092.html b/docs/docs/v2.1.0/dir_5ff04c1d4b766f0a4dd68c6f19ed2092.html new file mode 100644 index 00000000..40a7f3bc --- /dev/null +++ b/docs/docs/v2.1.0/dir_5ff04c1d4b766f0a4dd68c6f19ed2092.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: summary Directory Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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summary Directory Reference
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+Files

file  summary.sql_in
 Summary function for descriptive statistics.
 
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+
User Documentation for Apache MADlib
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src Directory Reference
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+
+ + + + +

+Directories

directory  pg_gp
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_68267d1309a1af8e8297ef4c3efbcdba.html b/docs/docs/v2.1.0/dir_68267d1309a1af8e8297ef4c3efbcdba.html new file mode 100644 index 00000000..a91e5b59 --- /dev/null +++ b/docs/docs/v2.1.0/dir_68267d1309a1af8e8297ef4c3efbcdba.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: src Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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src Directory Reference
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+Directories

directory  ports
 
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User Documentation for Apache MADlib
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lda Directory Reference
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+Files

file  lda.sql_in
 SQL functions for Latent Dirichlet Allocation.
 
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+ + + + diff --git a/docs/docs/v2.1.0/dir_704eb8350b43e1ca74c0f90ed1ba450e.html b/docs/docs/v2.1.0/dir_704eb8350b43e1ca74c0f90ed1ba450e.html new file mode 100644 index 00000000..aeef776c --- /dev/null +++ b/docs/docs/v2.1.0/dir_704eb8350b43e1ca74c0f90ed1ba450e.html @@ -0,0 +1,134 @@ + + + + + + + + +MADlib: methods Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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methods Directory Reference
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+Directories

directory  array_ops
 
directory  sketch
 
directory  stemmer
 
directory  svec
 
directory  svec_util
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_70e9abe17564e15776adcab8550c7667.html b/docs/docs/v2.1.0/dir_70e9abe17564e15776adcab8550c7667.html new file mode 100644 index 00000000..5fab3b0e --- /dev/null +++ b/docs/docs/v2.1.0/dir_70e9abe17564e15776adcab8550c7667.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: crf Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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crf Directory Reference
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+Files

file  crf.sql_in
 SQL functions for conditional random field.
 
file  crf_data_loader.sql_in
 Create database tables and import POS/NER training/testing data to the database.
 
file  crf_feature_gen.sql_in
 SQL function for POS/NER feature extraction.
 
file  viterbi.sql_in
 concatenate a set of input values into arrays to feed into viterbi c function and create a human readable view of the output
 
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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kmeans Directory Reference
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+Files

file  kmeans.sql_in
 Set of functions for k-means clustering.
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_7513a8b3b7336e99c30a333cfb144104.html b/docs/docs/v2.1.0/dir_7513a8b3b7336e99c30a333cfb144104.html new file mode 100644 index 00000000..16d21639 --- /dev/null +++ b/docs/docs/v2.1.0/dir_7513a8b3b7336e99c30a333cfb144104.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: linear_systems Directory Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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linear_systems Directory Reference
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+Files

file  dense_linear_systems.sql_in
 SQL functions for linear systems.
 
file  sparse_linear_systems.sql_in
 SQL functions for linear systems.
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_7592ceb856cf018f9811e11407c61fda.html b/docs/docs/v2.1.0/dir_7592ceb856cf018f9811e11407c61fda.html new file mode 100644 index 00000000..d2a77d1a --- /dev/null +++ b/docs/docs/v2.1.0/dir_7592ceb856cf018f9811e11407c61fda.html @@ -0,0 +1,145 @@ + + + + + + + + +MADlib: deep_learning Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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deep_learning Directory Reference
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+Files

file  input_data_preprocessor.sql_in
 
file  keras_model_arch_table.sql_in
 
file  madlib_keras.sql_in
 Fit, evaluate and predict for one model.
 
file  madlib_keras_automl.sql_in
 Functions to run automated machine learning (autoML) methods for model architecture search and hyperparameter tuning.
 
file  madlib_keras_custom_function.sql_in
 Function to load serialized Python objects into a table.
 
file  madlib_keras_fit_multiple_model.sql_in
 
file  madlib_keras_gpu_info.sql_in
 Utility function to report number and type of GPUs in the database cluster.
 
file  madlib_keras_model_selection.sql_in
 Explore network architectures and hyperparameters by training many models a time.
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_834e55cf992733df24fbe86b49356157.html b/docs/docs/v2.1.0/dir_834e55cf992733df24fbe86b49356157.html new file mode 100644 index 00000000..e9493764 --- /dev/null +++ b/docs/docs/v2.1.0/dir_834e55cf992733df24fbe86b49356157.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: array_ops Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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array_ops Directory Reference
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+
+ + + + +

+Directories

directory  src
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_87d2e9694998410c1b0408bb775833a4.html b/docs/docs/v2.1.0/dir_87d2e9694998410c1b0408bb775833a4.html new file mode 100644 index 00000000..55ce2867 --- /dev/null +++ b/docs/docs/v2.1.0/dir_87d2e9694998410c1b0408bb775833a4.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: svec Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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svec Directory Reference
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+Directories

directory  src
 
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+ + + + diff --git a/docs/docs/v2.1.0/dir_8b8525adb4e4d2ae68fa3d70bbeff8da.html b/docs/docs/v2.1.0/dir_8b8525adb4e4d2ae68fa3d70bbeff8da.html new file mode 100644 index 00000000..bbf59d28 --- /dev/null +++ b/docs/docs/v2.1.0/dir_8b8525adb4e4d2ae68fa3d70bbeff8da.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: prob Directory Reference + + + + + + + + + + + + + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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prob Directory Reference
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+Files

file  prob.sql_in
 SQL functions for evaluating probability functions.
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_8cdb0d06bc3d9fdbe366fbcc82abc3e3.html b/docs/docs/v2.1.0/dir_8cdb0d06bc3d9fdbe366fbcc82abc3e3.html new file mode 100644 index 00000000..8ba38af1 --- /dev/null +++ b/docs/docs/v2.1.0/dir_8cdb0d06bc3d9fdbe366fbcc82abc3e3.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: tsa Directory Reference + + + + + + + + + + + + + + + + + + + +
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+ + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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tsa Directory Reference
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+Files

file  arima.sql_in
 Arima function for forecasting of timeseries data.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_8d53e1c0026e7e34b4cd68f8b91426d6.html b/docs/docs/v2.1.0/dir_8d53e1c0026e7e34b4cd68f8b91426d6.html new file mode 100644 index 00000000..192bc2b4 --- /dev/null +++ b/docs/docs/v2.1.0/dir_8d53e1c0026e7e34b4cd68f8b91426d6.html @@ -0,0 +1,153 @@ + + + + + + + + +MADlib: utilities Directory Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
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+ 2.1.0 +
+
User Documentation for Apache MADlib
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utilities Directory Reference
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+Files

file  cols2vec.sql_in
 A set of utilities to ease basic table transformations (such as *aggregating multiple columns in an array)
 
file  create_indicators.sql_in
 SQL functions for dummy coding categorical variables.
 
file  encode_categorical.sql_in
 SQL functions for encoding categorical variables to numerical values.
 
file  minibatch_preprocessing.sql_in
 Utility that prepares input data for use by models that support mini-batch as an optimization option.
 
file  path.sql_in
 SQL functions for pathing functions.
 
file  pivot.sql_in
 SQL functions for pivoting.
 
file  sessionize.sql_in
 SQL functions for sessionization functions.
 
file  text_utilities.sql_in
 SQL functions for carrying out routine text operations.
 
file  utilities.sql_in
 SQL functions for carrying out routine tasks.
 
file  vec2cols.sql_in
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_93c42bb4df0f3e1302223b6dfd48c81e.html b/docs/docs/v2.1.0/dir_93c42bb4df0f3e1302223b6dfd48c81e.html new file mode 100644 index 00000000..5abcfe98 --- /dev/null +++ b/docs/docs/v2.1.0/dir_93c42bb4df0f3e1302223b6dfd48c81e.html @@ -0,0 +1,132 @@ + + + + + + + + +MADlib: convex Directory Reference + + + + + + + + + + + + + + + + + + + +
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+
User Documentation for Apache MADlib
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convex Directory Reference
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+ + + + + + + + + + +

+Files

file  lmf.sql_in
 SQL functions for low-rank matrix factorization.
 
file  mlp.sql_in
 SQL functions for multilayer perceptron.
 
file  utils_regularization.sql_in
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_9db0190ed89ab407304aec250d1ef64f.html b/docs/docs/v2.1.0/dir_9db0190ed89ab407304aec250d1ef64f.html new file mode 100644 index 00000000..5b4adb57 --- /dev/null +++ b/docs/docs/v2.1.0/dir_9db0190ed89ab407304aec250d1ef64f.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: pca Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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+
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+
+ +
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+
pca Directory Reference
+
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+Files

file  pca.sql_in
 Principal Component Analysis.
 
file  pca_project.sql_in
 Principal Component Analysis Projection.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_9e42ee0a0235722f482630aa6cc99334.html b/docs/docs/v2.1.0/dir_9e42ee0a0235722f482630aa6cc99334.html new file mode 100644 index 00000000..85fca772 --- /dev/null +++ b/docs/docs/v2.1.0/dir_9e42ee0a0235722f482630aa6cc99334.html @@ -0,0 +1,135 @@ + + + + + + + + +MADlib: linalg Directory Reference + + + + + + + + + + + + + + + + + + + +
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+
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+
+ +
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+
+
linalg Directory Reference
+
+
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+Files

file  linalg.sql_in
 SQL functions for linear algebra.
 
file  matrix_ops.sql_in
 Implementation of matrix operations in SQL.
 
file  pivotalr_arrayops.sql_in
 
file  svd.sql_in
 Singular Value Decomposition.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_9f5e6edf0db58b0627c46b41dbbbb27f.html b/docs/docs/v2.1.0/dir_9f5e6edf0db58b0627c46b41dbbbb27f.html new file mode 100644 index 00000000..46a74036 --- /dev/null +++ b/docs/docs/v2.1.0/dir_9f5e6edf0db58b0627c46b41dbbbb27f.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: validation Directory Reference + + + + + + + + + + + + + + + + + + + +
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validation Directory Reference
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+Files

file  cross_validation.sql_in
 SQL functions for cross validation.
 
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postgres Directory Reference
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+Directories

directory  modules
 
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regress Directory Reference
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+Files

file  clustered_variance.sql_in
 
file  linear.sql_in
 SQL functions for linear regression.
 
file  logistic.sql_in
 SQL functions for logistic regression.
 
file  marginal.sql_in
 SQL functions for linear regression.
 
file  multilogistic.sql_in
 SQL functions for multinomial logistic regression.
 
file  robust.sql_in
 SQL functions for robust variance linear and logistic regression.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_b0d8a62e5a4314de84ce58e7cd249850.html b/docs/docs/v2.1.0/dir_b0d8a62e5a4314de84ce58e7cd249850.html new file mode 100644 index 00000000..56bf8e91 --- /dev/null +++ b/docs/docs/v2.1.0/dir_b0d8a62e5a4314de84ce58e7cd249850.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: sketch Directory Reference + + + + + + + + + + + + + + + + + + + +
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sketch Directory Reference
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directory  src
 
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directory  src
 
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knn Directory Reference
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+Files

file  knn.sql_in
 Set of functions for k-nearest neighbors.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_c2d3987992538edb8f634d5f4e0fae80.html b/docs/docs/v2.1.0/dir_c2d3987992538edb8f634d5f4e0fae80.html new file mode 100644 index 00000000..516b3218 --- /dev/null +++ b/docs/docs/v2.1.0/dir_c2d3987992538edb8f634d5f4e0fae80.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: pg_gp Directory Reference + + + + + + + + + + + + + + + + + + + +
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pg_gp Directory Reference
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+Files

file  sketch.sql_in
 SQL functions for sketch-based approximations of descriptive statistics.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_c8a9890f716ab6621b63d44c36a168eb.html b/docs/docs/v2.1.0/dir_c8a9890f716ab6621b63d44c36a168eb.html new file mode 100644 index 00000000..efa67ab9 --- /dev/null +++ b/docs/docs/v2.1.0/dir_c8a9890f716ab6621b63d44c36a168eb.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: src Directory Reference + + + + + + + + + + + + + + + + + + + +
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src Directory Reference
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+Directories

directory  pg_gp
 
+
+
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pmml Directory Reference
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+Files

file  table_to_pmml.sql_in
 
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+
+ + + + diff --git a/docs/docs/v2.1.0/dir_d662e943e8adcb86abe4b822d2348c9e.html b/docs/docs/v2.1.0/dir_d662e943e8adcb86abe4b822d2348c9e.html new file mode 100644 index 00000000..ec045eaf --- /dev/null +++ b/docs/docs/v2.1.0/dir_d662e943e8adcb86abe4b822d2348c9e.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: elastic_net Directory Reference + + + + + + + + + + + + + + + + + + + +
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elastic_net Directory Reference
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+Files

file  elastic_net.sql_in
 SQL functions for elastic net regularization.
 
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+
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mxgboost Directory Reference
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+Files

file  madlib_xgboost.sql_in
 SQL functions for xgboost.
 
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+
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modules Directory Reference
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+Directories

directory  assoc_rules
 
directory  bayes
 
directory  conjugate_gradient
 
directory  convex
 
directory  crf
 
directory  dbscan
 
directory  deep_learning
 
directory  elastic_net
 
directory  glm
 
directory  graph
 
directory  kmeans
 
directory  knn
 
directory  lda
 
directory  linalg
 
directory  linear_systems
 
directory  mxgboost
 
directory  pca
 
directory  pmml
 
directory  prob
 
directory  recursive_partitioning
 
directory  regress
 
directory  sample
 
directory  stats
 
directory  summary
 
directory  svm
 
directory  tsa
 
directory  utilities
 
directory  validation
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_df86748cb94fb6c2fa09e991cce090c0.html b/docs/docs/v2.1.0/dir_df86748cb94fb6c2fa09e991cce090c0.html new file mode 100644 index 00000000..b6f92ade --- /dev/null +++ b/docs/docs/v2.1.0/dir_df86748cb94fb6c2fa09e991cce090c0.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: assoc_rules Directory Reference + + + + + + + + + + + + + + + + + + + +
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assoc_rules Directory Reference
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+Files

file  assoc_rules.sql_in
 The assoc_rules function computes association rules for a given set of data. The data is assumed to have two dimensions; items (between which we are trying to discover associations), and a transaction id. This tranaction id groups the items by event and could also be a user id, date, etc. depending on the context of the data. This function assumes the data is stored in two columns with one transaction id and one item per row.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_e2e6d80cc57daae810c80cbdae687e33.html b/docs/docs/v2.1.0/dir_e2e6d80cc57daae810c80cbdae687e33.html new file mode 100644 index 00000000..b6ad0379 --- /dev/null +++ b/docs/docs/v2.1.0/dir_e2e6d80cc57daae810c80cbdae687e33.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: src Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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src Directory Reference
+
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+Directories

directory  pg_gp
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_e502304d8bc7f1ef2456a474c6d92acd.html b/docs/docs/v2.1.0/dir_e502304d8bc7f1ef2456a474c6d92acd.html new file mode 100644 index 00000000..08cda612 --- /dev/null +++ b/docs/docs/v2.1.0/dir_e502304d8bc7f1ef2456a474c6d92acd.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: glm Directory Reference + + + + + + + + + + + + + + + + + + + +
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glm Directory Reference
+
+
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+Files

file  glm.sql_in
 SQL functions for GLM (Poisson)
 
file  multiresponseglm.sql_in
 SQL functions for multinomial regression.
 
file  ordinal.sql_in
 SQL functions for ordinal regression.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_e6c126a997181663ba81c11cbf416bb1.html b/docs/docs/v2.1.0/dir_e6c126a997181663ba81c11cbf416bb1.html new file mode 100644 index 00000000..35d45a4b --- /dev/null +++ b/docs/docs/v2.1.0/dir_e6c126a997181663ba81c11cbf416bb1.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: sample Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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+
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sample Directory Reference
+
+
+ + + + + + + + + + + + + + +

+Files

file  balance_sample.sql_in
 SQL functions for balanced data sets sampling.
 
file  sample.sql_in
 SQL functions for random sampling.
 
file  stratified_sample.sql_in
 SQL functions for stratified sampling.
 
file  train_test_split.sql_in
 SQL functions for test train split.
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_efbcf68973d247bbf15f9eecae7f24e3.html b/docs/docs/v2.1.0/dir_efbcf68973d247bbf15f9eecae7f24e3.html new file mode 100644 index 00000000..7b91ce03 --- /dev/null +++ b/docs/docs/v2.1.0/dir_efbcf68973d247bbf15f9eecae7f24e3.html @@ -0,0 +1,126 @@ + + + + + + + + +MADlib: ports Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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ports Directory Reference
+
+
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+Directories

directory  postgres
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/dir_fe647384fff178c2cff5ce75fb4044e5.html b/docs/docs/v2.1.0/dir_fe647384fff178c2cff5ce75fb4044e5.html new file mode 100644 index 00000000..f64faba6 --- /dev/null +++ b/docs/docs/v2.1.0/dir_fe647384fff178c2cff5ce75fb4044e5.html @@ -0,0 +1,127 @@ + + + + + + + + +MADlib: pg_gp Directory Reference + + + + + + + + + + + + + + + + + + + +
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User Documentation for Apache MADlib
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pg_gp Directory Reference
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+Files

file  array_ops.sql_in
 implementation of array operations in SQL
 
+
+
+ + + + diff --git a/docs/docs/v2.1.0/distribution_8sql__in.html b/docs/docs/v2.1.0/distribution_8sql__in.html new file mode 100644 index 00000000..f1bc03b6 --- /dev/null +++ b/docs/docs/v2.1.0/distribution_8sql__in.html @@ -0,0 +1,314 @@ + + + + + + + + +MADlib: distribution.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
+
+ + + + + + + + +
+
+ 2.1.0 +
+
User Documentation for Apache MADlib
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+
+Functions
+
+
distribution.sql_in File Reference
+
+
+ +

SQL functions for collecting distributions. +More...

+ + + + + + + + + + + + + + +

+Functions

float8 [][] vectorized_distribution_transition (float8[][] distribution, integer[] indices, integer[] levels)
 
float8 [][] vectorized_distribution_final (float8[][] state)
 
aggregate float8 [][] vectorized_distribution_agg (integer[], integer[])
 
float8 [] discrete_distribution_transition (float8[] distribution, integer ind, float8 weight, integer level)
 
float8 [] discrete_distribution_final (float8[] state)
 
aggregate float8 [] discrete_distribution_agg (integer, float8, integer)
 
+

Function Documentation

+ +

◆ discrete_distribution_agg()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
aggregate float8 [] discrete_distribution_agg (integer ,
float8 ,
integer  
)
+
+ +
+
+ +

◆ discrete_distribution_final()

+ +
+
+ + + + + + + + +
float8 [] discrete_distribution_final (float8 [] state)
+
+ +
+
+ +

◆ discrete_distribution_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
float8 [] discrete_distribution_transition (float8 [] distribution,
integer ind,
float8 weight,
integer level 
)
+
+ +
+
+ +

◆ vectorized_distribution_agg()

+ +
+
+ + + + + + + + + + + + + + + + + + +
aggregate float8 [][] vectorized_distribution_agg (integer [],
integer [] 
)
+
+ +
+
+ +

◆ vectorized_distribution_final()

+ +
+
+ + + + + + + + +
float8 [][] vectorized_distribution_final (float8 state[][])
+
+ +
+
+ +

◆ vectorized_distribution_transition()

+ +
+
+ + + + + + + + + + + + + + + + + + + + + + + + +
float8 [][] vectorized_distribution_transition (float8 distribution[][],
integer [] indices,
integer [] levels 
)
+
+ +
+
+
+
+ + + + diff --git a/docs/docs/v2.1.0/doc.png b/docs/docs/v2.1.0/doc.png new file mode 100644 index 0000000000000000000000000000000000000000..17edabff95f7b8da13c9516a04efe05493c29501 GIT binary patch literal 746 zcmV7=@pnbNXRFEm&G8P!&WHG=d)>K?YZ1bzou)2{$)) zumDct!>4SyxL;zgaG>wy`^Hv*+}0kUfCrz~BCOViSb$_*&;{TGGn2^x9K*!Sf0=lV zpP=7O;GA0*Jm*tTYj$IoXvimpnV4S1Z5f$p*f$Db2iq2zrVGQUz~yq`ahn7ck(|CE z7Gz;%OP~J6)tEZWDzjhL9h2hdfoU2)Nd%T<5Kt;Y0XLt&<@6pQx!nw*5`@bq#?l*?3z{Hlzoc=Pr>oB5(9i6~_&-}A(4{Q$>c>%rV&E|a(r&;?i5cQB=} zYSDU5nXG)NS4HEs0it2AHe2>shCyr7`6@4*6{r@8fXRbTA?=IFVWAQJL&H5H{)DpM#{W(GL+Idzf^)uRV@oB8u$ z8v{MfJbTiiRg4bza<41NAzrl{=3fl_D+$t+^!xlQ8S}{UtY`e z;;&9UhyZqQRN%2pot{*Ei0*4~hSF_3AH2@fKU!$NSflS>{@tZpDT4`M2WRTTVH+D? z)GFlEGGHe?koB}i|1w45!BF}N_q&^HJ&-tyR{(afC6H7|aml|tBBbv}55C5DNP8p3 z)~jLEO4Z&2hZmP^i-e%(@d!(E|KRafiU8Q5u(wU((j8un3OR*Hvj+t literal 0 HcmV?d00001 diff --git a/docs/docs/v2.1.0/dot_inline_dotgraph_1.svg b/docs/docs/v2.1.0/dot_inline_dotgraph_1.svg new file mode 100644 index 00000000..57093b94 --- /dev/null +++ b/docs/docs/v2.1.0/dot_inline_dotgraph_1.svg @@ -0,0 +1,115 @@ + + + + + + +%3 + +cluster_0 + +1. Model Preparation + +cluster_1 + +2a. Train Single Model + +cluster_2 + +2b. Train Multiple Models + + +b + +Preprocess data + + +c + +Define model architectures + + +b->c + + + + +d + +Define custom functions (optional) + + +c->d + + + + +e + +Fit + + +d->e + + + + +g + +Define model configurations + + +d->g + + + + +j + +AutoML + + +d->j + + + + +f + +Inference + + +e->f + + + + +h + +Fit Multiple + + +g->h + + + + +i + +Inference + + +h->i + + + + +j->i + + + + + diff --git a/docs/docs/v2.1.0/doxygen.css b/docs/docs/v2.1.0/doxygen.css new file mode 100644 index 00000000..4f1ab919 --- /dev/null +++ b/docs/docs/v2.1.0/doxygen.css @@ -0,0 +1,1596 @@ +/* The standard CSS for doxygen 1.8.13 */ + +body, table, div, p, dl { + font: 400 14px/22px Roboto,sans-serif; +} + +p.reference, p.definition { + font: 400 14px/22px Roboto,sans-serif; +} + +/* @group Heading Levels */ + +h1.groupheader { + font-size: 150%; +} + +.title { + font: 400 14px/28px Roboto,sans-serif; + font-size: 150%; + font-weight: bold; + margin: 10px 2px; +} + +h2.groupheader { + border-bottom: 1px solid #879ECB; + color: #354C7B; + font-size: 150%; + font-weight: normal; + margin-top: 1.75em; + padding-top: 8px; + padding-bottom: 4px; + width: 100%; +} + +h3.groupheader { + font-size: 100%; +} + +h1, h2, h3, h4, h5, h6 { + -webkit-transition: text-shadow 0.5s linear; + -moz-transition: text-shadow 0.5s linear; + -ms-transition: text-shadow 0.5s linear; + -o-transition: text-shadow 0.5s linear; + transition: text-shadow 0.5s linear; + margin-right: 15px; +} + +h1.glow, h2.glow, h3.glow, h4.glow, h5.glow, h6.glow { + text-shadow: 0 0 15px cyan; +} + +dt { + font-weight: bold; +} + +div.multicol { + -moz-column-gap: 1em; + -webkit-column-gap: 1em; + -moz-column-count: 3; + -webkit-column-count: 3; +} + +p.startli, p.startdd { + margin-top: 2px; +} + +p.starttd { + margin-top: 0px; +} + +p.endli { + margin-bottom: 0px; +} + +p.enddd { + margin-bottom: 4px; +} + +p.endtd { + margin-bottom: 2px; +} + +/* @end */ + +caption { + font-weight: bold; +} + +span.legend { + font-size: 70%; + text-align: center; +} + +h3.version { + font-size: 90%; + text-align: center; +} + +div.qindex, div.navtab{ + background-color: #EBEFF6; + border: 1px solid #A3B4D7; + text-align: center; +} + +div.qindex, div.navpath { + width: 100%; + line-height: 140%; +} + +div.navtab { + margin-right: 15px; +} + +/* @group Link Styling */ + +a { + color: #3D578C; + font-weight: normal; + text-decoration: none; +} + +.contents a:visited { + color: #4665A2; +} + +a:hover { + text-decoration: underline; +} + +a.qindex { + font-weight: bold; +} + +a.qindexHL { + font-weight: bold; + background-color: #9CAFD4; + color: #ffffff; + border: 1px double #869DCA; +} + +.contents a.qindexHL:visited { + color: #ffffff; +} + +a.el { + font-weight: bold; +} + +a.elRef { +} + +a.code, a.code:visited, a.line, a.line:visited { + color: #4665A2; +} + +a.codeRef, a.codeRef:visited, a.lineRef, a.lineRef:visited { + color: #4665A2; +} + +/* @end */ + +dl.el { + margin-left: -1cm; +} + +pre.fragment { + border: 1px solid #C4CFE5; + background-color: #FBFCFD; + padding: 4px 6px; + margin: 4px 8px 4px 2px; + overflow: auto; + word-wrap: break-word; + font-size: 9pt; + line-height: 125%; + font-family: monospace, fixed; + font-size: 105%; +} + +div.fragment { + padding: 0px; + margin: 4px 8px 4px 2px; + background-color: #FBFCFD; + border: 1px solid #C4CFE5; +} + +div.line { + font-family: monospace, fixed; + font-size: 13px; + min-height: 13px; + line-height: 1.0; + text-wrap: unrestricted; + white-space: -moz-pre-wrap; /* Moz */ + white-space: -pre-wrap; /* Opera 4-6 */ + white-space: -o-pre-wrap; /* Opera 7 */ + white-space: pre-wrap; /* CSS3 */ + word-wrap: break-word; /* IE 5.5+ */ + text-indent: -53px; + padding-left: 53px; + padding-bottom: 0px; + margin: 0px; + -webkit-transition-property: background-color, box-shadow; + -webkit-transition-duration: 0.5s; + -moz-transition-property: background-color, box-shadow; + -moz-transition-duration: 0.5s; + -ms-transition-property: background-color, box-shadow; + -ms-transition-duration: 0.5s; + -o-transition-property: background-color, box-shadow; + -o-transition-duration: 0.5s; + transition-property: background-color, box-shadow; + transition-duration: 0.5s; +} + +div.line:after { + content:"\000A"; + white-space: pre; +} + +div.line.glow { + background-color: cyan; + box-shadow: 0 0 10px cyan; +} + + +span.lineno { + padding-right: 4px; + text-align: right; + border-right: 2px solid #0F0; + background-color: #E8E8E8; + white-space: pre; +} +span.lineno a { + background-color: #D8D8D8; +} + +span.lineno a:hover { + background-color: #C8C8C8; +} + +.lineno { + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +div.ah, span.ah { + background-color: black; + font-weight: bold; + color: #ffffff; + margin-bottom: 3px; + margin-top: 3px; + padding: 0.2em; + border: solid thin #333; + border-radius: 0.5em; + -webkit-border-radius: .5em; + -moz-border-radius: .5em; + box-shadow: 2px 2px 3px #999; + -webkit-box-shadow: 2px 2px 3px #999; + -moz-box-shadow: rgba(0, 0, 0, 0.15) 2px 2px 2px; + background-image: -webkit-gradient(linear, left top, left bottom, from(#eee), to(#000),color-stop(0.3, #444)); + background-image: -moz-linear-gradient(center top, #eee 0%, #444 40%, #000 110%); +} + +div.classindex ul { + list-style: none; + padding-left: 0; +} + +div.classindex span.ai { + display: inline-block; +} + +div.groupHeader { + margin-left: 16px; + margin-top: 12px; + font-weight: bold; +} + +div.groupText { + margin-left: 16px; + font-style: italic; +} + +body { + background-color: white; + color: black; + margin: 0; +} + +div.contents { + margin-top: 10px; + margin-left: 12px; + margin-right: 8px; +} + +td.indexkey { + background-color: #EBEFF6; + font-weight: bold; + border: 1px solid #C4CFE5; + margin: 2px 0px 2px 0; + padding: 2px 10px; + white-space: nowrap; + vertical-align: top; +} + +td.indexvalue { + background-color: #EBEFF6; + border: 1px solid #C4CFE5; + padding: 2px 10px; + margin: 2px 0px; +} + +tr.memlist { + background-color: #EEF1F7; +} + +p.formulaDsp { + text-align: center; +} + +img.formulaDsp { + +} + +img.formulaInl { + vertical-align: middle; +} + +div.center { + text-align: center; + margin-top: 0px; + margin-bottom: 0px; + padding: 0px; +} + +div.center img { + border: 0px; +} + +address.footer { + text-align: right; + padding-right: 12px; +} + +img.footer { + border: 0px; + vertical-align: middle; +} + +/* @group Code Colorization */ + +span.keyword { + color: #008000 +} + +span.keywordtype { + color: #604020 +} + +span.keywordflow { + color: #e08000 +} + +span.comment { + color: #800000 +} + +span.preprocessor { + color: #806020 +} + +span.stringliteral { + color: #002080 +} + +span.charliteral { + color: #008080 +} + +span.vhdldigit { + color: #ff00ff +} + +span.vhdlchar { + color: #000000 +} + +span.vhdlkeyword { + color: #700070 +} + +span.vhdllogic { + color: #ff0000 +} + +blockquote { + background-color: #F7F8FB; + border-left: 2px solid #9CAFD4; + margin: 0 24px 0 4px; + padding: 0 12px 0 16px; +} + +/* @end */ + +/* +.search { + color: #003399; + font-weight: bold; +} + +form.search { + margin-bottom: 0px; + margin-top: 0px; +} + +input.search { + font-size: 75%; + color: #000080; + font-weight: normal; + background-color: #e8eef2; +} +*/ + +td.tiny { + font-size: 75%; +} + +.dirtab { + padding: 4px; + border-collapse: collapse; + border: 1px solid #A3B4D7; +} + +th.dirtab { + background: #EBEFF6; + font-weight: bold; +} + +hr { + height: 0px; + border: none; + border-top: 1px solid #4A6AAA; +} + +hr.footer { + height: 1px; +} + +/* @group Member Descriptions */ + +table.memberdecls { + border-spacing: 0px; + padding: 0px; +} + +.memberdecls td, .fieldtable tr { + -webkit-transition-property: background-color, box-shadow; + -webkit-transition-duration: 0.5s; + -moz-transition-property: background-color, box-shadow; + -moz-transition-duration: 0.5s; + -ms-transition-property: background-color, box-shadow; + -ms-transition-duration: 0.5s; + -o-transition-property: background-color, box-shadow; + -o-transition-duration: 0.5s; + transition-property: background-color, box-shadow; + transition-duration: 0.5s; +} + +.memberdecls td.glow, .fieldtable tr.glow { + background-color: cyan; + box-shadow: 0 0 15px cyan; +} + +.mdescLeft, .mdescRight, +.memItemLeft, .memItemRight, +.memTemplItemLeft, .memTemplItemRight, .memTemplParams { + background-color: #F9FAFC; + border: none; + margin: 4px; + padding: 1px 0 0 8px; +} + +.mdescLeft, .mdescRight { + padding: 0px 8px 4px 8px; + color: #555; +} + +.memSeparator { + border-bottom: 1px solid #DEE4F0; + line-height: 1px; + margin: 0px; + padding: 0px; +} + +.memItemLeft, .memTemplItemLeft { + white-space: nowrap; +} + +.memItemRight { + width: 100%; +} + +.memTemplParams { + color: #4665A2; + white-space: nowrap; + font-size: 80%; +} + +/* @end */ + +/* @group Member Details */ + +/* Styles for detailed member documentation */ + +.memtitle { + padding: 8px; + border-top: 1px solid #A8B8D9; + border-left: 1px solid #A8B8D9; + border-right: 1px solid #A8B8D9; + border-top-right-radius: 4px; + border-top-left-radius: 4px; + margin-bottom: -1px; + background-image: url('nav_f.png'); + background-repeat: repeat-x; + background-color: #E2E8F2; + line-height: 1.25; + font-weight: 300; + float:left; +} + +.permalink +{ + font-size: 65%; + display: inline-block; + vertical-align: middle; +} + +.memtemplate { + font-size: 80%; + color: #4665A2; + font-weight: normal; + margin-left: 9px; +} + +.memnav { + background-color: #EBEFF6; + border: 1px solid #A3B4D7; + text-align: center; + margin: 2px; + margin-right: 15px; + padding: 2px; +} + +.mempage { + width: 100%; +} + +.memitem { + padding: 0; + margin-bottom: 10px; + margin-right: 5px; + -webkit-transition: box-shadow 0.5s linear; + -moz-transition: box-shadow 0.5s linear; + -ms-transition: box-shadow 0.5s linear; + -o-transition: box-shadow 0.5s linear; + transition: box-shadow 0.5s linear; + display: table !important; + width: 100%; +} + +.memitem.glow { + box-shadow: 0 0 15px cyan; +} + +.memname { + font-weight: 400; + margin-left: 6px; +} + +.memname td { + vertical-align: bottom; +} + +.memproto, dl.reflist dt { + border-top: 1px solid #A8B8D9; + border-left: 1px solid #A8B8D9; + border-right: 1px solid #A8B8D9; + padding: 6px 0px 6px 0px; + color: #253555; + font-weight: bold; + text-shadow: 0px 1px 1px rgba(255, 255, 255, 0.9); + background-color: #DFE5F1; + /* opera specific markup */ + box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15); + border-top-right-radius: 4px; + /* firefox specific markup */ + -moz-box-shadow: rgba(0, 0, 0, 0.15) 5px 5px 5px; + -moz-border-radius-topright: 4px; + /* webkit specific markup */ + -webkit-box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15); + -webkit-border-top-right-radius: 4px; + +} + +.overload { + font-family: "courier new",courier,monospace; + font-size: 65%; +} + +.memdoc, dl.reflist dd { + border-bottom: 1px solid #A8B8D9; + border-left: 1px solid #A8B8D9; + border-right: 1px solid #A8B8D9; + padding: 6px 10px 2px 10px; + background-color: #FBFCFD; + border-top-width: 0; + background-image:url('nav_g.png'); + background-repeat:repeat-x; + background-color: #FFFFFF; + /* opera specific markup */ + border-bottom-left-radius: 4px; + border-bottom-right-radius: 4px; + box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15); + /* firefox specific markup */ + -moz-border-radius-bottomleft: 4px; + -moz-border-radius-bottomright: 4px; + -moz-box-shadow: rgba(0, 0, 0, 0.15) 5px 5px 5px; + /* webkit specific markup */ + -webkit-border-bottom-left-radius: 4px; + -webkit-border-bottom-right-radius: 4px; + -webkit-box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15); +} + +dl.reflist dt { + padding: 5px; +} + +dl.reflist dd { + margin: 0px 0px 10px 0px; + padding: 5px; +} + +.paramkey { + text-align: right; +} + +.paramtype { + white-space: nowrap; +} + +.paramname { + color: #602020; + white-space: nowrap; +} +.paramname em { + font-style: normal; +} +.paramname code { + line-height: 14px; +} + +.params, .retval, .exception, .tparams { + margin-left: 0px; + padding-left: 0px; +} + +.params .paramname, .retval .paramname { + font-weight: bold; + vertical-align: top; +} + +.params .paramtype { + font-style: italic; + vertical-align: top; +} + +.params .paramdir { + font-family: "courier new",courier,monospace; + vertical-align: top; +} + +table.mlabels { + border-spacing: 0px; +} + +td.mlabels-left { + width: 100%; + padding: 0px; +} + +td.mlabels-right { + vertical-align: bottom; + padding: 0px; + white-space: nowrap; +} + +span.mlabels { + margin-left: 8px; +} + +span.mlabel { + background-color: #728DC1; + border-top:1px solid #5373B4; + border-left:1px solid #5373B4; + border-right:1px solid #C4CFE5; + border-bottom:1px solid #C4CFE5; + text-shadow: none; + color: white; + margin-right: 4px; + padding: 2px 3px; + border-radius: 3px; + font-size: 7pt; + white-space: nowrap; + vertical-align: middle; +} + + + +/* @end */ + +/* these are for tree view inside a (index) page */ + +div.directory { + margin: 10px 0px; + border-top: 1px solid #9CAFD4; + border-bottom: 1px solid #9CAFD4; + width: 100%; +} + +.directory table { + border-collapse:collapse; +} + +.directory td { + margin: 0px; + padding: 0px; + vertical-align: top; +} + +.directory td.entry { + white-space: nowrap; + padding-right: 6px; + padding-top: 3px; +} + +.directory td.entry a { + outline:none; +} + +.directory td.entry a img { + border: none; +} + +.directory td.desc { + width: 100%; + padding-left: 6px; + padding-right: 6px; + padding-top: 3px; + border-left: 1px solid rgba(0,0,0,0.05); +} + +.directory tr.even { + padding-left: 6px; + background-color: #F7F8FB; +} + +.directory img { + vertical-align: -30%; +} + +.directory .levels { + white-space: nowrap; + width: 100%; + text-align: right; + font-size: 9pt; +} + +.directory .levels span { + cursor: pointer; + padding-left: 2px; + padding-right: 2px; + color: #3D578C; +} + +.arrow { + color: #9CAFD4; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; + cursor: pointer; + font-size: 80%; + display: inline-block; + width: 16px; + height: 22px; +} + +.icon { + font-family: Arial, Helvetica; + font-weight: bold; + font-size: 12px; + height: 14px; + width: 16px; + display: inline-block; + background-color: #728DC1; + color: white; + text-align: center; + border-radius: 4px; + margin-left: 2px; + margin-right: 2px; +} + +.icona { + width: 24px; + height: 22px; + display: inline-block; +} + +.iconfopen { + width: 24px; + height: 18px; + margin-bottom: 4px; + background-image:url('folderopen.png'); + background-position: 0px -4px; + background-repeat: repeat-y; + vertical-align:top; + display: inline-block; +} + +.iconfclosed { + width: 24px; + height: 18px; + margin-bottom: 4px; + background-image:url('folderclosed.png'); + background-position: 0px -4px; + background-repeat: repeat-y; + vertical-align:top; + display: inline-block; +} + +.icondoc { + width: 24px; + height: 18px; + margin-bottom: 4px; + background-image:url('doc.png'); + background-position: 0px -4px; + background-repeat: repeat-y; + vertical-align:top; + display: inline-block; +} + +table.directory { + font: 400 14px Roboto,sans-serif; +} + +/* @end */ + +div.dynheader { + margin-top: 8px; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +address { + font-style: normal; + color: #2A3D61; +} + +table.doxtable caption { + caption-side: top; +} + +table.doxtable { + border-collapse:collapse; + margin-top: 4px; + margin-bottom: 4px; +} + +table.doxtable td, table.doxtable th { + border: 1px solid #2D4068; + padding: 3px 7px 2px; +} + +table.doxtable th { + background-color: #374F7F; + color: #FFFFFF; + font-size: 110%; + padding-bottom: 4px; + padding-top: 5px; +} + +table.fieldtable { + /*width: 100%;*/ + margin-bottom: 10px; + border: 1px solid #A8B8D9; + border-spacing: 0px; + -moz-border-radius: 4px; + -webkit-border-radius: 4px; + border-radius: 4px; + -moz-box-shadow: rgba(0, 0, 0, 0.15) 2px 2px 2px; + -webkit-box-shadow: 2px 2px 2px rgba(0, 0, 0, 0.15); + box-shadow: 2px 2px 2px rgba(0, 0, 0, 0.15); +} + +.fieldtable td, .fieldtable th { + padding: 3px 7px 2px; +} + +.fieldtable td.fieldtype, .fieldtable td.fieldname { + white-space: nowrap; + border-right: 1px solid #A8B8D9; + border-bottom: 1px solid #A8B8D9; + vertical-align: top; +} + +.fieldtable td.fieldname { + padding-top: 3px; +} + +.fieldtable td.fielddoc { + border-bottom: 1px solid #A8B8D9; + /*width: 100%;*/ +} + +.fieldtable td.fielddoc p:first-child { + margin-top: 0px; +} + +.fieldtable td.fielddoc p:last-child { + margin-bottom: 2px; +} + +.fieldtable tr:last-child td { + border-bottom: none; +} + +.fieldtable th { + background-image:url('nav_f.png'); + background-repeat:repeat-x; + background-color: #E2E8F2; + font-size: 90%; + color: #253555; + padding-bottom: 4px; + padding-top: 5px; + text-align:left; + font-weight: 400; + -moz-border-radius-topleft: 4px; + -moz-border-radius-topright: 4px; + -webkit-border-top-left-radius: 4px; + -webkit-border-top-right-radius: 4px; + border-top-left-radius: 4px; + border-top-right-radius: 4px; + border-bottom: 1px solid #A8B8D9; +} + + +.tabsearch { + top: 0px; + left: 10px; + height: 36px; + background-image: url('tab_b.png'); + z-index: 101; + overflow: hidden; + font-size: 13px; +} + +.navpath ul +{ + font-size: 11px; + background-image:url('tab_b.png'); + background-repeat:repeat-x; + background-position: 0 -5px; + height:30px; + line-height:30px; + color:#8AA0CC; + border:solid 1px #C2CDE4; + overflow:hidden; + margin:0px; + padding:0px; +} + +.navpath li +{ + list-style-type:none; + float:left; + padding-left:10px; + padding-right:15px; + background-image:url('bc_s.png'); + background-repeat:no-repeat; + background-position:right; + color:#364D7C; +} + +.navpath li.navelem a +{ + height:32px; + display:block; + text-decoration: none; + outline: none; + color: #283A5D; + font-family: 'Lucida Grande',Geneva,Helvetica,Arial,sans-serif; + text-shadow: 0px 1px 1px rgba(255, 255, 255, 0.9); + text-decoration: none; +} + +.navpath li.navelem a:hover +{ + color:#6884BD; +} + +.navpath li.footer +{ + list-style-type:none; + float:right; + padding-left:10px; + padding-right:15px; + background-image:none; + background-repeat:no-repeat; + background-position:right; + color:#364D7C; + font-size: 8pt; +} + + +div.summary +{ + float: right; + font-size: 8pt; + padding-right: 5px; + width: 50%; + text-align: right; +} + +div.summary a +{ + white-space: nowrap; +} + +table.classindex +{ + margin: 10px; + white-space: nowrap; + margin-left: 3%; + margin-right: 3%; + width: 94%; + border: 0; + border-spacing: 0; + padding: 0; +} + +div.ingroups +{ + font-size: 8pt; + width: 50%; + text-align: left; +} + +div.ingroups a +{ + white-space: nowrap; +} + +div.header +{ + background-image:url('nav_h.png'); + background-repeat:repeat-x; + background-color: #F9FAFC; + margin: 0px; + border-bottom: 1px solid #C4CFE5; +} + +div.headertitle +{ + padding: 5px 5px 5px 10px; +} + +dl +{ + padding: 0 0 0 10px; +} + +/* dl.note, dl.warning, dl.attention, dl.pre, dl.post, dl.invariant, dl.deprecated, dl.todo, dl.test, dl.bug */ +dl.section +{ + margin-left: 0px; + padding-left: 0px; +} + +dl.note +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #D0C000; +} + +dl.warning, dl.attention +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #FF0000; +} + +dl.pre, dl.post, dl.invariant +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #00D000; +} + +dl.deprecated +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #505050; +} + +dl.todo +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #00C0E0; +} + +dl.test +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #3030E0; +} + +dl.bug +{ + margin-left:-7px; + padding-left: 3px; + border-left:4px solid; + border-color: #C08050; +} + +dl.section dd { + margin-bottom: 6px; +} + + +#projectlogo +{ + text-align: center; + vertical-align: bottom; + border-collapse: separate; +} + +#projectlogo img +{ + border: 0px none; +} + +#projectalign +{ + vertical-align: middle; +} + +#projectname +{ + font: 300% Tahoma, Arial,sans-serif; + margin: 0px; + padding: 2px 0px; +} + +#projectbrief +{ + font: 120% Tahoma, Arial,sans-serif; + margin: 0px; + padding: 0px; +} + +#projectnumber +{ + font: 50% Tahoma, Arial,sans-serif; + margin: 0px; + padding: 0px; +} + +#titlearea +{ + padding: 0px; + margin: 0px; + width: 100%; + border-bottom: 1px solid #5373B4; +} + +.image +{ + text-align: center; +} + +.dotgraph +{ + text-align: center; +} + +.mscgraph +{ + text-align: center; +} + +.plantumlgraph +{ + text-align: center; +} + +.diagraph +{ + text-align: center; +} + +.caption +{ + font-weight: bold; +} + +div.zoom +{ + border: 1px solid #90A5CE; +} + +dl.citelist { + margin-bottom:50px; +} + +dl.citelist dt { + color:#334975; + float:left; + font-weight:bold; + margin-right:10px; + padding:5px; +} + +dl.citelist dd { + margin:2px 0; + padding:5px 0; +} + +div.toc { + padding: 14px 25px; + background-color: #F4F6FA; + border: 1px solid #D8DFEE; + border-radius: 7px 7px 7px 7px; + float: right; + height: auto; + margin: 0 8px 10px 10px; + width: 200px; +} + +div.toc li { + background: url("bdwn.png") no-repeat scroll 0 5px transparent; + font: 10px/1.2 Verdana,DejaVu Sans,Geneva,sans-serif; + margin-top: 5px; + padding-left: 10px; + padding-top: 2px; +} + +div.toc h3 { + font: bold 12px/1.2 Arial,FreeSans,sans-serif; + color: #4665A2; + border-bottom: 0 none; + margin: 0; +} + +div.toc ul { + list-style: none outside none; + border: medium none; + padding: 0px; +} + +div.toc li.level1 { + margin-left: 0px; +} + +div.toc li.level2 { + margin-left: 15px; +} + +div.toc li.level3 { + margin-left: 30px; +} + +div.toc li.level4 { + margin-left: 45px; +} + +.inherit_header { + font-weight: bold; + color: gray; + cursor: pointer; + -webkit-touch-callout: none; + -webkit-user-select: none; + -khtml-user-select: none; + -moz-user-select: none; + -ms-user-select: none; + user-select: none; +} + +.inherit_header td { + padding: 6px 0px 2px 5px; +} + +.inherit { + display: none; +} + +tr.heading h2 { + margin-top: 12px; + margin-bottom: 4px; +} + +/* tooltip related style info */ + +.ttc { + position: absolute; + display: none; +} + +#powerTip { + cursor: default; + white-space: nowrap; + background-color: white; + border: 1px solid gray; + border-radius: 4px 4px 4px 4px; + box-shadow: 1px 1px 7px gray; + display: none; + font-size: smaller; + max-width: 80%; + opacity: 0.9; + padding: 1ex 1em 1em; + position: absolute; + z-index: 2147483647; +} + +#powerTip div.ttdoc { + color: grey; + font-style: italic; +} + +#powerTip div.ttname a { + font-weight: bold; +} + +#powerTip div.ttname { + font-weight: bold; +} + +#powerTip div.ttdeci { + color: #006318; +} + +#powerTip div { + margin: 0px; + padding: 0px; + font: 12px/16px Roboto,sans-serif; +} + +#powerTip:before, #powerTip:after { + content: ""; + position: absolute; + margin: 0px; +} + +#powerTip.n:after, #powerTip.n:before, +#powerTip.s:after, #powerTip.s:before, +#powerTip.w:after, #powerTip.w:before, +#powerTip.e:after, #powerTip.e:before, +#powerTip.ne:after, #powerTip.ne:before, +#powerTip.se:after, #powerTip.se:before, +#powerTip.nw:after, #powerTip.nw:before, +#powerTip.sw:after, #powerTip.sw:before { + border: solid transparent; + content: " "; + height: 0; + width: 0; + position: absolute; +} + +#powerTip.n:after, #powerTip.s:after, +#powerTip.w:after, #powerTip.e:after, +#powerTip.nw:after, #powerTip.ne:after, +#powerTip.sw:after, #powerTip.se:after { + border-color: rgba(255, 255, 255, 0); +} + +#powerTip.n:before, #powerTip.s:before, +#powerTip.w:before, #powerTip.e:before, +#powerTip.nw:before, #powerTip.ne:before, +#powerTip.sw:before, #powerTip.se:before { + border-color: rgba(128, 128, 128, 0); +} + +#powerTip.n:after, #powerTip.n:before, +#powerTip.ne:after, #powerTip.ne:before, +#powerTip.nw:after, #powerTip.nw:before { + top: 100%; +} + +#powerTip.n:after, #powerTip.ne:after, #powerTip.nw:after { + border-top-color: #ffffff; + border-width: 10px; + margin: 0px -10px; +} +#powerTip.n:before { + border-top-color: #808080; + border-width: 11px; + margin: 0px -11px; +} +#powerTip.n:after, #powerTip.n:before { + left: 50%; +} + +#powerTip.nw:after, #powerTip.nw:before { + right: 14px; +} + +#powerTip.ne:after, #powerTip.ne:before { + left: 14px; +} + +#powerTip.s:after, #powerTip.s:before, +#powerTip.se:after, #powerTip.se:before, +#powerTip.sw:after, #powerTip.sw:before { + bottom: 100%; +} + +#powerTip.s:after, #powerTip.se:after, #powerTip.sw:after { + border-bottom-color: #ffffff; + border-width: 10px; + margin: 0px -10px; +} + +#powerTip.s:before, #powerTip.se:before, #powerTip.sw:before { + border-bottom-color: #808080; + border-width: 11px; + margin: 0px -11px; +} + +#powerTip.s:after, #powerTip.s:before { + left: 50%; +} + +#powerTip.sw:after, #powerTip.sw:before { + right: 14px; +} + +#powerTip.se:after, #powerTip.se:before { + left: 14px; +} + +#powerTip.e:after, #powerTip.e:before { + left: 100%; +} +#powerTip.e:after { + border-left-color: #ffffff; + border-width: 10px; + top: 50%; + margin-top: -10px; +} +#powerTip.e:before { + border-left-color: #808080; + border-width: 11px; + top: 50%; + margin-top: -11px; +} + +#powerTip.w:after, #powerTip.w:before { + right: 100%; +} +#powerTip.w:after { + border-right-color: #ffffff; + border-width: 10px; + top: 50%; + margin-top: -10px; +} +#powerTip.w:before { + border-right-color: #808080; + border-width: 11px; + top: 50%; + margin-top: -11px; +} + +@media print +{ + #top { display: none; } + #side-nav { display: none; } + #nav-path { display: none; } + body { overflow:visible; } + h1, h2, h3, h4, h5, h6 { page-break-after: avoid; } + .summary { display: none; } + .memitem { page-break-inside: avoid; } + #doc-content + { + margin-left:0 !important; + height:auto !important; + width:auto !important; + overflow:inherit; + display:inline; + } +} + +/* @group Markdown */ + +/* +table.markdownTable { + border-collapse:collapse; + margin-top: 4px; + margin-bottom: 4px; +} + +table.markdownTable td, table.markdownTable th { + border: 1px solid #2D4068; + padding: 3px 7px 2px; +} + +table.markdownTableHead tr { +} + +table.markdownTableBodyLeft td, table.markdownTable th { + border: 1px solid #2D4068; + padding: 3px 7px 2px; +} + +th.markdownTableHeadLeft th.markdownTableHeadRight th.markdownTableHeadCenter th.markdownTableHeadNone { + background-color: #374F7F; + color: #FFFFFF; + font-size: 110%; + padding-bottom: 4px; + padding-top: 5px; +} + +th.markdownTableHeadLeft { + text-align: left +} + +th.markdownTableHeadRight { + text-align: right +} + +th.markdownTableHeadCenter { + text-align: center +} +*/ + +table.markdownTable { + border-collapse:collapse; + margin-top: 4px; + margin-bottom: 4px; +} + +table.markdownTable td, table.markdownTable th { + border: 1px solid #2D4068; + padding: 3px 7px 2px; +} + +table.markdownTable tr { +} + +th.markdownTableHeadLeft, th.markdownTableHeadRight, th.markdownTableHeadCenter, th.markdownTableHeadNone { + background-color: #374F7F; 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+ var summary = $('#'+base+'-summary'); + var content = $('#'+base+'-content'); + var trigger = $('#'+base+'-trigger'); + var src=$(trigger).attr('src'); + if (content.is(':visible')===true) { + content.hide(); + summary.show(); + $(linkObj).addClass('closed').removeClass('opened'); + $(trigger).attr('src',src.substring(0,src.length-8)+'closed.png'); + } else { + content.show(); + summary.hide(); + $(linkObj).removeClass('closed').addClass('opened'); + $(trigger).attr('src',src.substring(0,src.length-10)+'open.png'); + } + return false; +} + +function updateStripes() +{ + $('table.directory tr'). + removeClass('even').filter(':visible:even').addClass('even'); +} + +function toggleLevel(level) +{ + $('table.directory tr').each(function() { + var l = this.id.split('_').length-1; + var i = $('#img'+this.id.substring(3)); + var a = $('#arr'+this.id.substring(3)); + if (l 1) { + var toc = $("#side-nav").append(''); + toc = $("#nav-toc"); + var footerHeight = footer.height(); + toc = toc.append('
    '); + toc = toc.find('ul'); + var indices = new Array(); + indices[0] = 0; + indices[1] = 0; + + var h1counts = $("h1").length; + headers.each(function(i) { + var current = $(this); + var levelTag = current[0].tagName.charAt(1); + if(h1counts==0) + levelTag--; + var cur_id = current.attr("id"); + + indices[levelTag-1]+=1; + var prefix = indices[0]; + if (levelTag >1) { + prefix+="."+indices[1]; + } + + // Uncomment to add number prefixes + // current.html(prefix + " " + current.html()); + for(var l = levelTag; l < 2; ++l){ + indices[l] = 0; + } + + if(cur_id == undefined) { + current.attr('id', 'title' + i); + current.addClass('anchor'); + toc.append("
  • " + current.text() + "
    • "); + } else { + toc.append("
  • " + current.text() + "
    • "); + } + }); + resizeHeight(); + } +} + + +var global_navtree_object; + +// Overloaded to remove links to sections/subsections +function getNode(o, po) +{ + po.childrenVisited = true; + var l = po.childrenData.length-1; + for (var i in po.childrenData) { + var nodeData = po.childrenData[i]; + if((!nodeData[1]) || (nodeData[1].indexOf('#')==-1)) // <- we added this line + po.children[i] = newNode(o, po, nodeData[0], nodeData[1], nodeData[2], i==l); + } +} + +// Overloaded to adjust the size of the navtree wrt the toc +function resizeHeight() +{ + var toc = $("#nav-toc"); + var tocHeight = toc.height(); // <- we added this line + var headerHeight = header.height(); + var footerHeight = footer.height(); + var windowHeight = $(window).height() - headerHeight - footerHeight; + content.css({height:windowHeight + "px"}); + navtree.css({height:(windowHeight-tocHeight) + "px"}); // <- we modified this line + sidenav.css({height:(windowHeight) + "px",top: headerHeight+"px"}); +} + +// Overloaded to save the root node into global_navtree_object +function initNavTree(toroot,relpath) +{ + var o = new Object(); + global_navtree_object = o; // <- we added this line + o.toroot = toroot; + o.node = new Object(); + o.node.li = document.getElementById("nav-tree-contents"); + o.node.childrenData = NAVTREE; + o.node.children = new Array(); + o.node.childrenUL = document.createElement("ul"); + o.node.getChildrenUL = function() { return o.node.childrenUL; }; + o.node.li.appendChild(o.node.childrenUL); + o.node.depth = 0; + o.node.relpath = relpath; + o.node.expanded = false; + o.node.isLast = true; + o.node.plus_img = document.createElement("span"); + o.node.plus_img.className = 'arrow'; + o.node.plus_img.innerHTML = arrowRight; + + if (localStorageSupported()) { + var navSync = $('#nav-sync'); + if (cachedLink()) { + showSyncOff(navSync,relpath); + navSync.removeClass('sync'); + } else { + showSyncOn(navSync,relpath); + } + navSync.click(function(){ toggleSyncButton(relpath); }); + } + + navTo(o,toroot,window.location.hash,relpath); + + $(window).bind('hashchange', function(){ + if (window.location.hash && window.location.hash.length>1){ + var a; + if ($(location).attr('hash')){ + var clslink=stripPath($(location).attr('pathname'))+':'+ + $(location).attr('hash').substring(1); + a=$('.item a[class$="'+clslink+'"]'); + } + if (a==null || !$(a).parent().parent().hasClass('selected')){ + $('.item').removeClass('selected'); + $('.item').removeAttr('id'); + } + var link=stripPath2($(location).attr('pathname')); + navTo(o,link,$(location).attr('hash'),relpath); + } else if (!animationInProgress) { + $('#doc-content').scrollTop(0); + $('.item').removeClass('selected'); + $('.item').removeAttr('id'); + navTo(o,toroot,window.location.hash,relpath); + } + }) + + $(window).load(showRoot); +} + +// return false if the the node has no children at all, or has only section/subsection children +function checkChildrenData(node) { + if (!(typeof(node.childrenData)==='string')) { + for (var i in node.childrenData) { + var url = node.childrenData[i][1]; + if(url.indexOf("#")==-1) + return true; + } + return false; + } + return (node.childrenData); +} + +// Modified to: +// 1 - remove the root node +// 2 - remove the section/subsection children +function createIndent(o,domNode,node,level) +{ + var level=-2; // <- we replaced level=-1 by level=-2 + var n = node; + while (n.parentNode) { level++; n=n.parentNode; } + if (checkChildrenData(node)) { // <- we modified this line to use checkChildrenData(node) instead of node.childrenData + var imgNode = document.createElement("span"); + imgNode.className = 'arrow'; + imgNode.style.paddingLeft=(16*level).toString()+'px'; + imgNode.innerHTML = arrowRight; + + node.plus_img = imgNode; + node.expandToggle = document.createElement("a"); + node.expandToggle.href = "javascript:void(0)"; + node.expandToggle.onclick = function() { + if (node.expanded) { + $(node.getChildrenUL()).slideUp("fast"); + node.plus_img.innerHTML = arrowRight; + node.expanded = false; + } else { + expandNode(o, node, false, false); + } + } + node.expandToggle.appendChild(imgNode); + domNode.appendChild(node.expandToggle); + } else { + var span = document.createElement("span"); + span.className = 'arrow'; + span.style.width = 16*(level+1)+'px'; + span.innerHTML = ' '; + domNode.appendChild(span); + } +} + +// Overloaded to automatically expand the selected node +function selectAndHighlight(hash,n) +{ + var a; + if (hash) { + var link=stripPath($(location).attr('pathname'))+':'+hash.substring(1); + a=$('.item a[class$="'+link+'"]'); + } + if (a && a.length) { + a.parent().parent().addClass('selected'); + a.parent().parent().attr('id','selected'); + highlightAnchor(); + } else if (n) { + $(n.itemDiv).addClass('selected'); + $(n.itemDiv).attr('id','selected'); + } + if ($('#nav-tree-contents .item:first').hasClass('selected')) { + $('#nav-sync').css('top','30px'); + } else { + $('#nav-sync').css('top','5px'); + } + expandNode(global_navtree_object, n, true, true); // <- we added this line + showRoot(); +} + + +$(document).ready(function() { + + (function (){ // wait until the first "selected" element has been created + try { + + // this line will triger an exception if there is no #selected element, i.e., before the tree structure is complete. + document.getElementById("selected").className = "item selected"; + + // ok, the default tree has been created, we can keep going... + + // we want to expand the function list by default + expandNode(global_navtree_object, global_navtree_object.node.children[0].children[0], true, true); + + // Hide the root node "MADlib" + // $(document.getElementsByClassName('index.html')[0]).parent().parent().css({display:"none"}); + + // Hide the "modules" node + $(document.getElementsByClassName('modules.html')[0]).parent().parent().css({display:"none"}); + + } catch (err) { + setTimeout(arguments.callee, 10); + } + })(); +}); diff --git a/docs/docs/v2.1.0/elastic__net_8sql__in.html b/docs/docs/v2.1.0/elastic__net_8sql__in.html new file mode 100644 index 00000000..fa42d0f3 --- /dev/null +++ b/docs/docs/v2.1.0/elastic__net_8sql__in.html @@ -0,0 +1,2467 @@ + + + + + + + + +MADlib: elastic_net.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    elastic_net.sql_in File Reference
    +
    +
    + +

    SQL functions for elastic net regularization. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    void elastic_net_train (text tbl_source, text tbl_result, text col_dep_var, text col_ind_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardize, text grouping_col, text optimizer, text optimizer_params, text excluded, integer max_iter, float8 tolerance)
     Interface for elastic net. More...
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardization, text grouping_columns, text optimizer, text optimizer_params, text excluded, integer max_iter)
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardization, text grouping_columns, text optimizer, text optimizer_params, text excluded)
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardization, text grouping_columns, text optimizer, text optimizer_params)
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardization, text grouping_columns, text optimizer)
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardization, text grouping_columns)
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value, boolean standardization)
     
    void elastic_net_train (text tbl_source, text tbl_result, text col_ind_var, text col_dep_var, text regress_family, float8 alpha, float8 lambda_value)
     
    text elastic_net_train ()
     Help function, to print out the supported families. More...
     
    text elastic_net_train (text family_or_optimizer)
     Help function, to print out the supported optimizer for a family or print out the parameter list for an optimizer. More...
     
    void elastic_net_predict (text tbl_model, text tbl_new_source, text col_id, text tbl_predict)
     Prediction and put the result in a table can be used together with General-CV. More...
     
    float8 elastic_net_predict (text regress_family, float8[] coefficients, float8 intercept, float8[] ind_var)
     Prediction use learned coefficients for a given example. More...
     
    float8 elastic_net_gaussian_predict (float8[] coefficients, float8 intercept, float8[] ind_var)
     Prediction for linear models use learned coefficients for a given example. More...
     
    boolean elastic_net_binomial_predict (float8[] coefficients, float8 intercept, float8[] ind_var)
     Prediction for logistic models use learned coefficients for a given example. More...
     
    float8 elastic_net_binomial_prob (float8[] coefficients, float8 intercept, float8[] ind_var)
     Compute the probability of belonging to the True class for a given observation. More...
     
    float8 __elastic_net_binomial_loglikelihood (float8[] coefficients, float8 intercept, boolean dep_var, float8[] ind_var)
     
    float8 [] __gaussian_igd_transition (float8[] state, float8[] ind_var, float8 dep_var, float8[] pre_state, float8 lambda, float8 alpha, integer dimension, float8 stepsize, integer total_rows, float8[] xmean, float8 ymean, float8 step_decay)
     
    float8 [] __gaussian_igd_merge (float8[] state1, float8[] state2)
     
    float8 [] __gaussian_igd_final (float8[] state)
     
    aggregate float8 [] __gaussian_igd_step (float8[], float8, float8[], float8, float8, integer, float8, integer, float8[], float8, float8)
     
    aggregate float8 [] __gaussian_igd_step_single_seg (float8[], float8, float8[], float8, float8, integer, float8, integer, float8[], float8, float8)
     
    float8 __gaussian_igd_state_diff (float8[] state1, float8[] state2)
     
    __elastic_net_result __gaussian_igd_result (float8[] in_state, float8[] feature_sq, float8 threshold, float8 tolerance)
     
    float8 [] __gaussian_fista_transition (float8[] state, float8[] ind_var, float8 dep_var, float8[] pre_state, float8 lambda, float8 alpha, integer dimension, integer total_rows, float8 max_stepsize, float8 eta, integer use_active_set, integer is_active, integer random_stepsize)
     
    float8 [] __gaussian_fista_merge (float8[] state1, float8[] state2)
     
    float8 [] __gaussian_fista_final (float8[] state)
     
    aggregate float8 [] __gaussian_fista_step (float8[], float8, float8[], float8, float8, integer, integer, float8, float8, integer, integer, integer)
     
    float8 __gaussian_fista_state_diff (float8[] state1, float8[] state2)
     
    __elastic_net_result __gaussian_fista_result (float8[] in_state)
     
    float8 [] __binomial_igd_transition (float8[] state, float8[] ind_var, boolean dep_var, float8[] pre_state, float8 lambda, float8 alpha, integer dimension, float8 stepsize, integer total_rows, float8[] xmean, float8 ymean, float8 step_decay)
     
    float8 [] __binomial_igd_merge (float8[] state1, float8[] state2)
     
    float8 [] __binomial_igd_final (float8[] state)
     
    aggregate float8 [] __binomial_igd_step (float8[], boolean, float8[], float8, float8, integer, float8, integer, float8[], float8, float8)
     
    aggregate float8 [] __binomial_igd_step_single_seg (float8[], boolean, float8[], float8, float8, integer, float8, integer, float8[], float8, float8)
     
    float8 __binomial_igd_state_diff (float8[] state1, float8[] state2)
     
    __elastic_net_result __binomial_igd_result (float8[] in_state, float8[] feature_sq, float8 threshold, float8 tolerance)
     
    float8 [] __binomial_fista_transition (float8[] state, float8[] ind_var, boolean dep_var, float8[] pre_state, float8 lambda, float8 alpha, integer dimension, integer total_rows, float8 max_stepsize, float8 eta, integer use_active_set, integer is_active, integer random_stepsize)
     
    float8 [] __binomial_fista_merge (float8[] state1, float8[] state2)
     
    float8 [] __binomial_fista_final (float8[] state)
     
    aggregate float8 [] __binomial_fista_step (float8[], boolean, float8[], float8, float8, integer, integer, float8, float8, integer, integer, integer)
     
    float8 __binomial_fista_state_diff (float8[] state1, float8[] state2)
     
    __elastic_net_result __binomial_fista_result (float8[] in_state)
     
    +

    Detailed Description

    +
    Date
    July 2012
    +
    See also
    For a brief introduction to elastic net, see the module description Elastic Net Regularization.
    +

    Function Documentation

    + +

    ◆ __binomial_fista_final()

    + +
    +
    + + + + + + + + +
    float8 [] __binomial_fista_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __binomial_fista_merge()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __binomial_fista_merge (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __binomial_fista_result()

    + +
    +
    + + + + + + + + +
    __elastic_net_result __binomial_fista_result (float8 [] in_state)
    +
    + +
    +
    + +

    ◆ __binomial_fista_state_diff()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 __binomial_fista_state_diff (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __binomial_fista_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __binomial_fista_step (float8 [],
    boolean ,
    float8 [],
    float8 ,
    float8 ,
    integer ,
    integer ,
    float8 ,
    float8 ,
    integer ,
    integer ,
    integer  
    )
    +
    + +
    +
    + +

    ◆ __binomial_fista_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __binomial_fista_transition (float8 [] state,
    float8 [] ind_var,
    boolean dep_var,
    float8 [] pre_state,
    float8 lambda,
    float8 alpha,
    integer dimension,
    integer total_rows,
    float8 max_stepsize,
    float8 eta,
    integer use_active_set,
    integer is_active,
    integer random_stepsize 
    )
    +
    + +
    +
    + +

    ◆ __binomial_igd_final()

    + +
    +
    + + + + + + + + +
    float8 [] __binomial_igd_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __binomial_igd_merge()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __binomial_igd_merge (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __binomial_igd_result()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    __elastic_net_result __binomial_igd_result (float8 [] in_state,
    float8 [] feature_sq,
    float8 threshold,
    float8 tolerance 
    )
    +
    + +
    +
    + +

    ◆ __binomial_igd_state_diff()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 __binomial_igd_state_diff (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __binomial_igd_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __binomial_igd_step (float8 [],
    boolean ,
    float8 [],
    float8 ,
    float8 ,
    integer ,
    float8 ,
    integer ,
    float8 [],
    float8 ,
    float8  
    )
    +
    + +
    +
    + +

    ◆ __binomial_igd_step_single_seg()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __binomial_igd_step_single_seg (float8 [],
    boolean ,
    float8 [],
    float8 ,
    float8 ,
    integer ,
    float8 ,
    integer ,
    float8 [],
    float8 ,
    float8  
    )
    +
    + +
    +
    + +

    ◆ __binomial_igd_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __binomial_igd_transition (float8 [] state,
    float8 [] ind_var,
    boolean dep_var,
    float8 [] pre_state,
    float8 lambda,
    float8 alpha,
    integer dimension,
    float8 stepsize,
    integer total_rows,
    float8 [] xmean,
    float8 ymean,
    float8 step_decay 
    )
    +
    + +
    +
    + +

    ◆ __elastic_net_binomial_loglikelihood()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 __elastic_net_binomial_loglikelihood (float8 [] coefficients,
    float8 intercept,
    boolean dep_var,
    float8 [] ind_var 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_fista_final()

    + +
    +
    + + + + + + + + +
    float8 [] __gaussian_fista_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __gaussian_fista_merge()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __gaussian_fista_merge (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_fista_result()

    + +
    +
    + + + + + + + + +
    __elastic_net_result __gaussian_fista_result (float8 [] in_state)
    +
    + +
    +
    + +

    ◆ __gaussian_fista_state_diff()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 __gaussian_fista_state_diff (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_fista_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __gaussian_fista_step (float8 [],
    float8 ,
    float8 [],
    float8 ,
    float8 ,
    integer ,
    integer ,
    float8 ,
    float8 ,
    integer ,
    integer ,
    integer  
    )
    +
    + +
    +
    + +

    ◆ __gaussian_fista_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __gaussian_fista_transition (float8 [] state,
    float8 [] ind_var,
    float8 dep_var,
    float8 [] pre_state,
    float8 lambda,
    float8 alpha,
    integer dimension,
    integer total_rows,
    float8 max_stepsize,
    float8 eta,
    integer use_active_set,
    integer is_active,
    integer random_stepsize 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_igd_final()

    + +
    +
    + + + + + + + + +
    float8 [] __gaussian_igd_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __gaussian_igd_merge()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __gaussian_igd_merge (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_igd_result()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    __elastic_net_result __gaussian_igd_result (float8 [] in_state,
    float8 [] feature_sq,
    float8 threshold,
    float8 tolerance 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_igd_state_diff()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 __gaussian_igd_state_diff (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __gaussian_igd_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __gaussian_igd_step (float8 [],
    float8 ,
    float8 [],
    float8 ,
    float8 ,
    integer ,
    float8 ,
    integer ,
    float8 [],
    float8 ,
    float8  
    )
    +
    + +
    +
    + +

    ◆ __gaussian_igd_step_single_seg()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __gaussian_igd_step_single_seg (float8 [],
    float8 ,
    float8 [],
    float8 ,
    float8 ,
    integer ,
    float8 ,
    integer ,
    float8 [],
    float8 ,
    float8  
    )
    +
    + +
    +
    + +

    ◆ __gaussian_igd_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __gaussian_igd_transition (float8 [] state,
    float8 [] ind_var,
    float8 dep_var,
    float8 [] pre_state,
    float8 lambda,
    float8 alpha,
    integer dimension,
    float8 stepsize,
    integer total_rows,
    float8 [] xmean,
    float8 ymean,
    float8 step_decay 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_binomial_predict()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    boolean elastic_net_binomial_predict (float8 [] coefficients,
    float8 intercept,
    float8 [] ind_var 
    )
    +
    +
    Parameters
    + + + + +
    coefficientsLogistic fitting coefficients
    interceptLogistic fitting intercept
    ind_varFeatures (independent variables)
    +
    +
    +

    returns a boolean value

    + +
    +
    + +

    ◆ elastic_net_binomial_prob()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 elastic_net_binomial_prob (float8 [] coefficients,
    float8 intercept,
    float8 [] ind_var 
    )
    +
    +
    Parameters
    + + + + +
    coefficientsLogistic fitting coefficients
    interceptLogistic fitting intercept
    ind_varFeatures (independent variables)
    +
    +
    +

    returns a double value, which is the probability of this data point being True class

    + +
    +
    + +

    ◆ elastic_net_gaussian_predict()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 elastic_net_gaussian_predict (float8 [] coefficients,
    float8 intercept,
    float8 [] ind_var 
    )
    +
    +
    Parameters
    + + + + +
    coefficientsLinear fitting coefficients
    interceptLinear fitting intercept
    ind_varFeatures (independent variables)
    +
    +
    +

    returns a double value

    + +
    +
    + +

    ◆ elastic_net_predict() [1/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_predict (text tbl_model,
    text tbl_new_source,
    text col_id,
    text tbl_predict 
    )
    +
    +
    Parameters
    + + + + + +
    tbl_modelThe result from elastic_net_train
    tbl_new_sourceData table
    col_idUnique ID associated with each row
    tbl_predictPrediction result
    +
    +
    + +
    +
    + +

    ◆ elastic_net_predict() [2/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 elastic_net_predict (text regress_family,
    float8 [] coefficients,
    float8 intercept,
    float8 [] ind_var 
    )
    +
    +
    Parameters
    + + + + + +
    regress_familymodel family
    coefficientsThe fitting coefficients
    interceptThe fitting intercept
    ind_varFeatures (independent variables)
    +
    +
    +
    Returns
    float8
    +

    Note: Please use function elastic_net_gaussian_predict() or elastic_net_binomial_predict() instead if you could. This may be deprecated in the future, as users are confused between this function and the table function with the same name.

    +

    When regress_family is 'binomial' or 'logistic', this function returns 1 for True and 0 for False

    + +
    +
    + +

    ◆ elastic_net_train() [1/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_dep_var,
    text col_ind_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardize,
    text grouping_col,
    text optimizer,
    text optimizer_params,
    text excluded,
    integer max_iter,
    float8 tolerance 
    )
    +
    +
    Parameters
    + + + + + + + + + + + + + + + +
    tbl_sourceName of data source table
    tbl_resultName of the table to store the results
    col_ind_varName of independent variable column, independent variable is an array
    col_dep_varName of dependent variable column
    regress_familyResponse type (gaussian or binomial)
    alphaThe elastic net parameter, [0, 1]
    lambda_valueThe regularization parameter
    standardizeWhether to normalize the variables (default True)
    grouping_colList of columns on which to apply grouping (currently only a placeholder)
    optimizerThe optimization algorithm, 'fista' or 'igd'. Default is 'fista'
    optimizer_paramsParameters of the above optimizer, the format is 'arg = value, ...'. Default is NULL
    excludedWhich columns to exclude? Default is NULL (applicable only if col_ind_var is set as * or a column of array, column names as 'col1, col2, ...' if col_ind_var is '*'; element indices as '1,2,3, ...' if col_ind_var is a column of array)
    max_iterMaximum number of iterations to run the algorithm (default value of 1000)
    toleranceIteration stopping criteria. Default is 1e-6
    +
    +
    + +
    +
    + +

    ◆ elastic_net_train() [2/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardization,
    text grouping_columns,
    text optimizer,
    text optimizer_params,
    text excluded,
    integer max_iter 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [3/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardization,
    text grouping_columns,
    text optimizer,
    text optimizer_params,
    text excluded 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [4/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardization,
    text grouping_columns,
    text optimizer,
    text optimizer_params 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [5/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardization,
    text grouping_columns,
    text optimizer 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [6/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardization,
    text grouping_columns 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [7/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value,
    boolean standardization 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [8/10]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void elastic_net_train (text tbl_source,
    text tbl_result,
    text col_ind_var,
    text col_dep_var,
    text regress_family,
    float8 alpha,
    float8 lambda_value 
    )
    +
    + +
    +
    + +

    ◆ elastic_net_train() [9/10]

    + +
    +
    + + + + + + + +
    text elastic_net_train ()
    +
    + +
    +
    + +

    ◆ elastic_net_train() [10/10]

    + +
    +
    + + + + + + + + +
    text elastic_net_train (text family_or_optimizer)
    +
    +
    Parameters
    + + +
    family_or_optimizerResponse type, 'gaussian' or 'binomial', or optimizer type
    +
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/encode__categorical_8sql__in.html b/docs/docs/v2.1.0/encode__categorical_8sql__in.html new file mode 100644 index 00000000..031f1b99 --- /dev/null +++ b/docs/docs/v2.1.0/encode__categorical_8sql__in.html @@ -0,0 +1,733 @@ + + + + + + + + +MADlib: encode_categorical.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    encode_categorical.sql_in File Reference
    +
    +
    + +

    SQL functions for encoding categorical variables to numerical values. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id, varchar top, varchar value_to_drop, boolean encode_null, varchar output_type, boolean output_dictionary, varchar distributed_by)
     Encode categorical columns using either one-hot encoding or dummy coding. More...
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id, varchar top, varchar value_to_drop, boolean encode_null, varchar output_type, boolean output_dictionary)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id, varchar top, varchar value_to_drop, boolean encode_null, varchar output_type)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id, varchar top, varchar value_to_drop, boolean encode_null)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id, varchar top, varchar value_to_drop)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id, varchar top)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude, varchar row_id)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols, varchar categorical_cols_to_exclude)
     
    void encode_categorical_variables (varchar source_table, varchar output_table, varchar categorical_cols)
     
    varchar encode_categorical_variables (varchar message)
     
    varchar encode_categorical_variables ()
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    Dec 2016
    +
    See also
    Encodes categorical variables to numerical values
    +

    Function Documentation

    + +

    ◆ encode_categorical_variables() [1/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id,
    varchar top,
    varchar value_to_drop,
    boolean encode_null,
    varchar output_type,
    boolean output_dictionary,
    varchar distributed_by 
    )
    +
    +
    Parameters
    + + + + + + + + + + + + +
    source_tableName of table containing categorical variable
    output_tableName of table to output dummy variables
    categorical_colsComma-separated list of column names to dummy code (can be '*')
    categorical_cols_to_excludeComma-separated list of column names to exclude (if categorical_cols = '*')
    row_idColumns from source table to index output table
    topParameter to include only top values of a categorical variable
    value_to_dropParameter to set reference column in dummy coding
    encode_nullBoolean to determine the behavior for rows with NULL value
    output_typeParameter to set output data type: 'column', 'array' or 'svec'
    output_dictionaryBoolean to simplify column naming and with a separate mapping table to actual values
    distributed_byComma-separated list of column names to use for distribution of output
    +
    +
    +
    Returns
    Void
    + +
    +
    + +

    ◆ encode_categorical_variables() [2/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id,
    varchar top,
    varchar value_to_drop,
    boolean encode_null,
    varchar output_type,
    boolean output_dictionary 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [3/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id,
    varchar top,
    varchar value_to_drop,
    boolean encode_null,
    varchar output_type 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [4/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id,
    varchar top,
    varchar value_to_drop,
    boolean encode_null 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [5/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id,
    varchar top,
    varchar value_to_drop 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [6/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id,
    varchar top 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [7/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude,
    varchar row_id 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [8/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols,
    varchar categorical_cols_to_exclude 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [9/11]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    void encode_categorical_variables (varchar source_table,
    varchar output_table,
    varchar categorical_cols 
    )
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [10/11]

    + +
    +
    + + + + + + + + +
    varchar encode_categorical_variables (varchar message)
    +
    + +
    +
    + +

    ◆ encode_categorical_variables() [11/11]

    + +
    +
    + + + + + + + +
    varchar encode_categorical_variables ()
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/example/madlib_pagerank_example.sql b/docs/docs/v2.1.0/example/madlib_pagerank_example.sql new file mode 100644 index 00000000..a1369c46 --- /dev/null +++ b/docs/docs/v2.1.0/example/madlib_pagerank_example.sql @@ -0,0 +1,172 @@ +/* ----------------------------------------------------------------------- *//** + * + * Licensed to the Apache Software Foundation (ASF) under one + * or more contributor license agreements. See the NOTICE file + * distributed with this work for additional information + * regarding copyright ownership. The ASF licenses this file + * to you under the Apache License, Version 2.0 (the + * "License"); you may not use this file except in compliance + * with the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, + * software distributed under the License is distributed on an + * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + * KIND, either express or implied. See the License for the + * specific language governing permissions and limitations + * under the License. + * + *//* ----------------------------------------------------------------------- */ + +DROP TABLE IF EXISTS vertex, edge; +CREATE TABLE vertex( + node_id INTEGER + ); +CREATE TABLE edge( + conn_src INTEGER, + conn_dest INTEGER, + user_id INTEGER +); +INSERT INTO vertex VALUES +(0), +(1), +(2), +(3), +(4), +(5), +(6); +INSERT INTO edge VALUES +(0, 1, 1), +(0, 2, 1), +(0, 4, 1), +(1, 2, 1), +(1, 3, 1), +(2, 3, 1), +(2, 5, 1), +(2, 6, 1), +(3, 0, 1), +(4, 0, 1), +(5, 6, 1), +(6, 3, 1), +(0, 1, 2), +(0, 2, 2), +(0, 4, 2), +(1, 2, 2), +(1, 3, 2), +(2, 3, 2), +(3, 0, 2), +(4, 0, 2), +(5, 6, 2), +(6, 3, 2); + +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary; +SELECT madlib.pagerank( + 'vertex', -- Vertex table + 'node_id', -- Vertex id column + 'edge', -- Edge table + 'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments + 'pagerank_out'); -- Output table of PageRank +SELECT * FROM pagerank_out ORDER BY pagerank DESC; + +SELECT * FROM pagerank_out_summary; + +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary; +SELECT madlib.pagerank( + 'vertex', -- Vertex table + 'node_id', -- Vertex id column + 'edge', -- Edge table + 'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments + 'pagerank_out', -- Output table of PageRank + 0.5); -- Damping factor +SELECT * FROM pagerank_out ORDER BY pagerank DESC; + +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary; +SELECT madlib.pagerank( + 'vertex', -- Vertex table + 'node_id', -- Vertex id column + 'edge', -- Edge table + 'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments + 'pagerank_out', -- Output table of PageRank + NULL, -- Default damping factor (0.85) + NULL, -- Default max iters (100) + 0.00000001, -- Threshold + 'user_id'); -- Grouping column name +SELECT * FROM pagerank_out ORDER BY user_id, pagerank DESC; + +SELECT * FROM pagerank_out_summary ORDER BY user_id; + +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary; +SELECT madlib.pagerank( + 'vertex', -- Vertex table + 'node_id', -- Vertex id column + 'edge', -- Edge table + 'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments + 'pagerank_out', -- Output table of PageRank + NULL, -- Default damping factor (0.85) + NULL, -- Default max iters (100) + NULL, -- Default Threshold + NULL, -- No Grouping + '{2,4}'); -- Personalization vertices +SELECT * FROM pagerank_out ORDER BY pagerank DESC; +SELECT * FROM pagerank_out_summary; + +DROP TABLE IF EXISTS vertex_multicol_pagerank, edge_multicol_pagerank; +CREATE TABLE vertex_multicol_pagerank( + node_id_major BIGINT, + node_id_minor BIGINT +); +CREATE TABLE edge_multicol_pagerank( + conn_src_major BIGINT, + conn_dest_major BIGINT, + user_id_major BIGINT, + conn_src_minor BIGINT, + conn_dest_minor BIGINT, + user_id_minor BIGINT +); +INSERT INTO vertex_multicol_pagerank VALUES +(0, 0), +(1, 1), +(2, 2), +(3, 3), +(4, 4), +(5, 5), +(6, 6); +INSERT INTO edge_multicol_pagerank VALUES +(0, 1, 1, 0, 1, 1), +(0, 2, 1, 0, 2, 1), +(0, 4, 1, 0, 4, 1), +(1, 2, 1, 1, 2, 1), +(1, 3, 1, 1, 3, 1), +(2, 3, 1, 2, 3, 1), +(2, 5, 1, 2, 5, 1), +(2, 6, 1, 2, 6, 1), +(3, 0, 1, 3, 0, 1), +(4, 0, 1, 4, 0, 1), +(5, 6, 1, 5, 6, 1), +(6, 3, 1, 6, 3, 1), +(0, 1, 2, 0, 1, 2), +(0, 2, 2, 0, 2, 2), +(0, 4, 2, 0, 4, 2), +(1, 2, 2, 1, 2, 2), +(1, 3, 2, 1, 3, 2), +(2, 3, 2, 2, 3, 2), +(3, 0, 2, 3, 0, 2), +(4, 0, 2, 4, 0, 2), +(5, 6, 2, 5, 6, 2), +(6, 3, 2, 6, 3, 2); + +DROP TABLE IF EXISTS pagerank_multicol_out, pagerank_multicol_out_summary; +SELECT madlib.pagerank( + 'vertex_multicol_pagerank', -- Vertex table + '[node_id_major,node_id_minor]', -- Vertex id column + 'edge_multicol_pagerank', -- Edge table + 'src=[conn_src_major,conn_src_minor], dest=[conn_dest_major,conn_dest_minor]', -- Comma delimted string of edge arguments + 'pagerank_multicol_out', -- Output table of PageRank + NULL, -- Default damping factor (0.85) + NULL, -- Default max iters (100) + NULL, -- Default Threshold + 'user_id_major,user_id_minor', -- Grouping Columns + '{{2,2},{4,4}}'); -- Personalization vertices +SELECT * FROM pagerank_multicol_out ORDER BY pagerank DESC; +SELECT * FROM pagerank_multicol_out_summary; diff --git a/docs/docs/v2.1.0/example/madlib_wcc_example.sql b/docs/docs/v2.1.0/example/madlib_wcc_example.sql new file mode 100644 index 00000000..9aadb0a9 --- /dev/null +++ b/docs/docs/v2.1.0/example/madlib_wcc_example.sql @@ -0,0 +1,170 @@ +/* ----------------------------------------------------------------------- *//** + * + * Licensed to the Apache Software Foundation (ASF) under one + * or more contributor license agreements. See the NOTICE file + * distributed with this work for additional information + * regarding copyright ownership. The ASF licenses this file + * to you under the Apache License, Version 2.0 (the + * "License"); you may not use this file except in compliance + * with the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, + * software distributed under the License is distributed on an + * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + * KIND, either express or implied. See the License for the + * specific language governing permissions and limitations + * under the License. + * + *//* ----------------------------------------------------------------------- */ + +DROP TABLE IF EXISTS vertex, edge; +CREATE TABLE vertex( + node_id INTEGER +); +CREATE TABLE edge( + conn_src INTEGER, + conn_dest INTEGER, + user_id INTEGER +); +INSERT INTO vertex VALUES +(0), +(1), +(2), +(3), +(4), +(5), +(6), +(10), +(11), +(12), +(13), +(14), +(15), +(16); +INSERT INTO edge VALUES +(0, 1, 1), +(0, 2, 1), +(1, 2, 1), +(1, 3, 1), +(2, 3, 1), +(2, 5, 1), +(2, 6, 1), +(3, 0, 1), +(5, 6, 1), +(6, 3, 1), +(10, 11, 2), +(10, 12, 2), +(11, 12, 2), +(11, 13, 2), +(12, 13, 2), +(13, 10, 2), +(15, 16, 2), +(15, 14, 2); + +DROP TABLE IF EXISTS wcc_out, wcc_out_summary; +SELECT madlib.weakly_connected_components( + 'vertex', -- Vertex table + 'node_id', -- Vertex id column + 'edge', -- Edge table + 'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments + 'wcc_out'); -- Output table of weakly connected components +SELECT * FROM wcc_out ORDER BY component_id, id; + +DROP TABLE IF EXISTS wcc_out, wcc_out_summary; +SELECT madlib.weakly_connected_components( + 'vertex', -- Vertex table + 'node_id', -- Vertex id column + 'edge', -- Edge table + 'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments + 'wcc_out', -- Output table of weakly connected components + 'user_id'); -- Grouping column name +SELECT * FROM wcc_out ORDER BY user_id, component_id, id; + +DROP TABLE IF EXISTS largest_cpt_table; +SELECT madlib.graph_wcc_largest_cpt( + 'wcc_out', -- WCC output table + 'largest_cpt_table'); -- output table containing largest component ID +SELECT * FROM largest_cpt_table ORDER BY component_id; + +DROP TABLE IF EXISTS histogram_table; +SELECT madlib.graph_wcc_histogram( + 'wcc_out', -- WCC output table + 'histogram_table'); -- output table containing the histogram of vertices +SELECT * FROM histogram_table ORDER BY component_id; + +DROP TABLE IF EXISTS vc_table; +SELECT madlib.graph_wcc_vertex_check( + 'wcc_out', -- WCC output table + '14,15', -- Pair of vertex IDs + 'vc_table'); -- output table containing components that contain the two vertices +SELECT * FROM vc_table ORDER BY component_id; + +DROP TABLE IF EXISTS reach_table; +SELECT madlib.graph_wcc_reachable_vertices( + 'wcc_out', -- WCC output table + '0', -- source vertex + 'reach_table'); -- output table containing all vertices reachable from source vertex +SELECT * FROM reach_table ORDER BY component_id, dest; + +DROP TABLE IF EXISTS count_table; +SELECT madlib.graph_wcc_num_cpts( + 'wcc_out', -- WCC output table + 'count_table'); -- output table containing number of components per group +SELECT * FROM count_table; + +DROP TABLE IF EXISTS vertex_multicol_wcc, edge_multicol_wcc; +CREATE TABLE vertex_multicol_wcc( + node_id_major BIGINT, + node_id_minor BIGINT +); +CREATE TABLE edge_multicol_wcc( + conn_src_major BIGINT, + conn_dest_major BIGINT, + user_id_major BIGINT, + conn_src_minor BIGINT, + conn_dest_minor BIGINT, + user_id_minor BIGINT +); +INSERT INTO vertex_multicol_wcc VALUES +(0, 0), +(1, 1), +(2, 2), +(3, 3), +(4, 4), +(5, 5), +(6, 6); +INSERT INTO edge_multicol_wcc VALUES +(0, 1, 1, 0, 1, 1), +(0, 2, 1, 0, 2, 1), +(0, 4, 1, 0, 4, 1), +(1, 2, 1, 1, 2, 1), +(1, 3, 1, 1, 3, 1), +(2, 3, 1, 2, 3, 1), +(2, 5, 1, 2, 5, 1), +(2, 6, 1, 2, 6, 1), +(3, 0, 1, 3, 0, 1), +(4, 0, 1, 4, 0, 1), +(5, 6, 1, 5, 6, 1), +(6, 3, 1, 6, 3, 1), +(0, 1, 2, 0, 1, 2), +(0, 2, 2, 0, 2, 2), +(0, 4, 2, 0, 4, 2), +(1, 2, 2, 1, 2, 2), +(1, 3, 2, 1, 3, 2), +(2, 3, 2, 2, 3, 2), +(3, 0, 2, 3, 0, 2), +(4, 0, 2, 4, 0, 2), +(5, 6, 2, 5, 6, 2), +(6, 3, 2, 6, 3, 2); + +DROP TABLE IF EXISTS wcc_multicol_out, wcc_multicol_out_summary; +SELECT madlib.weakly_connected_components( + 'vertex_multicol_wcc', -- Vertex table + '[node_id_major,node_id_minor]', -- Vertex id column + 'edge_multicol_wcc', -- Edge table + 'src=[conn_src_major,conn_src_minor], dest=[conn_dest_major,conn_dest_minor]', -- Comma delimted string of edge arguments + 'wcc_multicol_out', -- Output table of weakly connected components + 'user_id_major,user_id_minor'); -- Grouping column name +SELECT * FROM wcc_multicol_out ORDER BY user_id_major, user_id_minor, component_id, id; diff --git a/docs/docs/v2.1.0/example/madlib_xgboost_example.sql b/docs/docs/v2.1.0/example/madlib_xgboost_example.sql new file mode 100644 index 00000000..36c928cf --- /dev/null +++ b/docs/docs/v2.1.0/example/madlib_xgboost_example.sql @@ -0,0 +1,4288 @@ +/* ----------------------------------------------------------------------- *//** + * + * Licensed to the Apache Software Foundation (ASF) under one + * or more contributor license agreements. See the NOTICE file + * distributed with this work for additional information + * regarding copyright ownership. The ASF licenses this file + * to you under the Apache License, Version 2.0 (the + * "License"); you may not use this file except in compliance + * with the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, + * software distributed under the License is distributed on an + * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY + * KIND, either express or implied. See the License for the + * specific language governing permissions and limitations + * under the License. + * + *//* ----------------------------------------------------------------------- */ + + +DROP TABLE IF EXISTS abalone; +CREATE TABLE abalone ( + id integer, + sex char(1), + length float, + diameter float, + height float, + whole_weight float, + shucked_weight float, + viscera_weight float, + shell_weight float, + rings integer + ); + + +INSERT INTO abalone VALUES +(1,'M',0.455,0.365,0.095,0.514,0.2245,0.101,0.15,15), +(2,'M',0.35,0.265,0.09,0.2255,0.0995,0.0485,0.07,7), +(3,'F',0.53,0.42,0.135,0.677,0.2565,0.1415,0.21,9), +(4,'M',0.44,0.365,0.125,0.516,0.2155,0.114,0.155,10), +(5,'I',0.33,0.255,0.08,0.205,0.0895,0.0395,0.055,7), +(6,'I',0.425,0.3,0.095,0.3515,0.141,0.0775,0.12,8), +(7,'F',0.53,0.415,0.15,0.7775,0.237,0.1415,0.33,20), +(8,'F',0.545,0.425,0.125,0.768,0.294,0.1495,0.26,16), +(9,'M',0.475,0.37,0.125,0.5095,0.2165,0.1125,0.165,9), +(10,'F',0.55,0.44,0.15,0.8945,0.3145,0.151,0.32,19), +(11,'F',0.525,0.38,0.14,0.6065,0.194,0.1475,0.21,14), +(12,'M',0.43,0.35,0.11,0.406,0.1675,0.081,0.135,10), +(13,'M',0.49,0.38,0.135,0.5415,0.2175,0.095,0.19,11), +(14,'F',0.535,0.405,0.145,0.6845,0.2725,0.171,0.205,10), +(15,'F',0.47,0.355,0.1,0.4755,0.1675,0.0805,0.185,10), +(16,'M',0.5,0.4,0.13,0.6645,0.258,0.133,0.24,12), +(17,'I',0.355,0.28,0.085,0.2905,0.095,0.0395,0.115,7), +(18,'F',0.44,0.34,0.1,0.451,0.188,0.087,0.13,10), +(19,'M',0.365,0.295,0.08,0.2555,0.097,0.043,0.1,7), +(20,'M',0.45,0.32,0.1,0.381,0.1705,0.075,0.115,9), +(21,'M',0.355,0.28,0.095,0.2455,0.0955,0.062,0.075,11), +(22,'I',0.38,0.275,0.1,0.2255,0.08,0.049,0.085,10), +(23,'F',0.565,0.44,0.155,0.9395,0.4275,0.214,0.27,12), +(24,'F',0.55,0.415,0.135,0.7635,0.318,0.21,0.2,9), +(25,'F',0.615,0.48,0.165,1.1615,0.513,0.301,0.305,10), +(26,'F',0.56,0.44,0.14,0.9285,0.3825,0.188,0.3,11), +(27,'F',0.58,0.45,0.185,0.9955,0.3945,0.272,0.285,11), 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#Regularization on weights (eta). For smaller values, increase n_estimators + 'max_depth': [9],#Larger values could lead to overfitting + 'subsample': [0.85],#introduce randomness in samples picked to prevent overfitting + 'colsample_bytree': [0.85],#introduce randomness in features picked to prevent overfitting + 'min_child_weight': [10],#larger values will prevent over-fitting + 'n_estimators':[100] #More estimators, lesser variance (better fit on test set) + } + $$, -- XGBoost grid search parameters + '', -- Class weights + 0.8, -- Training set size ratio + NULL -- Variable used to do the test/train split. +); + +SELECT * FROM xgb_out_summary; + +DROP TABLE IF EXISTS xgb_score_out, xgb_score_out_metrics, xgb_score_out_roc_curve; +SELECT madlib.xgboost_predict( + 'abalone', -- test_table + 'xgb_out', -- model_table + 'xgb_score_out', -- predict_output_table + 'id', -- id_column + 'sex' -- class_label +); +SELECT * FROM xgb_score_out LIMIT 10; +SELECT * FROM xgb_score_out_roc_curve limit 10; +SELECT * FROM xgb_score_out_metrics; + +DROP TABLE IF EXISTS xgb_out, xgb_out_summary; +SELECT madlib.xgboost( + 'abalone', -- Training table + 'xgb_out', -- Grid search results table. + 'id', -- Id column + 'sex', -- Class label column + '*', -- Independent variables + NULL, -- Columns to exclude from features + $$ + { + 'learning_rate': [0.01,0.1], #Regularization on weights (eta). For smaller values, increase n_estimators + 'max_depth': [9,12],#Larger values could lead to overfitting + 'subsample': [0.85],#introduce randomness in samples picked to prevent overfitting + 'colsample_bytree': [0.85],#introduce randomness in features picked to prevent overfitting + 'min_child_weight': [10],#larger values will prevent over-fitting + 'n_estimators':[100] #More estimators, lesser variance (better fit on test set) + } + $$, -- XGBoost grid search parameters + '', -- Class weights + 0.8, -- Training set size ratio + NULL -- Variable used to do the test/train split. +); + +SELECT * FROM xgb_out_summary; + +DROP TABLE IF EXISTS xgb_score_out, xgb_score_out_metrics, xgb_score_out_roc_curve; +SELECT madlib.xgboost_predict( + 'abalone', -- test_table + 'xgb_out', -- model_table + 'xgb_score_out', -- predict_output_table + 'id', -- id_column + 'sex', -- class_label + 2 -- model_filters +); +SELECT * FROM xgb_score_out LIMIT 10; diff --git a/docs/docs/v2.1.0/folderclosed.png b/docs/docs/v2.1.0/folderclosed.png new file mode 100644 index 0000000000000000000000000000000000000000..bb8ab35edce8e97554e360005ee9fc5bffb36e66 GIT binary patch literal 616 zcmV-u0+;=XP)a9#ETzayK)T~Jw&MMH>OIr#&;dC}is*2Mqdf&akCc=O@`qC+4i z5Iu3w#1M@KqXCz8TIZd1wli&kkl2HVcAiZ8PUn5z_kG@-y;?yK06=cA0U%H0PH+kU zl6dp}OR(|r8-RG+YLu`zbI}5TlOU6ToR41{9=uz^?dGTNL;wIMf|V3`d1Wj3y!#6` zBLZ?xpKR~^2x}?~zA(_NUu3IaDB$tKma*XUdOZN~c=dLt_h_k!dbxm_*ibDM zlFX`g{k$X}yIe%$N)cn1LNu=q9_CS)*>A zsX_mM4L@`(cSNQKMFc$RtYbx{79#j-J7hk*>*+ZZhM4Hw?I?rsXCi#mRWJ=-0LGV5a-WR0Qgt<|Nqf)C-@80`5gIz45^_20000IqP)X=#(TiCT&PiIIVc55T}TU}EUh*{q$|`3@{d>{Tc9Bo>e= zfmF3!f>fbI9#GoEHh0f`i5)wkLpva0ztf%HpZneK?w-7AK@b4Itw{y|Zd3k!fH?q2 zlhckHd_V2M_X7+)U&_Xcfvtw60l;--DgZmLSw-Y?S>)zIqMyJ1#FwLU*%bl38ok+! zh78H87n`ZTS;uhzAR$M`zZ`bVhq=+%u9^$5jDplgxd44}9;IRqUH1YHH|@6oFe%z( zo4)_>E$F&^P-f(#)>(TrnbE>Pefs9~@iN=|)Rz|V`sGfHNrJ)0gJb8xx+SBmRf@1l zvuzt=vGfI)<-F9!o&3l?>9~0QbUDT(wFdnQPv%xdD)m*g%!20>Bc9iYmGAp<9YAa( z0QgYgTWqf1qN++Gqp z8@AYPTB3E|6s=WLG?xw0tm|U!o=&zd+H0oRYE;Dbx+Na9s^STqX|Gnq%H8s(nGDGJ j8vwW|`Ts`)fSK|Kx=IK@RG@g200000NkvXXu0mjfauFEA literal 0 HcmV?d00001 diff --git a/docs/docs/v2.1.0/glm_8sql__in.html b/docs/docs/v2.1.0/glm_8sql__in.html new file mode 100644 index 00000000..1a7449e8 --- /dev/null +++ b/docs/docs/v2.1.0/glm_8sql__in.html @@ -0,0 +1,1910 @@ + + + + + + + + +MADlib: glm.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
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    + 2.1.0 +
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    User Documentation for Apache MADlib
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    +Functions
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    +
    glm.sql_in File Reference
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    +
    + +

    SQL functions for GLM (Poisson) +More...

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    +Functions

    bytea8 __glm_merge_states (bytea8 state1, bytea8 state2)
     
    bytea8 __glm_final (bytea8 state)
     
    bytea8 __glm_poisson_log_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_poisson_log_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_poisson_identity_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_poisson_identity_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_poisson_sqrt_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_poisson_sqrt_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_gaussian_identity_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_gaussian_identity_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_gaussian_log_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_gaussian_log_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_gaussian_inverse_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_gaussian_inverse_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_gamma_log_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_gamma_log_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_gamma_inverse_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_gamma_inverse_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_gamma_identity_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_gamma_identity_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_binomial_probit_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_binomial_probit_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_inverse_gaussian_identity_transition (bytea8, float8, float8[], bytea8)
     
    bytea8 __glm_binomial_logit_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_binomial_logit_agg (float8 y, float8[] x, bytea8 previous_state)
     
    __glm_result_type __glm_result_z_stats (bytea8 state)
     
    aggregate bytea8 __glm_inverse_gaussian_identity_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_inverse_gaussian_log_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_inverse_gaussian_log_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_inverse_gaussian_inverse_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_inverse_gaussian_inverse_agg (float8 y, float8[] x, bytea8 previous_state)
     
    bytea8 __glm_inverse_gaussian_sqr_inverse_transition (bytea8, float8, float8[], bytea8)
     
    aggregate bytea8 __glm_inverse_gaussian_sqr_inverse_agg (float8 y, float8[] x, bytea8 previous_state)
     
    __glm_result_type __glm_result_t_stats (bytea8 state)
     
    float8 __glm_loglik_diff (bytea8 state1, bytea8 state2)
     
    void glm (varchar source_table, varchar model_table, varchar dependent_varname, varchar independent_varname, varchar family_params, varchar grouping_col, varchar optim_params, boolean verbose)
     
    void glm (varchar source_table, varchar model_table, varchar dependent_varname, varchar independent_varname, varchar family_params, varchar grouping_col, varchar optim_params)
     
    void glm (varchar source_table, varchar model_table, varchar dependent_varname, varchar independent_varname, varchar family_params, varchar grouping_col)
     
    void glm (varchar source_table, varchar model_table, varchar dependent_varname, varchar independent_varname, varchar family_params)
     
    text glm (text message)
     
    text glm ()
     
    float8 glm_predict (float8[] coef, float8[] col_ind_var, text link)
     Predict the estimated mean value for the response variable given a specific predictor variable value in a generalized linear model. More...
     
    boolean glm_predict_binomial (float8[] coef, float8[] col_ind_var, text link)
     Predict the output category for the response variable given a specific predictor variable value in a generalized linear model. More...
     
    float8 glm_predict_poisson (float8[] coef, float8[] col_ind_var, text link)
     Predict the estimated count for the response variable given a specific predictor variable value in a generalized linear model. More...
     
    text glm_predict (text message)
     
    text glm_predict ()
     
    text glm_predict_poisson (text message)
     
    text glm_predict_binomial (text message)
     
    +

    Detailed Description

    +
    Date
    June 2014
    +
    See also
    For a brief introduction to GLM (Poisson), see the module description grp_poisson.
    +

    Function Documentation

    + +

    ◆ __glm_binomial_logit_agg()

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    aggregate bytea8 __glm_binomial_logit_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_binomial_logit_transition()

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    bytea8 __glm_binomial_logit_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_binomial_probit_agg()

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    aggregate bytea8 __glm_binomial_probit_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_binomial_probit_transition()

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    bytea8 __glm_binomial_probit_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_final()

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    bytea8 __glm_final (bytea8 state)
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    ◆ __glm_gamma_identity_agg()

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    aggregate bytea8 __glm_gamma_identity_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_gamma_identity_transition()

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    bytea8 __glm_gamma_identity_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_gamma_inverse_agg()

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    aggregate bytea8 __glm_gamma_inverse_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_gamma_inverse_transition()

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    bytea8 __glm_gamma_inverse_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_gamma_log_agg()

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    aggregate bytea8 __glm_gamma_log_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_gamma_log_transition()

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    bytea8 __glm_gamma_log_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_gaussian_identity_agg()

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    aggregate bytea8 __glm_gaussian_identity_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
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    ◆ __glm_gaussian_identity_transition()

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    bytea8 __glm_gaussian_identity_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_gaussian_inverse_agg()

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    aggregate bytea8 __glm_gaussian_inverse_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
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    ◆ __glm_gaussian_inverse_transition()

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    bytea8 __glm_gaussian_inverse_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_gaussian_log_agg()

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    aggregate bytea8 __glm_gaussian_log_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_gaussian_log_transition()

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    bytea8 __glm_gaussian_log_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_inverse_gaussian_identity_agg()

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    aggregate bytea8 __glm_inverse_gaussian_identity_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_inverse_gaussian_identity_transition()

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    bytea8 __glm_inverse_gaussian_identity_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_inverse_gaussian_inverse_agg()

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    aggregate bytea8 __glm_inverse_gaussian_inverse_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_inverse_gaussian_inverse_transition()

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    bytea8 __glm_inverse_gaussian_inverse_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_inverse_gaussian_log_agg()

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    aggregate bytea8 __glm_inverse_gaussian_log_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_inverse_gaussian_log_transition()

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    bytea8 __glm_inverse_gaussian_log_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_inverse_gaussian_sqr_inverse_agg()

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    aggregate bytea8 __glm_inverse_gaussian_sqr_inverse_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_inverse_gaussian_sqr_inverse_transition()

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    bytea8 __glm_inverse_gaussian_sqr_inverse_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_loglik_diff()

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    float8 __glm_loglik_diff (bytea8 state1,
    bytea8 state2 
    )
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    ◆ __glm_merge_states()

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    bytea8 __glm_merge_states (bytea8 state1,
    bytea8 state2 
    )
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    ◆ __glm_poisson_identity_agg()

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    aggregate bytea8 __glm_poisson_identity_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_poisson_identity_transition()

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    bytea8 __glm_poisson_identity_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_poisson_log_agg()

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    aggregate bytea8 __glm_poisson_log_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_poisson_log_transition()

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    bytea8 __glm_poisson_log_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_poisson_sqrt_agg()

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    aggregate bytea8 __glm_poisson_sqrt_agg (float8 y,
    float8 [] x,
    bytea8 previous_state 
    )
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    ◆ __glm_poisson_sqrt_transition()

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    bytea8 __glm_poisson_sqrt_transition (bytea8 ,
    float8 ,
    float8 [],
    bytea8  
    )
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    ◆ __glm_result_t_stats()

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    __glm_result_type __glm_result_t_stats (bytea8 state)
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    ◆ __glm_result_z_stats()

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    __glm_result_type __glm_result_z_stats (bytea8 state)
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    ◆ glm() [1/6]

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    void glm (varchar source_table,
    varchar model_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar family_params,
    varchar grouping_col,
    varchar optim_params,
    boolean verbose 
    )
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    ◆ glm() [2/6]

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    void glm (varchar source_table,
    varchar model_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar family_params,
    varchar grouping_col,
    varchar optim_params 
    )
    +
    + +
    +
    + +

    ◆ glm() [3/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void glm (varchar source_table,
    varchar model_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar family_params,
    varchar grouping_col 
    )
    +
    + +
    +
    + +

    ◆ glm() [4/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void glm (varchar source_table,
    varchar model_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar family_params 
    )
    +
    + +
    +
    + +

    ◆ glm() [5/6]

    + +
    +
    + + + + + + + + +
    text glm (text message)
    +
    + +
    +
    + +

    ◆ glm() [6/6]

    + +
    +
    + + + + + + + +
    text glm ()
    +
    + +
    +
    + +

    ◆ glm_predict() [1/3]

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    float8 glm_predict (float8 [] coef,
    float8 [] col_ind_var,
    text link 
    )
    +
    +
    Parameters
    + + + + +
    coefCoefficients obtained by running generalized linear model.
    col_indPredictor variable array
    linkLink function used in training. Can be one of probit/logit
    +
    +
    +
    Returns
    Numeric value of the predicted mean
    +

    This function computes the dot product of the independent variables and the coefficients. This requires the length of the two vectors to be the same.

    + +
    +
    + +

    ◆ glm_predict() [2/3]

    + +
    +
    + + + + + + + + +
    text glm_predict (text message)
    +
    + +
    +
    + +

    ◆ glm_predict() [3/3]

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    text glm_predict ()
    +
    + +
    +
    + +

    ◆ glm_predict_binomial() [1/2]

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    boolean glm_predict_binomial (float8 [] coef,
    float8 [] col_ind_var,
    text link 
    )
    +
    +
    Parameters
    + + + + +
    coefCoefficients obtained by running generalized linear model.
    col_indPredictor variable array
    linkLink function used in training. Can be one of probit/logit.
    +
    +
    +
    Returns
    True/False Boolean value corresponding to output category True if predicted probability >= 0.5, False otherwise
    +

    This function computes the dot product of the independent variables and the coefficients. This requires the length of the two vectors to be the same.

    + +
    +
    + +

    ◆ glm_predict_binomial() [2/2]

    + +
    +
    + + + + + + + + +
    text glm_predict_binomial (text message)
    +
    + +
    +
    + +

    ◆ glm_predict_poisson() [1/2]

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    float8 glm_predict_poisson (float8 [] coef,
    float8 [] col_ind_var,
    text link 
    )
    +
    +
    Parameters
    + + + + +
    coefCoefficients obtained by running generalized linear model.
    col_indPredictor variable array
    linkLink function used in training
    +
    +
    +
    Returns
    Numeric value of the predicted count, obtained by rounding the predicted mean to the nearest integral value.
    +

    This function computes the dot product of the independent variables and the coefficients. This requires the length of the two vectors to be the same.

    + +
    +
    + +

    ◆ glm_predict_poisson() [2/2]

    + +
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    + + + + + + + + +
    text glm_predict_poisson (text message)
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/graph_legend.html b/docs/docs/v2.1.0/graph_legend.html new file mode 100644 index 00000000..1165ed50 --- /dev/null +++ b/docs/docs/v2.1.0/graph_legend.html @@ -0,0 +1,145 @@ + + + + + + + + +MADlib: Graph Legend + + + + + + + + + + + + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    Graph Legend
    +
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    This page explains how to interpret the graphs that are generated by doxygen.

    +

    Consider the following example:

    /*! Invisible class because of truncation */
    class Invisible { };
    /*! Truncated class, inheritance relation is hidden */
    class Truncated : public Invisible { };
    /* Class not documented with doxygen comments */
    class Undocumented { };
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    class PublicBase : public Truncated { };
    /*! A template class */
    template<class T> class Templ { };
    /*! Class that is inherited using protected inheritance */
    class ProtectedBase { };
    /*! Class that is inherited using private inheritance */
    class PrivateBase { };
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    class Used { };
    /*! Super class that inherits a number of other classes */
    class Inherited : public PublicBase,
    protected ProtectedBase,
    private PrivateBase,
    public Undocumented,
    public Templ<int>
    {
    private:
    Used *m_usedClass;
    };

    This will result in the following graph:

    +

    The boxes in the above graph have the following meaning:

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    + + + + diff --git a/docs/docs/v2.1.0/graph_legend.md5 b/docs/docs/v2.1.0/graph_legend.md5 new file mode 100644 index 00000000..a06ed050 --- /dev/null +++ b/docs/docs/v2.1.0/graph_legend.md5 @@ -0,0 +1 @@ +387ff8eb65306fa251338d3c9bd7bfff \ No newline at end of file diff --git a/docs/docs/v2.1.0/graph_legend.svg b/docs/docs/v2.1.0/graph_legend.svg new file mode 100644 index 00000000..11700fb1 --- /dev/null +++ b/docs/docs/v2.1.0/graph_legend.svg @@ -0,0 +1,121 @@ + + + + + + +Graph Legend + + +Node9 + +Inherited + + +Node10 + + +PublicBase + + + + +Node10->Node9 + + + + +Node11 + + +Truncated + + + + +Node11->Node10 + + + + +Node13 + + +ProtectedBase + + + + +Node13->Node9 + + + + +Node14 + + +PrivateBase + + + + +Node14->Node9 + + + + +Node15 + +Undocumented + + +Node15->Node9 + + + + +Node16 + + +Templ< int > + + + + +Node16->Node9 + + + + +Node17 + + +Templ< T > + + + + +Node17->Node16 + + +< int > + + +Node18 + + +Used + + + + +Node18->Node9 + + +m_usedClass + + + diff --git a/docs/docs/v2.1.0/group__grp__apsp.html b/docs/docs/v2.1.0/group__grp__apsp.html new file mode 100644 index 00000000..f892c8c9 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__apsp.html @@ -0,0 +1,388 @@ + + + + + + + + +MADlib: All Pairs Shortest Path + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    +
    +
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    All Pairs Shortest Path
    Graph
    +
    +
    +
    Contents +

    The all pairs shortest paths (APSP) algorithm finds the length (summed weights) of the shortest paths between all pairs of vertices, such that the sum of the weights of the path edges is minimized.

    +
    Warning
    APSP is an expensive algorithm for run-time because it finds the shortest path between all nodes in the graph. It is recommended that you start with a small graph to get a sense of run-time for your use case, then increase size carefully from there. The worst case run-time for this implementation is O(V^2 * E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, but it depends on the graph. On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance.
    +

    APSP
    +graph_apsp( vertex_table,
+            vertex_id,
+            edge_table,
+            edge_args,
+            out_table,
+            grouping_cols
+          )
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    +
    +
    vertex_id
    +

    TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous.

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex, destination vertex and edge weight. Column naming convention is described below in the 'edge_args' parameter.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'.
      • +
    • dest (INTEGER or BIGINT): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    • weight (FLOAT8): Name of the column containing the edge weights in the edge table. Default column name is 'weight'.
      • +
    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the result of APSP. It contains a row for every vertex of every group and have the following columns (in addition to the grouping columns):

      +
    • source_vertex: The id for the source vertex. Will use the input edge column 'src' for column naming.
      • +
    • dest_vertex: The id for the destination vertex. Will use the input edge column 'dest' for column naming.
      • +
    • weight: The total weight of the shortest path from the source vertex to the destination vertex. Will use the input parameter 'weight' for column naming.
      • +
    • parent: The parent of the destination vertex in the shortest path from source. Parent will equal dest_vertex if there are no intermediate vertices. Will use 'parent' for column naming.
      • +
    +

    A summary table named <out_table>_summary is also created. This is an internal table that keeps a record of the input parameters and is used by the path retrieval function described below.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default = NULL. List of columns used to group the input into discrete subgraphs. These columns must exist in the edge table. When this value is null, no grouping is used and a single APSP result is generated.
    +
    +
    Path Retrieval
    +

    The path retrieval function returns the shortest path from the source vertex to a specified desination vertex.

    +
    +graph_apsp_get_path( apsp_table,
+                     source_vertex,
+                     dest_vertex,
+                     path_table
+                    )
+

    Arguments

    +
    apsp_table
    +

    TEXT. Name of the table that contains the APSP output.

    +

    +
    +
    source_vertex
    +

    INTEGER or BIGINT. The vertex that will be the source of the desired path.

    +

    +
    +
    dest_vertex
    +

    INTEGER or BIGINT. The vertex that will be the destination of the desired path.

    +

    +
    +
    path_table
    +

    TEXT. Name of the output table that contains the path. It contains a row for every group and has the following columns:

      +
    • grouping_cols: The grouping columns given in the creation of the APSP table. If there are no grouping columns, these columns will not exist and the table will have a single row.
      • +
    • path (ARRAY): The shortest path from the source vertex to the destination vertex.
      • +
    +

    +
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER
+        );
+CREATE TABLE edge(
+        src INTEGER,
+        dest INTEGER,
+        weight FLOAT8
+        );
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6),
+(7);
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+
      2. +
    2. Calculate the shortest paths: 
      +DROP TABLE IF EXISTS out, out_summary;
+SELECT madlib.graph_apsp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         'out');        -- Output table of shortest paths
+SELECT * FROM out ORDER BY src,dest;
+
      + src | dest |  weight  | parent
+-----+------+----------+--------
+   0 |    0 |        0 |      0
+   0 |    1 |        1 |      1
+   0 |    2 |        1 |      2
+   0 |    3 |        2 |      2
+   0 |    4 |       10 |      4
+   0 |    5 |        2 |      2
+   0 |    6 |        3 |      5
+   0 |    7 |        4 |      6
+   1 |    0 |        4 |      3
+   1 |    1 |        0 |      1
+   1 |    2 |        2 |      2
+   1 |    3 |        3 |      2
+   1 |    4 |       14 |      0
+   1 |    5 |        3 |      2
+   1 |    6 |        4 |      5
+   1 |    7 |        5 |      6
+(showing only 16 of 64 rows)
+
      3. +
    3. Get the shortest path from vertex 0 to vertex 5: 
      +DROP TABLE IF EXISTS out_path;
+SELECT madlib.graph_apsp_get_path('out',0,5,'out_path');
+SELECT * FROM out_path;
+
      +  path
+---------
+ {0,2,5}
+
      4. +
    4. Now let's do a similar example except using different column names in the tables (i.e., not the defaults). Create the vertex and edge tables: 
      +DROP TABLE IF EXISTS vertex_alt, edge_alt;
+CREATE TABLE vertex_alt AS SELECT id AS v_id FROM vertex;
+CREATE TABLE edge_alt AS SELECT src AS e_src, dest, weight AS e_weight FROM edge;
+
      5. +
    5. Calculate the shortest paths: 
      +DROP TABLE IF EXISTS out_alt, out_alt_summary;
+SELECT madlib.graph_apsp(
+                         'vertex_alt',                  -- Vertex table
+                         'v_id',                        -- Vertex id column
+                         'edge_alt',                    -- Edge table
+                         'src=e_src, weight=e_weight',  -- Edge arguments
+                         'out_alt');                    -- Output table of shortest paths
+SELECT * FROM out_alt ORDER BY e_src, dest;
+
      + e_src | dest | e_weight | parent
+-------+------+----------+--------
+     0 |    0 |        0 |      0
+     0 |    1 |        1 |      1
+     0 |    2 |        1 |      2
+     0 |    3 |        2 |      2
+     0 |    4 |       10 |      4
+     0 |    5 |        2 |      2
+     0 |    6 |        3 |      5
+     0 |    7 |        4 |      6
+     1 |    0 |        4 |      3
+     1 |    1 |        0 |      1
+     1 |    2 |        2 |      2
+     1 |    3 |        3 |      2
+     1 |    4 |       14 |      0
+     1 |    5 |        3 |      2
+     1 |    6 |        4 |      5
+     1 |    7 |        5 |      6
+(showing only 16 of 64 rows)
+
      6. +
    6. Create a graph with 2 groups and find APSP for each group: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+  SELECT *, 0 AS grp FROM edge
+  UNION
+  SELECT *, 1 AS grp FROM edge WHERE src < 6 AND dest < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+
      7. +
    7. Find APSP for all groups: 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         'out_gr',      -- Output table of shortest paths
+                         'grp'          -- Grouping columns
+);
+SELECT * FROM out_gr WHERE src < 2 ORDER BY grp,src,dest;
+
      + grp | src | dest | weight | parent
+-----+-----+------+--------+--------
+   0 |   0 |    0 |      0 |      0
+   0 |   0 |    1 |      1 |      1
+   0 |   0 |    2 |      1 |      2
+   0 |   0 |    3 |      2 |      2
+   0 |   0 |    4 |     10 |      4
+   0 |   0 |    5 |      2 |      2
+   0 |   0 |    6 |      4 |      2
+   0 |   0 |    7 |      5 |      6
+   0 |   1 |    0 |      4 |      3
+   0 |   1 |    1 |      0 |      1
+   0 |   1 |    2 |      2 |      2
+   0 |   1 |    3 |      3 |      2
+   0 |   1 |    4 |     14 |      0
+   0 |   1 |    5 |      3 |      2
+   0 |   1 |    6 |      4 |      5
+   0 |   1 |    7 |      5 |      6
+   1 |   0 |    0 |      0 |      0
+   1 |   0 |    1 |      1 |      1
+   1 |   0 |    2 |      1 |      2
+   1 |   0 |    3 |      2 |      2
+   1 |   0 |    4 |     10 |      4
+   1 |   0 |    5 |    -10 |      4
+   1 |   1 |    0 |      4 |      3
+   1 |   1 |    1 |      0 |      1
+   1 |   1 |    2 |      2 |      2
+   1 |   1 |    3 |      3 |      2
+   1 |   1 |    4 |     14 |      0
+   1 |   1 |    5 |     -6 |      4
+(28 rows)
+
      8. +
    8. Find the path from vertex 0 to vertex 5 in every group 
      +DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_apsp_get_path('out_gr',0,5,'out_gr_path');
+SELECT * FROM out_gr_path ORDER BY grp;
+
      + grp |  path
+-----+---------
+   0 | {0,2,5}
+   1 | {0,4,5}
+
      9. +
    +

    Notes
    +
      +
    1. Graphs with negative edges are supported but graphs with negative cycles are not.
      2. +
    2. The implementation for APSP is analogous to a matrix multiplication operation. Please refer to the MADlib design document and references [1] and [2] for more details.
      3. +
    3. Also see the Grail project [3] for more background on graph analytics processing in relational databases.
      4. +
    +

    Literature
    +

    [1] http://www.columbia.edu/~cs2035/courses/ieor6614.S11/apsp.pdf

    +

    [2] http://users.cecs.anu.edu.au/~Alistair.Rendell/Teaching/apac_comp3600/module4/all_pairs_shortest_paths.xhtml

    +

    [3] The case against specialized graph analytics engines, J. Fan, G. Soosai Raj, and J. M. Patel. CIDR 2015. http://cidrdb.org/cidr2015/Papers/CIDR15_Paper20.pdf

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__arima.html b/docs/docs/v2.1.0/group__grp__arima.html new file mode 100644 index 00000000..9cdd0e7c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__arima.html @@ -0,0 +1,411 @@ + + + + + + + + +MADlib: ARIMA + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    ARIMA
    Time Series Analysis
    +
    +
    +
    Contents +

    Given a time series of data X, the Autoregressive Integrated Moving Average (ARIMA) model is a tool for understanding and, perhaps, predicting future values in the series. The model consists of three parts, an autoregressive (AR) part, a moving average (MA) part, and an integrated (I) part where an initial differencing step can be applied to remove any non-stationarity in the signal. The model is generally referred to as an ARIMA(p, d, q) model where parameters p, d, and q are non-negative integers that refer to the order of the autoregressive, integrated, and moving average parts of the model respectively.

    +

    Training Function
    +

    The ARIMA training function has the following syntax. 

    +arima_train( input_table,
+       output_table,
+       timestamp_column,
+       timeseries_column,
+       grouping_columns,
+       include_mean,
+       non_seasonal_orders,
+       optimizer_params
+     )
+

    Arguments

    +
    input_table
    +

    TEXT. The name of the table containing time series data.

    +

    +
    +
    output_table
    +

    TEXT. The name of the table to store the ARIMA model. Three tables are created, with names based on the value of the output_table argument in the training function:

    +
      +
    1. output_table: Table containing the ARIMA model. Contains the following columns: + + + + + + + + + + + + +
      mean Model mean (only if 'include_mean' is TRUE)
      mean_std_error Standard errors for mean
      ar_params Auto-regressions parameters of the ARIMA model
      ar_std_errors Standard errors for AR parameters
      ma_params Moving average parameters of the ARIMA model
      ma_std_errors Standard errors for MA parameters
      +
      2. +
    2. output_table_summary: Table containing descriptive statistics of the ARIMA model. Contains the following columns: + + + + + + + + + + + + + + + + + + +
      input_table Table name with the source data
      timestamp_col Column name in the source table that contains the timestamp index to data
      timeseries_col Column name in the source table that contains the data values
      non_seasonal_orders Orders of the non-seasonal ARIMA model
      include_mean TRUE if intercept was included in ARIMA model
      residual_variance Variance of the residuals
      log_likelihood Log likelihood value (when using MLE)
      iter_num The number of iterations executed
      exec_time Total time taken to train the model
      +
      3. +
    3. output_table_residual: Table containing the residuals for each data point in 'input_table'. Contains the following columns: + + + + +
      timestamp_col Same as the 'timestamp_col' parameter (all indices from source table included except the first d elements, where d is the differencing order value from 'non_seasonal_orders')
      residual Residual value for each data point
      +
      4. +
    +

    +

    +
    +
    timestamp_column
    +

    TEXT. The name of the column containing the timestamp (index) data. This could be a serial index (INTEGER) or date/time value (TIMESTAMP).

    +

    +
    +
    timeseries_column
    +

    TEXT. The name of the column containing the time series data. This data is currently restricted to DOUBLE PRECISION.

    +

    +
    +
    grouping_columns (not currently implemented)
    +

    TEXT, default: NULL.

    +

    A comma-separated list of column names used to group the input dataset into discrete groups, training one ARIMA model per group. It is similar to the SQL GROUP BY clause. When this value is null, no grouping is used and a single result model is generated.

    +
    Note
    Grouping is not currently implemented for ARIMA, but will be added in the future. Any non-NULL value for this parameter is ignored.
    +
    +
    include_mean (optional)
    +

    BOOLEAN, default: FALSE. Mean value of the data series is added in the ARIMA model if this variable is True.

    +

    +
    +
    non_seasonal_orders (optional)
    +

    INTEGER[], default: 'ARRAY[1,1,1]'. Orders of the ARIMA model. The orders are [p, d, q], where parameters p, d, and q are non-negative integers that refer to the order of the autoregressive, integrated, and moving average parts of the model respectively.

    +

    +
    +
    optimizer_params (optional)
    +
    TEXT. Comma-separated list of optimizer-specific parameters of the form ‘name=value'. The order of the parameters does not matter. The following parameters are recognized:
      +
    • max_iter: Maximum number of iterations to run learning algorithm (Default = 100)
      • +
    • tau: Computes the initial step size for gradient algorithm (Default = 0.001)
      • +
    • e1: Algorithm-specific threshold for convergence (Default = 1e-15)
      • +
    • e2: Algorithm-specific threshold for convergence (Default = 1e-15)
      • +
    • e3: Algorithm-specific threshold for convergence (Default = 1e-15)
      • +
    • hessian_delta: Delta parameter to compute a numerical approximation of the Hessian matrix (Default = 1e-6)
      • +
    +
    +
    +

    Forecasting Function
    +

    The ARIMA forecast function has the following syntax. 

    +arima_forecast( model_table,
+                output_table,
+                steps_ahead
+              )
+

    Arguments

    +
    model_table
    +

    TEXT. The name of the table containing the ARIMA model trained on the time series dataset.

    +

    +
    +
    output_table
    +

    TEXT. The name of the table to store the forecasted values. The output table produced by the forecast function contains the following columns.

    + + + + + + +
    group_by_cols Grouping column values (if grouping parameter is provided)
    step_ahead Time step for the forecast
    forecast_value Forecast of the current time step
    +

    +
    +
    steps_ahead
    +
    INTEGER. The number of steps to forecast at the end of the time series.
    +
    +

    Examples
      +
    1. View online help for the ARIMA training function. 
      +SELECT madlib.arima_train();
+
      2. +
    2. Create an input data set. 
      +DROP TABLE IF EXISTS arima_beer;
+CREATE TABLE arima_beer (time_id integer NOT NULL, value double precision NOT NULL );
+COPY arima_beer (time_id, value) FROM stdin WITH DELIMITER '|';
+1  | 93.2
+2  | 96.0
+3  | 95.2
+4  | 77.0
+5  | 70.9
+6  | 64.7
+7  | 70.0
+8  | 77.2
+9  | 79.5
+10 | 100.5
+11 | 100.7
+12 | 107.0
+13 | 95.9
+14 | 82.7
+15 | 83.2
+16 | 80.0
+17 | 80.4
+18 | 67.5
+19 | 75.7
+20 | 71.0
+21 | 89.2
+22 | 101.0
+23 | 105.2
+24 | 114.0
+25 | 96.2
+26 | 84.4
+27 | 91.2
+28 | 81.9
+29 | 80.5
+30 | 70.4
+31 | 74.7
+32 | 75.9
+33 | 86.2
+34 | 98.7
+35 | 100.9
+36 | 113.7
+37 | 89.7
+38 | 84.4
+39 | 87.2
+40 | 85.5
+\.
+
      3. +
    3. Train an ARIMA model. 
      +-- Train ARIMA model with 'grouping_columns'=NULL, 'include_mean'=TRUE,
+--   and 'non_seasonal_orders'=[1,1,1]
+SELECT madlib.arima_train( 'arima_beer',
+                           'arima_beer_output',
+                           'time_id',
+                           'value',
+                           NULL,
+                           FALSE,
+                           ARRAY[1, 1, 1]
+                         );
+
      4. +
    4. Examine the ARIMA model. 
      +\x ON
+SELECT * FROM arima_beer_output;
+
      Result: 
      +-[ RECORD 1 ]-+------------------
+ar_params     | {0.221954769696}
+ar_std_errors | {0.575367782602}
+ma_params     | {-0.140623564576}
+ma_std_errors | {0.533445214346}
+
      5. +
    5. View the summary statistics table. 
      +SELECT * FROM arima_beer_output_summary;
+
      Result: 
      +-[ RECORD 1 ]-------+---------------
+input_table         | arima_beer
+timestamp_col       | time_id
+timeseries_col      | value
+non_seasonal_orders | {1,1,1}
+include_mean        | f
+residual_variance   | 100.989970539
+log_likelihood      | -145.331516396
+iter_num            | 28
+exec_time (s)       | 2.75
+
      6. +
    6. View the residuals. 
      +\x OFF
+SELECT * FROM arima_beer_output_residual;
+
      Result: 
      + time_id |      residual
+---------+--------------------
+       2 |                  0
+       4 |   -18.222328834394
+       6 |  -5.49616627282665
+...
+      35 |   1.06298837051437
+      37 |  -25.0886854003757
+      39 |   3.48401666299571
+(40 rows)
+
      7. +
    7. Use the ARIMA forecast function to forecast 10 future values. 
      +SELECT madlib.arima_forecast( 'arima_beer_output',
+                              'arima_beer_forecast_output',
+                              10
+                            );
+SELECT * FROM arima_beer_forecast_output;
+
      Result: 
      + steps_ahead | forecast_value
+-------------+----------------
+           1 |  85.3802343659
+           3 |  85.3477516875
+           5 |  85.3461514635
+           7 |  85.3460726302
+           9 |  85.3460687465
+           2 |  85.3536518121
+           4 |  85.3464421267
+           6 |  85.3460869494
+           8 |  85.3460694519
+          10 |    85.34606859
+(10 rows)
+
      8. +
    +
    +

    Technical Background
    An ARIMA model is an auto-regressive integrated moving average model. An ARIMA model is typically expressed in the form

    +\[ (1 - \phi(B)) Y_t = (1 + \theta(B)) Z_t, \] +

    +
    +

    where \(B\) is the backshift operator. The time \( t \) is from \( 1 \) to \( N \).

    +

    ARIMA models involve the following variables:

      +
    • The values of the time series: \( X_t \).
      • +
    • Parameters of the model: \( p \), \( q \), and \( d \); \( d \) is the differencing order, \( p \) is the order of the AR operator, and \( q \) is the order of the MA operator.
      • +
    • The AR operator: \( \phi(B) \).
      • +
    • The MA operator: \( \theta(B) \).
      • +
    • The lag difference: \( Y_{t} \), where \( Y_{t} = (1-B)^{d}(X_{t} - \mu) \).
      • +
    • The mean value: \( \mu \), which is set to be zero for \( d>0 \) and estimated from the data when d=0.
      • +
    • The error terms: \( Z_t \).
      • +
    +

    The auto regression operator models the prediction for the next observation as some linear combination of the previous observations. More formally, an AR operator of order \( p \) is defined as

    +

    +\[ \phi(B) Y_t= \phi_1 Y_{t-1} + \dots + \phi_{p} Y_{t-p} \] +

    +

    The moving average operator is similar, and it models the prediction for the next observation as a linear combination of the errors in the previous prediction errors. More formally, the MA operator of order \( q \) is defined as

    +

    +\[ \theta(B) Z_t = \theta_{1} Z_{t-1} + \dots + \theta_{q} Z_{t-q}. \] +

    +

    We estimate the parameters using the Levenberg-Marquardt Algorithm. In mathematics and computing, the Levenberg-Marquardt algorithm (LMA), also known as the damped least-squares (DLS) method, provides a numerical solution to the problem of minimizing a function, generally nonlinear, over a space of parameters of the function.

    +

    Like other numeric minimization algorithms, LMA is an iterative procedure. To start a minimization, the user has to provide an initial guess for the parameter vector, $p$, as well as some tuning parameters \(\tau, \epsilon_1, \epsilon_2, \epsilon_3,\).

    +

    Literature
    +

    [1] Rob J Hyndman and George Athanasopoulos: Forecasting: principles and practice, http://otexts.com/fpp/

    +

    [2] Robert H. Shumway, David S. Stoffer: Time Series Analysis and Its Applications With R Examples, Third edition Springer Texts in Statistics, 2010

    +

    [3] Henri Gavin: The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems, 2011

    +

    Related Topics
    +

    File arima.sql_in documenting the ARIMA functions

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__array.html b/docs/docs/v2.1.0/group__grp__array.html new file mode 100644 index 00000000..d999cbbc --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__array.html @@ -0,0 +1,349 @@ + + + + + + + + +MADlib: Array Operations + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    +
    Array Operations
    Data Types and Transformations » Arrays and Matrices
    +
    +
    +
    Contents +

    This module provides a set of basic array operations implemented in C and SQL. It is a support module for several machine learning algorithms that require fast array operations.

    +

    Implementation Notes
    +

    All functions (except normalize() and array_filter()) described in this module work with 2-D arrays.

    +

    These functions support several numeric types:

      +
    • SMALLINT
      • +
    • INTEGER
      • +
    • BIGINT
      • +
    • REAL
      • +
    • DOUBLE PRECISION (FLOAT8)
      • +
    • NUMERIC (internally casted into FLOAT8, loss of precisions can happen)
      • +
    +

    Additionally, array_unnest_2d_to_1d() supports other data types such as TEXT or VARCHAR.

    +

    Several of the function require NO NULL VALUES, while others omit NULLs and return results. See details in description of individual functions.

    +

    Array Operations
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    array_add()

    Adds two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    sum()

    Aggregate, sums vector element-wisely. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_sub()

    Subtracts two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_mult()

    Element-wise product of two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_div()

    Element-wise division of two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_dot()

    Dot-product of two arrays. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_contains()

    Checks whether one array contains the other. This function returns TRUE if each non-zero element in the right array equals to the element with the same index in the left array.

    +

    +
    array_max()

    This function finds the maximum value in the array. NULLs are ignored. Return type is the same as the input type.

    +

    +
    array_max_index()

    This function finds the maximum value and corresponding index in the array. NULLs are ignored. Return type is array in format [max, index], and its element type is the same as the input type.

    +

    +
    array_min()

    This function finds the minimum value in the array. NULLs are ignored. Return type is the same as the input type.

    +

    +
    array_min_index()

    This function finds the minimum value and corresponding index in the array. NULLs are ignored. Return type is array in format [min, index], and its element type is the same as the input type.

    +

    +
    array_sum()

    This function finds the sum of the values in the array. NULLs are ignored. Return type is the same as the input type.

    +

    +
    array_sum_big()

    This function finds the sum of the values in the array. NULLs are ignored. Return type is always FLOAT8 regardless of input. This function is meant to replace array_sum() in cases when a sum may overflow the element type.

    +

    +
    array_abs_sum()

    This function finds the sum of abs of the values in the array. NULLs are ignored. Return type is the same as the input type.

    +

    +
    array_abs()

    This function takes an array as the input and finds abs of each element in the array, returning the resulting array. It requires that all the values are NON-NULL.

    +

    +
    array_mean()

    This function finds the mean of the values in the array. NULLs are ignored.

    +

    +
    array_stddev()

    This function finds the standard deviation of the values in the array. NULLs are ignored.

    +

    +
    array_of_float()

    This function creates an array of set size (the argument value) of FLOAT8, initializing the values to 0.0.

    +

    +
    array_of_bigint()

    This function creates an array of set size (the argument value) of BIGINT, initializing the values to 0.

    +

    +
    array_fill()

    This functions set every value in the array to some desired value (provided as the argument).

    +

    +
    array_filter()

    This function takes an array as the input and keep only elements that satisfy the operator on specified scalar. It requires that the array is 1-D and all the values are NON-NULL. Return type is the same as the input type. By default, this function removes all zeros.

    +

    +
    array_scalar_mult()

    This function takes an array as the input and executes element-wise multiplication by the scalar provided as the second argument, returning the resulting array. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_scalar_add()

    This function takes an array as the input and executes element-wise addition of the scalar provided as the second argument, returning the resulting array. It requires that all the values are NON-NULL. Return type is the same as the input type.

    +

    +
    array_sqrt()

    This function takes an array as the input and finds square root of each element in the array, returning the resulting array. It requires that all the values are NON-NULL.

    +

    +
    array_pow()

    This function takes an array and a float8 as the input and finds power of each element in the array, returning the resulting array. It requires that all the values are NON-NULL.

    +

    +
    array_square()

    This function takes an array as the input and finds square of each element in the array, returning the resulting array. It requires that all the values are NON-NULL.

    +

    +
    normalize()

    This function normalizes an array as sum of squares to be 1. It requires that the array is 1-D and all the values are NON-NULL.

    +

    +
    array_unnest_2d_to_1d()

    This function takes a 2-D array as the input and unnests it by one level. It returns a set of 1-D arrays that correspond to rows of the input array as well as an ID column with values corresponding to row positions occupied by those 1-D arrays within the 2-D array.

    +

    +
    +
    +

    Examples
    +
      +
    1. Create a database table with two integer array columns and add some data. 
      +CREATE TABLE array_tbl ( id integer,
+                         array1 integer[],
+                         array2 integer[]
+                       );
+INSERT INTO array_tbl VALUES
+                       ( 1, '{1,2,3,4,5,6,7,8,9}', '{9,8,7,6,5,4,3,2,1}' ),
+                       ( 2, '{1,1,0,1,1,2,3,99,8}','{0,0,0,-5,4,1,1,7,6}' );
+
      2. +
    2. Find the minimum, maximum, mean, and standard deviation of the array1 column. 
      +SELECT id, madlib.array_min(array1), madlib.array_max(array1),
+           madlib.array_min_index(array1), madlib.array_max_index(array1),
+           madlib.array_mean(array1), madlib.array_stddev(array1)
+FROM array_tbl;
+
      Result: 
      +id | array_min | array_max | array_min_index | array_max_index |    array_mean    |   array_stddev
+----+-----------+-----------+---------------+---------------+------------------+------------------
+  1 |         1 |         9 | {1,1}         | {9,9}         |                5 | 2.73861278752583
+  2 |         0 |        99 | {0,3}         | {99,8}        | 12.8888888888889 | 32.3784050118457(2 rows)
+
      3. +
    3. Perform array addition and subtraction. 
      +SELECT id, madlib.array_add(array1,array2),
+          madlib.array_sub(array1,array2)
+FROM array_tbl;
+
      Result: 
      + id |          array_add           |        array_sub
+ ---+------------------------------+-------------------------
+  2 | {1,1,0,-4,5,3,4,106,14}      | {1,1,0,6,-3,1,2,92,2}
+  1 | {10,10,10,10,10,10,10,10,10} | {-8,-6,-4,-2,0,2,4,6,8}
+(2 rows)
+
      4. +
    4. Perform element-wise array multiplication and division. The row with id=2 is excluded because the divisor array contains zero, which would cause a divide-by-zero error. 
      +SELECT id, madlib.array_mult(array1,array2),
+           madlib.array_div(array1,array2)
+FROM array_tbl
+WHERE 0 != ALL(array2);
      Result: 
      + id |         array_mult         |      array_div
+ ---+----------------------------+---------------------
+  1 | {9,16,21,24,25,24,21,16,9} | {0,0,0,0,1,1,2,4,9}
+(1 row)
+
      5. +
    5. Calculate the dot product of the arrays. 
      +SELECT id, madlib.array_dot(array1, array2)
+FROM array_tbl;
+
      Result: 
      + id | array_dot
+ ---+----------
+  2 |       745
+  1 |       165
+(2 rows)
+
      6. +
    6. Multiply an array by a scalar 3. 
      +SELECT id, madlib.array_scalar_mult(array1,3)
+FROM array_tbl;
+
      Result: 
      + id |     array_scalar_mult
+ ---+--------------------------
+  1 | {3,6,9,12,15,18,21,24,27}
+  2 | {3,3,0,3,3,6,9,297,24}
+(2 rows)
+
      7. +
    7. Construct a nine-element array with each element set to the value 1.3. 
      +SELECT madlib.array_fill(madlib.array_of_float(9), 1.3::float);
+
      Result: 
      +              array_fill
+ --------------------------------------
+ {1.3,1.3,1.3,1.3,1.3,1.3,1.3,1.3,1.3}
+(1 row)
+
      8. +
    8. Unnest a column of 2-D arrays into sets of 1-D arrays. 
      +SELECT id, (madlib.array_unnest_2d_to_1d(val)).*
+FROM (
+  SELECT 1::INT AS id, ARRAY[[1.3,2.0,3.2],[10.3,20.0,32.2]]::FLOAT8[][] AS val
+  UNION ALL
+  SELECT 2, ARRAY[[pi(),pi()/2],[2*pi(),pi()],[pi()/4,4*pi()]]::FLOAT8[][]
+) t
+ORDER BY 1,2;
+
      Result: 
      + id | unnest_row_id |            unnest_result
+----+---------------+--------------------------------------
+  1 |             1 | {1.3,2,3.2}
+  1 |             2 | {10.3,20,32.2}
+  2 |             1 | {3.14159265358979,1.5707963267949}
+  2 |             2 | {6.28318530717959,3.14159265358979}
+  2 |             3 | {0.785398163397448,12.5663706143592}
+(5 rows)
+
      If the function is called without the .* notation then it will return a composite record type with two attributes: the row ID and corresponding unnested array result.
      9. +
    +

    Related Topics
    +

    File array_ops.sql_in for list of functions and usage.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__arraysmatrix.html b/docs/docs/v2.1.0/group__grp__arraysmatrix.html new file mode 100644 index 00000000..6bbf50cd --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__arraysmatrix.html @@ -0,0 +1,166 @@ + + + + + + + + +MADlib: Arrays and Matrices + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
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    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Arrays and Matrices
    Data Types and Transformations
    +
    +
    +

    Detailed Description

    +

    These modules provide basic mathematical operations to be run on array and matrices.

    +

    For a distributed system, a matrix cannot simply be represented as a 2D array of numbers in memory. We provide two forms of distributed representation of a matrix:

    +
      +
    • Dense: The matrix is represented as a distributed collection of 1-D arrays. An example 3x10 matrix would be the below table: 
      + row_id |         row_vec
+--------+-------------------------
+   1    | {9,6,5,8,5,6,6,3,10,8}
+   2    | {8,2,2,6,6,10,2,1,9,9}
+   3    | {3,9,9,9,8,6,3,9,5,6}
+
      • +
    • Sparse: The matrix is represented using the row and column indices for each non-zero entry of the matrix. Example: 
      + row_id | col_id | value
+--------+--------+-------
+      1 |      1 |     9
+      1 |      5 |     6
+      1 |      6 |     6
+      2 |      1 |     8
+      3 |      1 |     3
+      3 |      2 |     9
+      4 |      7 |     0
+(6 rows)
+
        All matrix operations work with either form of representation.
      • +
    +

    In many cases, a matrix function can be decomposed to vector operations applied independently on each row of a matrix (or corresponding rows of two matrices). We have also provided access to these internal vector operations (Array Operations) for greater flexibility. Matrix operations like matrix_add use the corresponding vector operation (array_add) and also include additional validation and formating. Other functions like matrix_mult are complex and use a combination of such vector operations and other SQL operations.

    +

    It's important to note that these array functions are only available for the dense format representation of the matrix. In general, the scope of a single array function invocation is limited to only an array (1-dimensional or 2-dimensional) that fits in memory. When such function is executed on a table of arrays, the function is called multiple times - once for each array (or pair of arrays). On contrary, scope of a single matrix function invocation is the complete matrix stored as a distributed table.

    + + + + + + + + + + + + + + + + + +

    +Modules

     Array Operations
     Provides fast array operations supporting other MADlib modules.
     
     Matrix Operations
     Provides fast matrix operations supporting other MADlib modules.
     
     Matrix Factorization
     Linear algebra methods that factorize a matrix into a product of matrices.
     
     Norms and Distance Functions
     Provides utility functions for basic linear algebra operations.
     
     Sparse Vectors
     Implements a sparse vector data type that provides compressed storage of vectors that may have many duplicate elements.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__arraysmatrix.js b/docs/docs/v2.1.0/group__grp__arraysmatrix.js new file mode 100644 index 00000000..f112873e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__arraysmatrix.js @@ -0,0 +1,8 @@ +var group__grp__arraysmatrix = +[ + [ "Array Operations", "group__grp__array.html", null ], + [ "Matrix Operations", "group__grp__matrix.html", null ], + [ "Matrix Factorization", "group__grp__matrix__factorization.html", "group__grp__matrix__factorization" ], + [ "Norms and Distance Functions", "group__grp__linalg.html", null ], + [ "Sparse Vectors", "group__grp__svec.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__assoc__rules.html b/docs/docs/v2.1.0/group__grp__assoc__rules.html new file mode 100644 index 00000000..564f00fa --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__assoc__rules.html @@ -0,0 +1,406 @@ + + + + + + + + +MADlib: Apriori Algorithm + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    User Documentation for Apache MADlib
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    Apriori Algorithm
    Unsupervised Learning » Association Rules
    +
    +
    +
    Contents +

    This module implements the association rules data mining technique on a transactional data set. Given the names of a table and the columns, minimum support and confidence values, this function generates all single and multidimensional association rules that meet the minimum thresholds.

    +

    Association rule mining is a widely used technique for discovering relationships between variables in a large data set (e.g., items in a store that are commonly purchased together). The classic market basket analysis example using association rules is the "beer and diapers" rule. According to data mining urban legend, a study of customer purchase behavior in a supermarket found that men often purchased beer and diapers together. After making this discovery, the managers strategically placed beer and diapers closer together on the shelves and saw a dramatic increase in sales. In addition to market basket analysis, association rules are also used in bioinformatics, web analytics, and several other fields.

    +

    This type of data mining algorithm uses transactional data. Every transaction event has a unique identifier, and each transaction consists of a set of items (or itemset). Purchases are considered binary (either it was purchased or not), and this implementation does not take into consideration the quantity of each item. For the MADlib association rules function, it is assumed that the data is stored in two columns with one item and transaction id per row. Transactions with multiple items will span multiple rows with one row per item.

    +
    +    trans_id | product
+    ---------+---------
+           1 | 1
+           1 | 2
+           1 | 3
+           1 | 4
+           2 | 3
+           2 | 4
+           2 | 5
+           3 | 1
+           3 | 4
+           3 | 6
+    ...
+

    Rules
    +

    Association rules take the form "If X, then Y", where X and Y are non-empty itemsets. X and Y are called the antecedent and consequent, or the left-hand-side and right-hand-side, of the rule respectively. Using our previous example, the association rule may state "If {diapers}, then {beer}" with .2 support and .85 confidence.

    +

    The following metrics are defined for any given itemset "X".

      +
    • Count: The number of transactions that contain X
      • +
    • Support: The ratio of transactions that contain X to all transactions, T

      +\[ S (X) = \frac{Total X}{Total transactions} \] +

      +
      • +
    +

    Given any association rule "If X, then Y", the association rules function will also calculate the following metrics:

      +
    • Count: The number of transactions that contain X,Y
      • +
    • Support: The ratio of transactions that contain X,Y to all transactions, T

      +\[ S (X \Rightarrow Y) = \frac{Total(X \cup Y)}{Total transactions} \] +

      +
      • +
    • Confidence: The ratio of transactions that contain \( X,Y \) to transactions that contain \( X \). One could view this metric as the conditional probability of \( Y \) , given \( X \) . \( P(Y|X) \)

      +\[ C (X \Rightarrow Y) = \frac{s(X \cap Y )}{s(X)} \] +

      +
      • +
    • Lift: The ratio of observed support of \( X,Y \) to the expected support of \( X,Y \) , assuming \( X \) and \( Y \) are independent.

      +\[ L (X \Rightarrow Y) = \frac{s(X \cap Y )}{s(X) \cdot s(Y)} \] +

      +
      • +

    • Conviction: The ratio of expected support of \( X \) occurring without \( Y \) assuming \( X \) and \( \neg Y \) are independent, to the observed support of \( X \) occuring without \( Y \). If conviction is greater than 1, then this metric shows that incorrect predictions ( \( X \Rightarrow Y \) ) occur less often than if these two actions were independent. This metric can be viewed as the ratio that the association rule would be incorrect if the actions were independent (i.e. a conviction of 1.5 indicates that if the variables were independent, this rule would be incorrect 50% more often.)

      +

      +\[ Conv (X \Rightarrow Y) = \frac{1 - S(Y)}{1 - C(X \Rightarrow Y)} \] +

      +
      • +
    +

    Apriori Algorithm
    +

    Although there are many algorithms that generate association rules, the classic algorithm is called Apriori [1] which we have implemented in this module. It is a breadth-first search, as opposed to depth-first searches like Eclat. Frequent itemsets of order \( n \) are generated from sets of order \( n - 1 \). Using the downward closure property, all sets must have frequent subsets. There are two steps in this algorithm; generating frequent itemsets, and using these itemsets to construct the association rules. A simplified version of the algorithm is as follows, and assumes a minimum level of support and confidence is provided:

    +

    Initial step

      +
    1. Generate all itemsets of order 1.
      2. +
    2. Eliminate itemsets that have support less than minimum support.
      3. +
    +

    Main algorithm

      +
    1. For \( n \ge 2 \), generate itemsets of order \( n \) by combining the itemsets of order \( n - 1 \). This is done by doing the union of two itemsets that have identical items except one.
      2. +
    2. Eliminate itemsets that have (n-1) order subsets with insufficient support.
      3. +
    3. Eliminate itemsets with insufficient support.
      4. +
    4. Repeat until itemsets cannot be generated, or maximum itemset size is exceeded.
      5. +
    +

    Association rule generation

    +

    Given a frequent itemset \( A \) generated from the Apriori algorithm, and all subsets \( B \) , we generate rules such that \( B \Rightarrow (A - B) \) meets minimum confidence requirements.

    +
    Note
    Beware of combinatorial explosion. The Apriori algorithm can potentially generate a huge number of rules, even for fairly simple data sets, resulting in run times that are unreasonably long. To avoid this, it is recommended to cap the maximum itemset size to a small number to start with, then increase it gradually. Similarly, max_LHS_size and max_RHS_size limit the number of items on the LHS and RHS of the rules and can significantly reduce run times. Support and confidence values are parameters that can also be used to control rule generation.
    +

    Function Syntax
    Association rules has the following syntax: 
    +assoc_rules( support,
+             confidence,
+             tid_col,
+             item_col,
+             input_table,
+             output_schema,
+             verbose,
+             max_itemset_size,
+             max_LHS_size,
+             max_RHS_size
+           );
    This generates all association rules that satisfy the specified minimum support and confidence.
    +

    Arguments

    +
    support
    +

    Minimum level of support needed for each itemset to be included in result.

    +

    +
    +
    confidence
    +

    Minimum level of confidence needed for each rule to be included in result.

    +

    +
    +
    tid_col
    +

    Name of the column storing the transaction ids.

    +

    +
    +
    item_col
    +

    Name of the column storing the products.

    +

    +
    +
    input_table
    +

    Name of the table containing the input data.

    +

    The input data is expected to be of the following form: 

    {TABLE|VIEW} input_table (
+    trans_id INTEGER,
+    product TEXT
+)

    The algorithm maps the product names to consecutive integer ids starting at 1. If they are already structured this way, then the ids will not change.

    +

    +
    +
    output_schema
    +

    The name of the schema where the final results will be stored. The schema must be created before calling the function. Alternatively, use NULL to output to the current schema.

    +

    The results containing the rules, support, count, confidence, lift, and conviction are stored in the table assoc_rules in the schema specified by output_schema.

    +

    The table has the following columns.

    + + + + + + + + + + + + + + + + +
    ruleid integer
    pre text
    post text
    count integer
    support double
    confidence double
    lift double
    conviction double
    +

    On Greenplum Database, the table is distributed by the ruleid column.

    +

    The pre and post columns are the itemsets of left and right hand sides of the association rule respectively. The support, confidence, lift, and conviction columns are calculated as described earlier.

    +

    +
    +
    verbose (optional)
    +

    BOOLEAN, default: FALSE. Determines if details are printed for each iteration as the algorithm progresses.

    +

    +
    +
    max_itemset_size (optional)
    +

    INTEGER, default: 10. Determines the maximum size of frequent itemsets that are used for generating association rules. Must be 2 or more. This parameter can be used to reduce run time for data sets where itemset size is large, which is a common situation. If your query is not returning or is running too long, try using a lower value for this parameter.

    +

    +
    +
    max_LHS_size (optional)
    +

    INTEGER, default: NULL. Determines the maximum size of the left hand side of the rule. Must be 1 or more. This parameter can be used to reduce run time.

    +

    +
    +
    max_RHS_size (optional)
    +
    INTEGER, default: NULL. Determines the maximum size of the right hand side of the rule. Must be 1 or more. This parameter can be used to reduce run time. For example, setting to 1 can significantly reduce run time if this makes sense for your use case. (The apriori algorithm in the R package arules [2] only supports a RHS of 1.)
    +
    +

    Examples
    +

    Let's look at some sample transactional data and generate association rules.

    +
      +
    1. Create an input dataset: 
      +DROP TABLE IF EXISTS test_data;
+CREATE TABLE test_data (
+    trans_id INT,
+    product TEXT
+);
+INSERT INTO test_data VALUES
+(1, 'beer'),
+(1, 'diapers'),
+(1, 'chips'),
+(2, 'beer'),
+(2, 'diapers'),
+(3, 'beer'),
+(3, 'diapers'),
+(4, 'beer'),
+(4, 'chips'),
+(5, 'beer'),
+(6, 'beer'),
+(6, 'diapers'),
+(6, 'chips'),
+(7, 'beer'),
+(7, 'diapers');
+
      2. +
    2. Let \( min(support) = .25 \) and \( min(confidence) = .5 \), and the output schema is set to NULL indicating output to the current schema. In this example we set verbose to TRUE so that we have some insight into progress of the function. We can now generate association rules as follows: 
      +DROP TABLE IF EXISTS assoc_rules;
+SELECT * FROM madlib.assoc_rules( .25,            -- Support
+                                  .5,             -- Confidence
+                                  'trans_id',     -- Transaction id col
+                                  'product',      -- Product col
+                                  'test_data',    -- Input data
+                                  NULL,           -- Output schema
+                                  TRUE            -- Verbose output
+                                );
+
      Result (iteration details not shown): 
      + output_schema | output_table | total_rules |   total_time
+---------------+--------------+-------------+-----------------
+ public        | assoc_rules  |           7 | 00:00:00.569254
+(1 row)
+
      The association rules are stored in the assoc_rules table: 
      +SELECT * FROM assoc_rules
+ORDER BY support DESC, confidence DESC;
+
      Result: 
      + ruleid |       pre       |      post      | count |      support      |    confidence     |       lift        |    conviction
+--------+-----------------+----------------+-------+-------------------+-------------------+-------------------+-------------------
+      2 | {diapers}       | {beer}         |     5 | 0.714285714285714 |                 1 |                 1 |                 0
+      6 | {beer}          | {diapers}      |     5 | 0.714285714285714 | 0.714285714285714 |                 1 |                 1
+      5 | {chips}         | {beer}         |     3 | 0.428571428571429 |                 1 |                 1 |                 0
+      4 | {chips,diapers} | {beer}         |     2 | 0.285714285714286 |                 1 |                 1 |                 0
+      1 | {chips}         | {diapers,beer} |     2 | 0.285714285714286 | 0.666666666666667 | 0.933333333333333 | 0.857142857142857
+      7 | {chips}         | {diapers}      |     2 | 0.285714285714286 | 0.666666666666667 | 0.933333333333333 | 0.857142857142857
+      3 | {beer,chips}    | {diapers}      |     2 | 0.285714285714286 | 0.666666666666667 | 0.933333333333333 | 0.857142857142857
+(7 rows)
+
      3. +
    3. Limit association rules generated from itemsets of size at most 2. This parameter is a good way to reduce long run times. 
      +DROP TABLE IF EXISTS assoc_rules;
+SELECT * FROM madlib.assoc_rules( .25,            -- Support
+                                  .5,             -- Confidence
+                                  'trans_id',     -- Transaction id col
+                                  'product',      -- Product col
+                                  'test_data',    -- Input data
+                                  NULL,           -- Output schema
+                                  TRUE,           -- Verbose output
+                                  2               -- Max itemset size
+                                );
+
      Result (iteration details not shown): 
      + output_schema | output_table | total_rules |   total_time
+---------------+--------------+-------------+-----------------
+ public        | assoc_rules  |           4 | 00:00:00.565176
+(1 row)
+
      The association rules are again stored in the assoc_rules table: 
      +SELECT * FROM assoc_rules
+ORDER BY support DESC, confidence DESC;
+
      Result: 
      + ruleid |    pre    |   post    | count |      support      |    confidence     |       lift        |    conviction
+--------+-----------+-----------+-------+-------------------+-------------------+-------------------+-------------------
+      1 | {diapers} | {beer}    |     5 | 0.714285714285714 |                 1 |                 1 |                 0
+      2 | {beer}    | {diapers} |     5 | 0.714285714285714 | 0.714285714285714 |                 1 |                 1
+      3 | {chips}   | {beer}    |     3 | 0.428571428571429 |                 1 |                 1 |                 0
+      4 | {chips}   | {diapers} |     2 | 0.285714285714286 | 0.666666666666667 | 0.933333333333333 | 0.857142857142857
+(4 rows)
+
      4. +
    4. Post-processing can now be done on the output table in the case that you want to filter the results. For example, if you want any single item on the left hand side and a particular item on the right hand side: 
      +SELECT * FROM assoc_rules WHERE array_upper(pre,1) = 1 AND post = array['beer'];
+
      Result: 
      + ruleid |    pre    |  post  | count |      support      | confidence | lift | conviction
+--------+-----------+--------+-------+-------------------+------------+------+------------
+      1 | {diapers} | {beer} |     5 | 0.714285714285714 |          1 |    1 |          0
+      3 | {chips}   | {beer} |     3 | 0.428571428571429 |          1 |    1 |          0
+(2 rows)
+
      5. +
    5. Limit the size of right hand side to 1. This parameter is a good way to reduce long run times. 
      +DROP TABLE IF EXISTS assoc_rules;
+SELECT * FROM madlib.assoc_rules( .25,            -- Support
+                                  .5,             -- Confidence
+                                  'trans_id',     -- Transaction id col
+                                  'product',      -- Product col
+                                  'test_data',    -- Input data
+                                  NULL,           -- Output schema
+                                  TRUE,           -- Verbose output
+                                  NULL,           -- Max itemset size
+                                  NULL,           -- Max LHS size
+                                  1               -- Max RHS size
+                                );
+
      Result (iteration details not shown): 
      + output_schema | output_table | total_rules |   total_time
+---------------+--------------+-------------+-----------------
+ public        | assoc_rules  |           6 | 00:00:00.031362
+(1 row)
+
      The association rules are again stored in the assoc_rules table: 
      +SELECT * FROM assoc_rules
+ORDER BY support DESC, confidence DESC;
+
      Result: 
      + ruleid |       pre       |   post    | count |      support      |    confidence     |       lift        |    conviction
+--------+-----------------+-----------+-------+-------------------+-------------------+-------------------+-------------------
+      4 | {diapers}       | {beer}    |     5 | 0.714285714285714 |                 1 |                 1 |                 0
+      3 | {beer}          | {diapers} |     5 | 0.714285714285714 | 0.714285714285714 |                 1 |                 1
+      1 | {chips}         | {beer}    |     3 | 0.428571428571429 |                 1 |                 1 |                 0
+      6 | {diapers,chips} | {beer}    |     2 | 0.285714285714286 |                 1 |                 1 |                 0
+      2 | {chips}         | {diapers} |     2 | 0.285714285714286 | 0.666666666666667 | 0.933333333333333 | 0.857142857142857
+      5 | {beer,chips}    | {diapers} |     2 | 0.285714285714286 | 0.666666666666667 | 0.933333333333333 | 0.857142857142857
+(6 rows)
+
      6. +
    +

    Notes
    +

    The association rules function always creates a table named assoc_rules. Make a copy of this table before running the function again if you would like to keep multiple association rule tables. This behavior will be improved in a later release.

    +

    Literature
    +

    [1] https://en.wikipedia.org/wiki/Apriori_algorithm

    +

    [2] https://cran.r-project.org/web/packages/arules/arules.pdf

    +

    Related Topics
    +

    File assoc_rules.sql_in documenting the SQL function.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__association__rules.html b/docs/docs/v2.1.0/group__grp__association__rules.html new file mode 100644 index 00000000..e81a337a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__association__rules.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: Association Rules + + + + + + + + + + + + + + + + + + + +
    +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    +Modules
    +
    +
    Association Rules
    Unsupervised Learning
    +
    +
    +

    Detailed Description

    +

    Methods used to discover patterns in transactional datasets.

    + + + + + +

    +Modules

     Apriori Algorithm
     Computes association rules for a given set of data.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__association__rules.js b/docs/docs/v2.1.0/group__grp__association__rules.js new file mode 100644 index 00000000..e10c849b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__association__rules.js @@ -0,0 +1,4 @@ +var group__grp__association__rules = +[ + [ "Apriori Algorithm", "group__grp__assoc__rules.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__automl.html b/docs/docs/v2.1.0/group__grp__automl.html new file mode 100644 index 00000000..7867e2f3 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__automl.html @@ -0,0 +1,1037 @@ + + + + + + + + +MADlib: AutoML + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    AutoML
    Deep Learning » Train Multiple Models
    +
    +
    +
    Contents +

    This module contains automated machine learning (autoML) methods for model architecture search and hyperparameter tuning.

    +

    The goal of autoML when training deep nets is to reduce the amount of hand-tuning by data scientists to produce a model of acceptable accuracy, compared to manual methods like grid or random search. The two autoML methods implemented here are Hyperband and Hyperopt. If you want to use grid or random search, please refer to Define Model Configurations.

    +

    Hyperband is an effective model selection algorithm that utilizes the idea of successive halving. It accelerates random search through adaptive resource allocation and early stopping [1]. The implementation here is designed to keep MPP database cluster resources as busy as possible when executing the Hyperband schedule.

    +

    There is also a utility function for printing out the Hyperband schedule for a given set of input parameters, to give you a sense of how long a run might take before starting.

    +

    Hyperopt is meta-modeling approach for automated hyperparameter optimization [2]. It intelligently explores the search space while narrowing down to the best estimated parameters. Within Hyperopt we support random search and Tree of Parzen Estimators (TPE) approach.

    +
    Note
    AutoML methods do not currently support multi-input or multi-output neural networks.
    +

    AutoML
    +
    +madlib_keras_automl(
+    source_table,
+    model_output_table,
+    model_arch_table,
+    model_selection_table,
+    model_id_list,
+    compile_params_grid,
+    fit_params_grid,
+    automl_method,
+    automl_params,
+    random_state,
+    object_table,
+    use_gpus,
+    validation_table,
+    metrics_compute_frequency,
+    name,
+    description,
+    use_caching
+    )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the training data. This is the name of the output table from the image preprocessor. Independent and dependent variables are specified in the preprocessor step which is why you do not need to explictly state them here. Configurations will be evaluated by the autoML methods on the basis of training loss, unless a validation table is specified below, in which case validation loss will be used.

    +

    +
    +
    model_output_table
    +
    TEXT. Name of the output table containing the multiple models created.
    Note
    'pg_temp' is not allowed as an output table schema. Details of output tables are shown below.
    +
    +
    model_arch_table
    +

    VARCHAR. Table containing model architectures and weights. For more information on this table refer to Define Model Architectures.

    +

    +
    +
    model_selection_table
    +

    VARCHAR. Model selection table created by this method. A summary table named <model_selection_table>_summary is also created. Contents of both of these tables are described below.

    +

    +
    +
    model_id_list
    +

    INTEGER[]. Array of model IDs from the 'model_arch_table' to be included in the run combinations. For hyperparameter search, this will typically be one model ID. For model architecture search, this will be the different model IDs that you want to try.

    +

    +
    +
    compile_params_grid
    +

    VARCHAR. String representation of a Python dictionary of compile parameters to be tested. Each entry of the dictionary should consist of keys as compile parameter names, and values as a Python list of compile parameter values to be passed to Keras. Also, optimizer parameters are a nested dictionary to allow different optimizer types to have different parameters or ranges of parameters. Here is an example:

    +
    +  $$
+    {'loss': ['categorical_crossentropy'],
+     'optimizer_params_list': [
+        {'optimizer': ['SGD'], 'lr': [0.0001, 0.001, 'log'], 'momentum': [0.95, 0.99, 'log_near_one']},
+        {'optimizer': ['Adam'], 'lr': [0.01, 0.1, 'log'], 'decay': [1e-6, 1e-4, 'log']}],
+     'metrics': ['accuracy']
+    }
+  $$
+

    The following types of sampling are supported: 'linear', 'log' and 'log_near_one'. The 'log_near_one' sampling is useful for exponentially weighted average types of parameters like momentum, which are very sensitive to changes near 1. It has the effect of producing more values near 1 than regular log-based sampling. However, 'log_near_one' is only supported for Hyperband, not for Hyperopt.

    +
    Note
      +
    • Custom loss functions and custom metrics can be used as defined in Define Custom Functions. List the custom function name and provide the name of the table where the serialized Python objects reside using the parameter 'object_table' below.
      • +
    • The following loss function is not supported: sparse_categorical_crossentropy. The following metrics are not supported: sparse_categorical_accuracy, sparse_top_k_categorical_accuracy.
      • +
    • The Keras accuracy parameter top_k_categorical_accuracy returns top 5 accuracy by default. If you want a different top k value, use the helper function Top k Accuracy Function to create a custom Python function to compute the top k accuracy that you want.
      • +
    +
    +
    +
    fit_params_grid
    +

    VARCHAR. String representation of a Python dictionary of fit parameters to be tested. Each entry of the dictionary should consist of keys as fit parameter names, and values as a Python list of fit parameter values to be passed to Keras. Here is an example:

    +
    +  $$
+    {'batch_size': [32, 64, 128, 256],
+     'epochs': [10, 20, 30]
+    }
+  $$
+
    Note
    Callbacks are not currently supported except for TensorBoard which you can specify in the usual way, e.g., 'callbacks': ['[TensorBoard(log_dir="/tmp/logs/fit")]']
    +
    +
    automl_method (optional)
    +

    VARCHAR, default 'hyperband'. Name of the autoML algorithm to run. Can be either 'hyperband' or 'hyperopt' (case insensitive).

    +
    Note
    If you select 'hyperopt', then the Hyperopt package must be installed on the main node of the database cluster [3]. Hyperband does not need any separate package installation.
    +

    +
    +
    automl_params (optional)
    +

    VARCHAR, default depends on the method. Parameters for the chosen autoML method in a comma-separated string of key-value pairs. Please refer to references [1] and [2] for more details on the definition of these parameters.

    +
    +
    Hyperband params:
    +
    +
    R
    +
    Default: 6. Maximum amount of resources (i.e., iterations) to allocate to a single configuration in a round of Hyperband.
    +
    eta
    +
    Default: 3. Controls the proportion of configurations discarded in each round of successive halving. For example, for eta=3 will keep the best 1/3 the configurations for the next round.
    +
    skip_last
    +
    Default: 0. The number of last rounds to skip. For example, 'skip_last=1' will skip the last round (i.e., last entry in each bracket), which is standard random search and can be expensive when run for the total R iterations.
    +
    +
    +
    Hyperopt params:
    +
    +
    num_configs
    +
    Default: 20. Number of trials to evaluate.
    +
    num_iterations
    +
    Default: 5. Number of iterations to run for each trial.
    +
    algorithm
    +
    Default: 'tpe'. Name of the algorithm to explore the search space in Hyperopt ('rand' or 'tpe').
    +
    +

    +
    +
    random_state (optional)
    +
    INTEGER, default NULL. Pseudo random number generator state used for random uniform sampling from lists of possible values. Pass an integer to evaluate a fixed set of configurations.
    Note
    Specifying a random state does not guarantee result reproducibility of the best configuration or the best train/validation accuracy/loss. It only guarantees that the same set of configurations will be chosen for evaluation.
    +
    +
    object_table (optional)
    +

    VARCHAR, default: NULL. Name of the table containing Python objects in the case that custom loss functions, metrics or top k categorical accuracy are specified in the 'compile_params_grid'.

    +

    +
    +
    validation_table (optional)
    +

    TEXT, default: none. Name of the table containing the validation dataset. Note that the validation dataset must be preprocessed in the same way as the training dataset, so this is the name of the output table from running the image preprocessor on the validation dataset. Using a validation dataset can mean a longer training time depending on its size, and the configurations in autoML will be evaluated on the basis of validation loss instead of training loss.

    +

    +
    +
    metrics_compute_frequency (optional)
    +

    INTEGER, default: once at the end of training. Frequency to compute per-iteration metrics for the training dataset and validation dataset (if specified). There can be considerable cost to computing metrics every iteration, especially if the training dataset is large. This parameter is a way of controlling the frequency of those computations. For example, if you specify 5, then metrics will be computed every 5 iterations as well as at the end of training. If you use the default, metrics will be computed only once after training has completed.

    +

    +
    +
    name (optional)
    +

    TEXT, default: NULL. Free text string to provide a name, if desired.

    +

    +
    +
    description (optional)
    +

    TEXT, default: NULL. Free text string to provide a description, if desired.

    +

    +
    +
    use_caching (optional)
    +

    BOOLEAN, default: FALSE. Use caching of images in memory on the segment in order to speed up processing.

    +
    Note
    When set to TRUE, image byte arrays on each segment are maintained in cache (GD). This can speed up training significantly, however the memory usage per segment increases. In effect, it requires enough available memory on a segment so that all images residing on that segment can be read into memory.
    +
    +
    +

    Output tables
    + The model selection output table <model_selection_table> has only one row containing the best model configuration from autoML, based on the training/validation loss. It contains the following columns:

    + + + + + + + + +
    mst_key INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters.
    model_id VARCHAR. Model architecture ID from the 'model_arch_table'.
    compile_params VARCHAR. Keras compile parameters.
    fit_params VARCHAR. Keras fit parameters.
    +

    A summary table named <model_selection_table>_summary is also created, which contains the following columns:

    + + + + +
    model_arch_table VARCHAR. Name of the model architecture table containing the model architecture IDs.
    object_table VARCHAR. Name of the object table containing the serialized Python objects for custom loss functions, custom metrics and top k categorical accuracy. If there are none, this field will be blank.
    +

    The model output table produced by autoML contains columns below. There is one row per model configuration generated:

    + + + + + + +
    mst_key INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters, as defined in the 'model_selection_table'.
    model_weights BYTEA8. Byte array containing the weights of the neural net.
    model_arch TEXT. A JSON representation of the model architecture used in training.
    +

    An info table named <model_output_table>_info is also created, which has the columns below. There is one row per model:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    mst_key INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters, for each model configuration generated.
    model_id INTEGER. ID that defines model in the 'model_arch_table'.
    compile_params Compile parameters passed to Keras.
    fit_params Fit parameters passed to Keras.
    model_type General identifier for type of model trained. Currently says 'madlib_keras'.
    model_size Size of the model in KB. Models are stored in 'bytea' data format which is used for binary strings in PostgreSQL type databases.
    metrics_elapsed_time Array of elapsed time for metric computations as per the 'metrics_compute_frequency' parameter. Useful for drawing a curve showing loss, accuracy or other metrics as a function of time. For example, if 'metrics_compute_frequency=5' this would be an array of elapsed time for every 5th iteration, plus the last iteration.
    metrics_type Metric specified in the 'compile_params'.
    training_metrics_final Final value of the training metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
    training_loss_final Final value of the training loss after all iterations have completed.
    training_metrics Array of training metrics as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of metrics for every 5th iteration, plus the last iteration.
    training_loss Array of training losses as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of losses for every 5th iteration, plus the last iteration.
    validation_metrics_final Final value of the validation metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
    validation_loss_final Final value of the validation loss after all iterations have completed.
    validation_metrics Array of validation metrics as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of metrics for every 5th iteration, plus the last iteration.
    validation_loss Array of validation losses as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of losses for every 5th iteration, plus the last iteration.
    metrics_iters

    Array indicating the iterations for which metrics are calculated, as derived from the parameters 'metrics_compute_frequency' and iterations decided by the autoML algorithm. For example, if 'num_iterations=5' and 'metrics_compute_frequency=2', then 'metrics_iters' value would be {2,4,5} indicating that metrics were computed at iterations 2, 4 and 5 (at the end). If 'num_iterations=5' and 'metrics_compute_frequency=1', then 'metrics_iters' value would be {1,2,3,4,5} indicating that metrics were computed at every iteration.

    +

    Note that 'metrics_iters' values are for the overall iterations. For some models, the count might start at a later iteration based on the schedule. This representation is selected to simplify representing the results in iteration-metric graphs.

    +
    s Bracket number from Hyperband schedule. This column is not present for Hyperopt.
    i Latest evaluated round number from Hyperband schedule. This column is not present for Hyperopt.
    +

    A summary table named <model_output_table>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    source_table Source table used for training.
    validation_table Name of the table containing the validation dataset (if specified).
    model Name of the output table containing the model for each model selection tuple.
    model_info Name of the output table containing the model performance and other info for each model selection tuple.
    dependent_varname Dependent variable column from the original source table in the image preprocessing step.
    independent_varname Independent variables column from the original source table in the image preprocessing step.
    model_arch_table Name of the table containing the model architecture and (optionally) the initial model weights.
    model selection table Name of the mst table containing the best configuration.
    automl_method Name of the autoML method used.
    automl_params AutoML parameter values.
    random_state Chosen random seed.
    metrics_compute_frequency Frequency that per-iteration metrics are computed for the training dataset and validation datasets.
    name Name of the training run (free text).
    description Description of the training run (free text).
    start_training_time Timestamp for start of training.
    end_training_time Timestamp for end of training.
    madlib_version Version of MADlib used.
    num_classes Count of distinct classes values used.
    <dependent_varname>_class_values Array of actual class values used for a particular dependent variable. A column will be generated for each dependent variable.
    dependent_vartype Data type of the dependent variable.
    normalizing_constant Normalizing constant used from the image preprocessing step.
    +

    Print Hyperband Schedule
    +

    This utility prints out the schedule for a set of input parameters. It does not run the Hyperband method, rather it just prints out the schedule so you can see what the brackets look like. Refer to [1] for information on Hyperband schedules. 

    +hyperband_schedule(
+    schedule_table,
+    R,
+    eta,
+    skip_last
+    )
+

    Arguments

    +
    schedule_table
    +

    VARCHAR. Name of output table containing hyperband schedule.

    +

    +
    +
    R
    +

    INTEGER. Maximum number of resources (i.e., iterations) to allocate to a single configuration in a round of Hyperband.

    +

    +
    +
    eta
    +

    INTEGER. Controls the proportion of configurations discarded in each round of successive halving. For example, for eta=3 will keep the best 1/3 the configurations for the next round.

    +

    +
    +
    skip_last
    +

    INTEGER. The number of last rounds to skip. For example, 'skip_last=1' will skip the last round (i.e., last entry in each bracket), which is standard random search and can be expensive when run for the total R iterations.

    +

    +
    +
    +

    Output table
    + The hyperband schedule output table contains the following columns:

    + + + + + + + + +
    s INTEGER. Bracket number.
    i INTEGER. Round (depth) in bracket.
    n_i INTEGER. Number of configurations in this round.
    r_i INTEGER. Resources (iterations) in this round.
    +

    Examples
    +
    Note
    Deep learning works best on very large datasets, but that is not convenient for a quick introduction to the syntax. So in this example we use an MLP on the well known iris data set from https://archive.ics.uci.edu/ml/datasets/iris. For more realistic examples with images please refer to the deep learning notebooks at https://github.com/apache/madlib-site/tree/asf-site/community-artifacts.
    +

    Setup

    +
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS iris_data;
+CREATE TABLE iris_data(
+    id serial,
+    attributes numeric[],
+    class_text varchar
+);
+INSERT INTO iris_data(id, attributes, class_text) VALUES
+(1,ARRAY[5.1,3.5,1.4,0.2],'Iris-setosa'),
+(2,ARRAY[4.9,3.0,1.4,0.2],'Iris-setosa'),
+(3,ARRAY[4.7,3.2,1.3,0.2],'Iris-setosa'),
+(4,ARRAY[4.6,3.1,1.5,0.2],'Iris-setosa'),
+(5,ARRAY[5.0,3.6,1.4,0.2],'Iris-setosa'),
+(6,ARRAY[5.4,3.9,1.7,0.4],'Iris-setosa'),
+(7,ARRAY[4.6,3.4,1.4,0.3],'Iris-setosa'),
+(8,ARRAY[5.0,3.4,1.5,0.2],'Iris-setosa'),
+(9,ARRAY[4.4,2.9,1.4,0.2],'Iris-setosa'),
+(10,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(11,ARRAY[5.4,3.7,1.5,0.2],'Iris-setosa'),
+(12,ARRAY[4.8,3.4,1.6,0.2],'Iris-setosa'),
+(13,ARRAY[4.8,3.0,1.4,0.1],'Iris-setosa'),
+(14,ARRAY[4.3,3.0,1.1,0.1],'Iris-setosa'),
+(15,ARRAY[5.8,4.0,1.2,0.2],'Iris-setosa'),
+(16,ARRAY[5.7,4.4,1.5,0.4],'Iris-setosa'),
+(17,ARRAY[5.4,3.9,1.3,0.4],'Iris-setosa'),
+(18,ARRAY[5.1,3.5,1.4,0.3],'Iris-setosa'),
+(19,ARRAY[5.7,3.8,1.7,0.3],'Iris-setosa'),
+(20,ARRAY[5.1,3.8,1.5,0.3],'Iris-setosa'),
+(21,ARRAY[5.4,3.4,1.7,0.2],'Iris-setosa'),
+(22,ARRAY[5.1,3.7,1.5,0.4],'Iris-setosa'),
+(23,ARRAY[4.6,3.6,1.0,0.2],'Iris-setosa'),
+(24,ARRAY[5.1,3.3,1.7,0.5],'Iris-setosa'),
+(25,ARRAY[4.8,3.4,1.9,0.2],'Iris-setosa'),
+(26,ARRAY[5.0,3.0,1.6,0.2],'Iris-setosa'),
+(27,ARRAY[5.0,3.4,1.6,0.4],'Iris-setosa'),
+(28,ARRAY[5.2,3.5,1.5,0.2],'Iris-setosa'),
+(29,ARRAY[5.2,3.4,1.4,0.2],'Iris-setosa'),
+(30,ARRAY[4.7,3.2,1.6,0.2],'Iris-setosa'),
+(31,ARRAY[4.8,3.1,1.6,0.2],'Iris-setosa'),
+(32,ARRAY[5.4,3.4,1.5,0.4],'Iris-setosa'),
+(33,ARRAY[5.2,4.1,1.5,0.1],'Iris-setosa'),
+(34,ARRAY[5.5,4.2,1.4,0.2],'Iris-setosa'),
+(35,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(36,ARRAY[5.0,3.2,1.2,0.2],'Iris-setosa'),
+(37,ARRAY[5.5,3.5,1.3,0.2],'Iris-setosa'),
+(38,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(39,ARRAY[4.4,3.0,1.3,0.2],'Iris-setosa'),
+(40,ARRAY[5.1,3.4,1.5,0.2],'Iris-setosa'),
+(41,ARRAY[5.0,3.5,1.3,0.3],'Iris-setosa'),
+(42,ARRAY[4.5,2.3,1.3,0.3],'Iris-setosa'),
+(43,ARRAY[4.4,3.2,1.3,0.2],'Iris-setosa'),
+(44,ARRAY[5.0,3.5,1.6,0.6],'Iris-setosa'),
+(45,ARRAY[5.1,3.8,1.9,0.4],'Iris-setosa'),
+(46,ARRAY[4.8,3.0,1.4,0.3],'Iris-setosa'),
+(47,ARRAY[5.1,3.8,1.6,0.2],'Iris-setosa'),
+(48,ARRAY[4.6,3.2,1.4,0.2],'Iris-setosa'),
+(49,ARRAY[5.3,3.7,1.5,0.2],'Iris-setosa'),
+(50,ARRAY[5.0,3.3,1.4,0.2],'Iris-setosa'),
+(51,ARRAY[7.0,3.2,4.7,1.4],'Iris-versicolor'),
+(52,ARRAY[6.4,3.2,4.5,1.5],'Iris-versicolor'),
+(53,ARRAY[6.9,3.1,4.9,1.5],'Iris-versicolor'),
+(54,ARRAY[5.5,2.3,4.0,1.3],'Iris-versicolor'),
+(55,ARRAY[6.5,2.8,4.6,1.5],'Iris-versicolor'),
+(56,ARRAY[5.7,2.8,4.5,1.3],'Iris-versicolor'),
+(57,ARRAY[6.3,3.3,4.7,1.6],'Iris-versicolor'),
+(58,ARRAY[4.9,2.4,3.3,1.0],'Iris-versicolor'),
+(59,ARRAY[6.6,2.9,4.6,1.3],'Iris-versicolor'),
+(60,ARRAY[5.2,2.7,3.9,1.4],'Iris-versicolor'),
+(61,ARRAY[5.0,2.0,3.5,1.0],'Iris-versicolor'),
+(62,ARRAY[5.9,3.0,4.2,1.5],'Iris-versicolor'),
+(63,ARRAY[6.0,2.2,4.0,1.0],'Iris-versicolor'),
+(64,ARRAY[6.1,2.9,4.7,1.4],'Iris-versicolor'),
+(65,ARRAY[5.6,2.9,3.6,1.3],'Iris-versicolor'),
+(66,ARRAY[6.7,3.1,4.4,1.4],'Iris-versicolor'),
+(67,ARRAY[5.6,3.0,4.5,1.5],'Iris-versicolor'),
+(68,ARRAY[5.8,2.7,4.1,1.0],'Iris-versicolor'),
+(69,ARRAY[6.2,2.2,4.5,1.5],'Iris-versicolor'),
+(70,ARRAY[5.6,2.5,3.9,1.1],'Iris-versicolor'),
+(71,ARRAY[5.9,3.2,4.8,1.8],'Iris-versicolor'),
+(72,ARRAY[6.1,2.8,4.0,1.3],'Iris-versicolor'),
+(73,ARRAY[6.3,2.5,4.9,1.5],'Iris-versicolor'),
+(74,ARRAY[6.1,2.8,4.7,1.2],'Iris-versicolor'),
+(75,ARRAY[6.4,2.9,4.3,1.3],'Iris-versicolor'),
+(76,ARRAY[6.6,3.0,4.4,1.4],'Iris-versicolor'),
+(77,ARRAY[6.8,2.8,4.8,1.4],'Iris-versicolor'),
+(78,ARRAY[6.7,3.0,5.0,1.7],'Iris-versicolor'),
+(79,ARRAY[6.0,2.9,4.5,1.5],'Iris-versicolor'),
+(80,ARRAY[5.7,2.6,3.5,1.0],'Iris-versicolor'),
+(81,ARRAY[5.5,2.4,3.8,1.1],'Iris-versicolor'),
+(82,ARRAY[5.5,2.4,3.7,1.0],'Iris-versicolor'),
+(83,ARRAY[5.8,2.7,3.9,1.2],'Iris-versicolor'),
+(84,ARRAY[6.0,2.7,5.1,1.6],'Iris-versicolor'),
+(85,ARRAY[5.4,3.0,4.5,1.5],'Iris-versicolor'),
+(86,ARRAY[6.0,3.4,4.5,1.6],'Iris-versicolor'),
+(87,ARRAY[6.7,3.1,4.7,1.5],'Iris-versicolor'),
+(88,ARRAY[6.3,2.3,4.4,1.3],'Iris-versicolor'),
+(89,ARRAY[5.6,3.0,4.1,1.3],'Iris-versicolor'),
+(90,ARRAY[5.5,2.5,4.0,1.3],'Iris-versicolor'),
+(91,ARRAY[5.5,2.6,4.4,1.2],'Iris-versicolor'),
+(92,ARRAY[6.1,3.0,4.6,1.4],'Iris-versicolor'),
+(93,ARRAY[5.8,2.6,4.0,1.2],'Iris-versicolor'),
+(94,ARRAY[5.0,2.3,3.3,1.0],'Iris-versicolor'),
+(95,ARRAY[5.6,2.7,4.2,1.3],'Iris-versicolor'),
+(96,ARRAY[5.7,3.0,4.2,1.2],'Iris-versicolor'),
+(97,ARRAY[5.7,2.9,4.2,1.3],'Iris-versicolor'),
+(98,ARRAY[6.2,2.9,4.3,1.3],'Iris-versicolor'),
+(99,ARRAY[5.1,2.5,3.0,1.1],'Iris-versicolor'),
+(100,ARRAY[5.7,2.8,4.1,1.3],'Iris-versicolor'),
+(101,ARRAY[6.3,3.3,6.0,2.5],'Iris-virginica'),
+(102,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
+(103,ARRAY[7.1,3.0,5.9,2.1],'Iris-virginica'),
+(104,ARRAY[6.3,2.9,5.6,1.8],'Iris-virginica'),
+(105,ARRAY[6.5,3.0,5.8,2.2],'Iris-virginica'),
+(106,ARRAY[7.6,3.0,6.6,2.1],'Iris-virginica'),
+(107,ARRAY[4.9,2.5,4.5,1.7],'Iris-virginica'),
+(108,ARRAY[7.3,2.9,6.3,1.8],'Iris-virginica'),
+(109,ARRAY[6.7,2.5,5.8,1.8],'Iris-virginica'),
+(110,ARRAY[7.2,3.6,6.1,2.5],'Iris-virginica'),
+(111,ARRAY[6.5,3.2,5.1,2.0],'Iris-virginica'),
+(112,ARRAY[6.4,2.7,5.3,1.9],'Iris-virginica'),
+(113,ARRAY[6.8,3.0,5.5,2.1],'Iris-virginica'),
+(114,ARRAY[5.7,2.5,5.0,2.0],'Iris-virginica'),
+(115,ARRAY[5.8,2.8,5.1,2.4],'Iris-virginica'),
+(116,ARRAY[6.4,3.2,5.3,2.3],'Iris-virginica'),
+(117,ARRAY[6.5,3.0,5.5,1.8],'Iris-virginica'),
+(118,ARRAY[7.7,3.8,6.7,2.2],'Iris-virginica'),
+(119,ARRAY[7.7,2.6,6.9,2.3],'Iris-virginica'),
+(120,ARRAY[6.0,2.2,5.0,1.5],'Iris-virginica'),
+(121,ARRAY[6.9,3.2,5.7,2.3],'Iris-virginica'),
+(122,ARRAY[5.6,2.8,4.9,2.0],'Iris-virginica'),
+(123,ARRAY[7.7,2.8,6.7,2.0],'Iris-virginica'),
+(124,ARRAY[6.3,2.7,4.9,1.8],'Iris-virginica'),
+(125,ARRAY[6.7,3.3,5.7,2.1],'Iris-virginica'),
+(126,ARRAY[7.2,3.2,6.0,1.8],'Iris-virginica'),
+(127,ARRAY[6.2,2.8,4.8,1.8],'Iris-virginica'),
+(128,ARRAY[6.1,3.0,4.9,1.8],'Iris-virginica'),
+(129,ARRAY[6.4,2.8,5.6,2.1],'Iris-virginica'),
+(130,ARRAY[7.2,3.0,5.8,1.6],'Iris-virginica'),
+(131,ARRAY[7.4,2.8,6.1,1.9],'Iris-virginica'),
+(132,ARRAY[7.9,3.8,6.4,2.0],'Iris-virginica'),
+(133,ARRAY[6.4,2.8,5.6,2.2],'Iris-virginica'),
+(134,ARRAY[6.3,2.8,5.1,1.5],'Iris-virginica'),
+(135,ARRAY[6.1,2.6,5.6,1.4],'Iris-virginica'),
+(136,ARRAY[7.7,3.0,6.1,2.3],'Iris-virginica'),
+(137,ARRAY[6.3,3.4,5.6,2.4],'Iris-virginica'),
+(138,ARRAY[6.4,3.1,5.5,1.8],'Iris-virginica'),
+(139,ARRAY[6.0,3.0,4.8,1.8],'Iris-virginica'),
+(140,ARRAY[6.9,3.1,5.4,2.1],'Iris-virginica'),
+(141,ARRAY[6.7,3.1,5.6,2.4],'Iris-virginica'),
+(142,ARRAY[6.9,3.1,5.1,2.3],'Iris-virginica'),
+(143,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
+(144,ARRAY[6.8,3.2,5.9,2.3],'Iris-virginica'),
+(145,ARRAY[6.7,3.3,5.7,2.5],'Iris-virginica'),
+(146,ARRAY[6.7,3.0,5.2,2.3],'Iris-virginica'),
+(147,ARRAY[6.3,2.5,5.0,1.9],'Iris-virginica'),
+(148,ARRAY[6.5,3.0,5.2,2.0],'Iris-virginica'),
+(149,ARRAY[6.2,3.4,5.4,2.3],'Iris-virginica'),
+(150,ARRAY[5.9,3.0,5.1,1.8],'Iris-virginica');
+
      Create a test/validation dataset from the training data: 
      +DROP TABLE IF EXISTS iris_train, iris_test;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.train_test_split('iris_data',     -- Source table
+                               'iris',          -- Output table root name
+                                0.8,            -- Train proportion
+                                NULL,           -- Test proportion (0.2)
+                                NULL,           -- Strata definition
+                                NULL,           -- Output all columns
+                                NULL,           -- Sample without replacement
+                                TRUE            -- Separate output tables
+                              );
+SELECT COUNT(*) FROM iris_train;
+
      + count
+------+
+   120
+
      2. +
    2. Call the preprocessor for deep learning. For the training dataset: 
      +\x on
+DROP TABLE IF EXISTS iris_train_packed, iris_train_packed_summary;
+SELECT madlib.training_preprocessor_dl('iris_train',         -- Source table
+                                       'iris_train_packed',  -- Output table
+                                       'class_text',         -- Dependent variable
+                                       'attributes'          -- Independent variable
+                                        );
+SELECT * FROM iris_train_packed_summary;
+
      +-[ RECORD 1 ]-------+---------------------------------------------
+source_table        | iris_train
+output_table        | iris_train_packed
+dependent_varname   | class_text
+independent_varname | attributes
+dependent_vartype   | character varying
+class_values        | {Iris-setosa,Iris-versicolor,Iris-virginica}
+buffer_size         | 60
+normalizing_const   | 1.0
+num_classes         | 3
+
      For the validation dataset: 
      +DROP TABLE IF EXISTS iris_test_packed, iris_test_packed_summary;
+SELECT madlib.validation_preprocessor_dl('iris_test',          -- Source table
+                                         'iris_test_packed',   -- Output table
+                                         'class_text',         -- Dependent variable
+                                         'attributes',         -- Independent variable
+                                         'iris_train_packed'   -- From training preprocessor step
+                                          );
+SELECT * FROM iris_test_packed_summary;
+
      +-[ RECORD 1 ]-------+---------------------------------------------
+source_table        | iris_test
+output_table        | iris_test_packed
+dependent_varname   | class_text
+independent_varname | attributes
+dependent_vartype   | character varying
+class_values        | {Iris-setosa,Iris-versicolor,Iris-virginica}
+buffer_size         | 15
+normalizing_const   | 1.0
+num_classes         | 3
+
      3. +
    3. Define and load model architecture. Use Keras to define the model architecture with 1 hidden layer: 
      +from tensorflow.keras.models import Sequential
+from tensorflow.keras.layers import Dense
+model1 = Sequential()
+model1.add(Dense(10, activation='relu', input_shape=(4,)))
+model1.add(Dense(10, activation='relu'))
+model1.add(Dense(3, activation='softmax'))
+model1.summary()
+
      _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_1 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_2 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_3 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 193
+Trainable params: 193
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model1.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      Define model architecture with 2 hidden layers: 
      +model2 = Sequential()
+model2.add(Dense(10, activation='relu', input_shape=(4,)))
+model2.add(Dense(10, activation='relu'))
+model2.add(Dense(10, activation='relu'))
+model2.add(Dense(3, activation='softmax'))
+model2.summary()
+
      Layer (type)                 Output Shape              Param #
+=================================================================
+dense_4 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_5 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_6 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_7 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 303
+Trainable params: 303
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model2.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      Load into model architecture table: 
      +DROP TABLE IF EXISTS model_arch_library;
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,         -- JSON blob
+                               NULL,                  -- Weights
+                               'Sophie',              -- Name
+                               'MLP with 1 hidden layer'       -- Descr
+);
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,         -- JSON blob
+                               NULL,                  -- Weights
+                               'Maria',               -- Name
+                               'MLP with 2 hidden layers'       -- Descr
+);
+
      4. +
    +

    Hyperband

    +
      +
    1. Print Hyperband schedule for example input parameters 'R=9' and 'eta=3': 
      +DROP TABLE IF EXISTS hb_schedule;
+SELECT madlib.hyperband_schedule ('hb_schedule',
+                                   81,
+                                   3,
+                                   0);
+SELECT * FROM hb_schedule ORDER BY s DESC, i;
+
      + s | i | n_i | r_i
+---+---+-----+-----
+ 4 | 0 |  81 |   1
+ 4 | 1 |  27 |   3
+ 4 | 2 |   9 |   9
+ 4 | 3 |   3 |  27
+ 4 | 4 |   1 |  81
+ 3 | 0 |  27 |   3
+ 3 | 1 |   9 |   9
+ 3 | 2 |   3 |  27
+ 3 | 3 |   1 |  81
+ 2 | 0 |   9 |   9
+ 2 | 1 |   3 |  27
+ 2 | 2 |   1 |  81
+ 1 | 0 |   6 |  27
+ 1 | 1 |   2 |  81
+ 0 | 0 |   5 |  81
+(15 rows)
+
      2. +
    2. Run Hyperband method with 'R=9' and 'eta=3': 
      +DROP TABLE IF EXISTS automl_output, automl_output_info, automl_output_summary, automl_mst_table, automl_mst_table_summary;
+SELECT madlib.madlib_keras_automl('iris_train_packed',                -- source table
+                                  'automl_output',                    -- model output table
+                                  'model_arch_library',               -- model architecture table
+                                  'automl_mst_table',                 -- model selection output table
+                                  ARRAY[1,2],                         -- model IDs
+                                  $${
+                                      'loss': ['categorical_crossentropy'],
+                                      'optimizer_params_list': [
+                                          {'optimizer': ['Adam'],'lr': [0.001, 0.1, 'log']},
+                                          {'optimizer': ['RMSprop'],'lr': [0.001, 0.1, 'log']}
+                                      ],
+                                      'metrics': ['accuracy']
+                                  } $$,                               -- compile param grid
+                                  $${'batch_size': [4, 8], 'epochs': [1]}$$,  -- fit params grid
+                                  'hyperband',                        -- autoML method
+                                  'R=9, eta=3, skip_last=0',          -- autoML params
+                                  NULL,                               -- random state
+                                  NULL,                               -- object table
+                                  FALSE,                              -- use GPUs
+                                  'iris_test_packed',                 -- validation table
+                                  1,                                  -- metrics compute freq
+                                  NULL,                               -- name
+                                  NULL);                              -- descr
+
      3. +
    3. View the model summary: 
      +SELECT * FROM automl_output_summary;
+
      +-[ RECORD 1 ]-------------+---------------------------------------------
+source_table              | iris_train_packed
+validation_table          | iris_test_packed
+model                     | automl_output
+model_info                | automl_output_info
+dependent_varname         | class_text
+independent_varname       | attributes
+model_arch_table          | model_arch_library
+model_selection_table     | automl_mst_table
+automl_method             | hyperband
+automl_params             | R=9, eta=3, skip_last=0
+random_state              |
+object_table              |
+use_gpus                  | f
+metrics_compute_frequency | 1
+name                      |
+description               |
+start_training_time       | 2021-01-16 01:20:17
+end_training_time         | 2021-01-16 01:21:47
+madlib_version            | 2.1.0
+num_classes               | 3
+class_values              | {Iris-setosa,Iris-versicolor,Iris-virginica}
+dependent_vartype         | character varying
+normalizing_const         | 1
+
      4. +
    4. View results for a few models: 
      +SELECT * FROM automl_output_info ORDER BY validation_metrics_final DESC, validation_loss_final LIMIT 3;
+
      +-[ RECORD 1 ]------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------
+mst_key                  | 15
+model_id                 | 1
+compile_params           | optimizer='Adam(lr=0.005948073640447284)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'
+fit_params               | epochs=1,batch_size=8
+model_type               | madlib_keras
+model_size               | 0.7900390625
+metrics_elapsed_time     | {41.9598820209503,47.7600600719452,53.5559930801392,59.2904281616211,65.0303740501404,70.910637140274,76.6586999893188,82.3321261405945,88.0252130031586}
+metrics_type             | {accuracy}
+loss_type                | categorical_crossentropy
+training_metrics_final   | 0.975000023841858
+training_loss_final      | 0.174209594726562
+training_metrics         | {0.683333337306976,0.683333337306976,0.816666662693024,0.791666686534882,0.966666638851166,0.850000023841858,0.966666638851166,0.966666638851166,0.975000023841858}
+training_loss            | {0.658287584781647,0.56329345703125,0.489711940288544,0.417204052209854,0.333063006401062,0.325938105583191,0.237209364771843,0.216858893632889,0.174209594726562}
+validation_metrics_final | 0.933333337306976
+validation_loss_final    | 0.282542854547501
+validation_metrics       | {0.600000023841858,0.600000023841858,0.733333349227905,0.733333349227905,0.899999976158142,0.800000011920929,0.933333337306976,0.899999976158142,0.933333337306976}
+validation_loss          | {0.844917356967926,0.739157736301422,0.651688754558563,0.567608654499054,0.458681106567383,0.461867392063141,0.344642341136932,0.335768848657608,0.282542854547501}
+metrics_iters            | {5,6,7,8,9,10,11,12,13}
+s                        | 0
+i                        | 0
+-[ RECORD 2 ]------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------
+mst_key                  | 10
+model_id                 | 1
+compile_params           | optimizer='RMSprop(lr=0.01152123686692268)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'
+fit_params               | epochs=1,batch_size=8
+model_type               | madlib_keras
+model_size               | 0.7900390625
+metrics_elapsed_time     | {21.1628739833832,27.9904689788818,34.9025909900665}
+metrics_type             | {accuracy}
+loss_type                | categorical_crossentropy
+training_metrics_final   | 0.933333337306976
+training_loss_final      | 0.239687830209732
+training_metrics         | {0.699999988079071,0.699999988079071,0.933333337306976}
+training_loss            | {0.600760638713837,0.386314034461975,0.239687830209732}
+validation_metrics_final | 0.899999976158142
+validation_loss_final    | 0.369663149118423
+validation_metrics       | {0.533333361148834,0.600000023841858,0.899999976158142}
+validation_loss          | {0.723896682262421,0.539595663547516,0.369663149118423}
+metrics_iters            | {2,3,4}
+s                        | 1
+i                        | 0
+-[ RECORD 3 ]------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------
+mst_key                  | 2
+model_id                 | 1
+compile_params           | optimizer='RMSprop(lr=0.005464438486993435)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'
+fit_params               | epochs=1,batch_size=4
+model_type               | madlib_keras
+model_size               | 0.7900390625
+metrics_elapsed_time     | {11.6164019107819,20.9570059776306,27.7901480197906,34.7061359882355}
+metrics_type             | {accuracy}
+loss_type                | categorical_crossentropy
+training_metrics_final   | 0.925000011920929
+training_loss_final      | 0.17901936173439
+training_metrics         | {0.949999988079071,0.883333325386047,0.958333313465118,0.925000011920929}
+training_loss            | {0.547602951526642,0.321837723255157,0.197886273264885,0.17901936173439}
+validation_metrics_final | 0.866666674613953
+validation_loss_final    | 0.325421392917633
+validation_metrics       | {0.866666674613953,0.800000011920929,0.899999976158142,0.866666674613953}
+validation_loss          | {0.723824441432953,0.462396681308746,0.326263695955276,0.325421392917633}
+metrics_iters            | {1,2,3,4}
+s                        | 2
+i                        | 1
+
      5. +
    +

    Hyperopt

    +
      +
    1. Run Hyperopt for a set number of trials, i.e., model configurations: 
      +DROP TABLE IF EXISTS automl_output, automl_output_info, automl_output_summary, automl_mst_table, automl_mst_table_summary;
+SELECT madlib.madlib_keras_automl('iris_train_packed',                -- source table
+                                  'automl_output',                    -- model output table
+                                  'model_arch_library',               -- model architecture table
+                                  'automl_mst_table',                 -- model selection output table
+                                  ARRAY[1,2],                         -- model IDs
+                                  $${
+                                      'loss': ['categorical_crossentropy'],
+                                      'optimizer_params_list': [
+                                          {'optimizer': ['Adam'],'lr': [0.001, 0.1, 'log']},
+                                          {'optimizer': ['RMSprop'],'lr': [0.001, 0.1, 'log']}
+                                      ],
+                                      'metrics': ['accuracy']
+                                  } $$,                               -- compile param grid
+                                  $${'batch_size': [4, 8], 'epochs': [1]}$$,  -- fit params grid
+                                  'hyperopt',                         -- autoML method
+                                  'num_configs=20, num_iterations=10, algorithm=tpe',  -- autoML params
+                                  NULL,                               -- random state
+                                  NULL,                               -- object table
+                                  FALSE,                              -- use GPUs
+                                  'iris_test_packed',                 -- validation table
+                                  1,                                  -- metrics compute freq
+                                  NULL,                               -- name
+                                  NULL);                              -- descr
+
      2. +
    2. View the model summary: 
      +SELECT * FROM automl_output_summary;
+
      +-[ RECORD 1 ]-------------+-------------------------------------------------
+source_table              | iris_train_packed
+validation_table          | iris_test_packed
+model                     | automl_output
+model_info                | automl_output_info
+dependent_varname         | class_text
+independent_varname       | attributes
+model_arch_table          | model_arch_library
+model_selection_table     | automl_mst_table
+automl_method             | hyperopt
+automl_params             | num_configs=20, num_iterations=10, algorithm=tpe
+random_state              |
+object_table              |
+use_gpus                  | f
+metrics_compute_frequency | 1
+name                      |
+description               |
+start_training_time       | 2020-10-23 00:24:43
+end_training_time         | 2020-10-23 00:28:41
+madlib_version            | 2.1.0
+num_classes               | 3
+class_values              | {Iris-setosa,Iris-versicolor,Iris-virginica}
+dependent_vartype         | character varying
+normalizing_const         | 1
+
      3. +
    3. View results for a few models: 
      +SELECT * FROM automl_output_info ORDER BY validation_metrics_final DESC, validation_loss_final LIMIT 3;
+
      +-[ RECORD 1]----------------------------------------------------------------------------------------------------------
+mst_key                  | 4
+model_id                 | 1
+compile_params           | optimizer='Adam(lr=0.021044174547856155)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'
+fit_params               | epochs=1,batch_size=8
+model_type               | madlib_keras
+model_size               | 0.7900390625
+metrics_elapsed_time     | {24.9291331768036,27.1591901779175,29.3875880241394,31.4712460041046,33.6599950790405,35.9415881633759,38.0477111339569,40.2351109981537,42.3932039737701,44.4729251861572}
+metrics_type             | {accuracy}
+loss_type                | categorical_crossentropy
+training_metrics_final   | 0.958333313465118
+training_loss_final      | 0.116280987858772
+training_metrics         | {0.658333361148834,0.658333361148834,0.733333349227905,0.816666662693024,0.949999988079071,0.949999988079071,0.949999988079071,0.875,0.958333313465118,0.958333313465118}
+training_loss            | {0.681611657142639,0.50702965259552,0.41643014550209,0.349031865596771,0.2586330473423,0.234042942523956,0.204623967409134,0.337687611579895,0.116805233061314,0.116280987858772}
+validation_metrics_final | 1
+validation_loss_final    | 0.067971371114254
+validation_metrics       | {0.699999988079071,0.699999988079071,0.733333349227905,0.766666650772095,0.899999976158142,0.899999976158142,0.899999976158142,0.899999976158142,1,1}
+validation_loss          | {0.523795306682587,0.386897593736649,0.323715627193451,0.29447802901268,0.218715354800224,0.216124311089516,0.186037495732307,0.257792592048645,0.0693960413336754,0.067971371114254}
+metrics_iters            | {1,2,3,4,5,6,7,8,9,10}
+-[ RECORD 2]----------------------------------------------------------------------------------------------------------
+mst_key                  | 8
+model_id                 | 1
+compile_params           | optimizer='RMSprop(lr=0.055711748803920255)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'
+fit_params               | epochs=1,batch_size=4
+model_type               | madlib_keras
+model_size               | 0.7900390625
+metrics_elapsed_time     | {68.9713232517242,71.1428651809692,73.0566282272339,75.2099182605743,77.4740402698517,79.4580070972443,81.5958452224731,83.6865520477295,85.6433861255646,87.8569240570068}
+metrics_type             | {accuracy}
+loss_type                | categorical_crossentropy
+training_metrics_final   | 0.966666638851166
+training_loss_final      | 0.106823824346066
+training_metrics         | {0.658333361148834,0.699999988079071,0.875,0.691666662693024,0.699999988079071,0.791666686534882,0.774999976158142,0.966666638851166,0.966666638851166,0.966666638851166}
+training_loss            | {0.681002557277679,0.431159198284149,0.418115794658661,0.51969450712204,0.605500161647797,0.36535832285881,0.451890885829926,0.126570284366608,0.116986438632011,0.106823824346066}
+validation_metrics_final | 1
+validation_loss_final    | 0.0758842155337334
+validation_metrics       | {0.699999988079071,0.699999988079071,0.966666638851166,0.699999988079071,0.699999988079071,0.800000011920929,0.766666650772095,0.966666638851166,0.966666638851166,1}
+validation_loss          | {0.693905889987946,0.364648938179016,0.287941485643387,0.509377717971802,0.622031152248383,0.377092003822327,0.488217085599899,0.10258474200964,0.0973251685500145,0.0758842155337334}
+metrics_iters            | {1,2,3,4,5,6,7,8,9,10}
+-[ RECORD 3]----------------------------------------------------------------------------------------------------------
+mst_key                  | 13
+model_id                 | 1
+compile_params           | optimizer='RMSprop(lr=0.006381376508189085)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'
+fit_params               | epochs=1,batch_size=4
+model_type               | madlib_keras
+model_size               | 0.7900390625
+metrics_elapsed_time     | {141.029213190079,143.075024366379,145.330604314804,147.341159343719,149.579845190048,151.819869279861,153.939630270004,156.235336303711,158.536979198456,160.583434343338}
+metrics_type             | {accuracy}
+loss_type                | categorical_crossentropy
+training_metrics_final   | 0.975000023841858
+training_loss_final      | 0.0981351062655449
+training_metrics         | {0.875,0.933333337306976,0.875,0.975000023841858,0.975000023841858,0.908333361148834,0.949999988079071,0.966666638851166,0.975000023841858,0.975000023841858}
+training_loss            | {0.556384921073914,0.32896700501442,0.29009011387825,0.200998887419701,0.149432390928268,0.183790743350983,0.120595499873161,0.12202025949955,0.101290702819824,0.0981351062655449}
+validation_metrics_final | 1
+validation_loss_final    | 0.0775858238339424
+validation_metrics       | {0.899999976158142,0.966666638851166,0.766666650772095,1,1,0.933333337306976,0.966666638851166,0.966666638851166,1,1}
+validation_loss          | {0.442976772785187,0.249921068549156,0.268403559923172,0.167330235242844,0.134699374437332,0.140658855438232,0.0964709892868996,0.110730975866318,0.0810751244425774,0.0775858238339424}
+metrics_iters            | {1,2,3,4,5,6,7,8,9,10}
+
      4. +
    4. Run inference on one of the models generated by Hyperopt. In this example we use the validation set to predict on: 
      +DROP TABLE IF EXISTS iris_predict;
+SELECT madlib.madlib_keras_predict('automl_output',    -- model
+                                   'iris_test',        -- test_table
+                                   'id',               -- id column
+                                   'attributes',       -- independent var
+                                   'iris_predict',     -- output table
+                                    'response',        -- prediction type
+                                    FALSE,             -- use gpus
+                                    4                 -- MST key
+                                   );
+SELECT * FROM iris_predict ORDER BY id;
+
      + id  |   class_text    |    prob
+-----+-----------------+------------
+   5 | Iris-setosa     |  0.9998704
+   7 | Iris-setosa     | 0.99953365
+  10 | Iris-setosa     |  0.9993413
+  16 | Iris-setosa     |  0.9999825
+  17 | Iris-setosa     |  0.9999256
+  21 | Iris-setosa     |  0.9995347
+  23 | Iris-setosa     |  0.9999405
+  27 | Iris-setosa     |  0.9989955
+  30 | Iris-setosa     |  0.9990559
+  31 | Iris-setosa     |  0.9986846
+  32 | Iris-setosa     |  0.9992879
+  37 | Iris-setosa     | 0.99987197
+  39 | Iris-setosa     |  0.9989151
+  46 | Iris-setosa     |  0.9981341
+  47 | Iris-setosa     |  0.9999044
+  53 | Iris-versicolor |  0.9745001
+  54 | Iris-versicolor |  0.8989025
+  56 | Iris-versicolor | 0.97066855
+  63 | Iris-versicolor | 0.96652734
+  71 | Iris-versicolor | 0.84569126
+  77 | Iris-versicolor |  0.9564522
+  83 | Iris-versicolor |  0.9664927
+  85 | Iris-versicolor | 0.96553373
+  93 | Iris-versicolor | 0.96748537
+ 103 | Iris-virginica  |  0.9343488
+ 108 | Iris-virginica  | 0.91668576
+ 117 | Iris-virginica  |  0.7323582
+ 124 | Iris-virginica  | 0.72906417
+ 132 | Iris-virginica  | 0.50430095
+ 144 | Iris-virginica  |  0.9487652
+(30 rows)
+
      5. +
    +

    Notes
    +
      +
    1. Hyperopt must be installed on the main node of the database cluster if you want to use the Hyperopt method of autoML. You can pip install it in the usual way [3]. Hyperband does not require any separate package installation.
      2. +
    2. In practice you may need to do more than one run of an autoML method to arrive at a model with adequate accuracy. One approach is to set the search space to be quite broad initially, then observe which hyperparameter ranges and model architectures seem to be doing the best. Subesquent runs can then zoom in on those good ones in order to fine tune the model.
      3. +
    +

    Literature
    +

    [1] Li et al., "Hyperband: A Novel Bandit-Based Approach to +Hyperparameter Optimization", Journal of Machine Learning Research 18 (2018) 1-52.

    +

    [2] J. Bergstra, D. Yamins, D. D. Cox, "Making a Science of Model Search: +Hyperparameter Optimization in Hundreds of Dimensions for Vision Architectures," Proceedings of the 30th International Conference on Machine Learning, Atlanta, Georgia, USA, 2013. JMLR: W&CP volume 28.

    +

    [3] Python catalog for Hyperopt https://pypi.org/project/hyperopt/

    +

    Related Topics
    +

    madlib_keras_automl.sql_in

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__balance__sampling.html b/docs/docs/v2.1.0/group__grp__balance__sampling.html new file mode 100644 index 00000000..238ce12b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__balance__sampling.html @@ -0,0 +1,591 @@ + + + + + + + + +MADlib: Balanced Sampling + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
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    +
    +
    Balanced Sampling
    Sampling
    +
    +
    +
    Contents +

    Some classification algorithms only perform optimally when the number of samples in each class is roughly the same. Highly skewed datasets are common in many domains (e.g., fraud detection), so resampling to offset this imbalance can produce a better decision boundary.

    +

    This module offers a number of resampling techniques including undersampling majority classes, oversampling minority classes, and combinations of the two.

    +

    Balanced Sampling
    +
    +balance_sample( source_table,
+                output_table,
+                class_col,
+                class_sizes,
+                output_table_size,
+                grouping_cols,
+                with_replacement,
+                keep_null
+              )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the input data.

    +

    +
    +
    output_table
    +

    TEXT. Name of output table that contains the sampled data. The output table contains all columns present in the source table, plus a new generated id called "__madlib_id__" added as the first column.

    +

    +
    +
    class_col
    +

    TEXT, Name of the column containing the class to be balanced.

    +

    +
    +
    class_sizes (optional)
    +

    VARCHAR, default ‘uniform’. Parameter to define the size of the different class values. (Class values are sometimes also called levels). Can be set to the following:

    +
      +
    • +‘uniform’: All class values will be resampled to have the same number of rows.
      • +
    • +'undersample': Undersample such that all class values end up with the same number of observations as the minority class. Done without replacement by default unless the parameter ‘with_replacement’ is set to TRUE.
      • +
    • +'oversample': Oversample with replacement such that all class values end up with the same number of observations as the majority class. Not affected by the parameter ‘with_replacement’ since oversampling is always done with replacement. Short forms of the above will work too, e.g., 'uni' works the same as 'uniform'.
      • +
    +

    Alternatively, you can also explicitly set class size in a string containing a comma-delimited list. Order does not matter and all class values do not need to be specified. Use the format “class_value_1=x, class_value_2=y, …” where 'class_value' in the list must exist in the column 'class_col'. Set to an integer representing the desired number of observations. E.g., ‘red=3000, blue=4000’ means you want to resample the dataset to result in exactly 3000 red and 4000 blue rows in the ‘output_table’.

    +
    Note
    The allowed names for class values follows object naming rules in PostgreSQL [1]. Quoted identifiers are allowed and should be enclosed in double quotes in the usual way. If for some reason the class values in the examples above were “ReD” and “BluE” then the comma delimited list for ‘class_size’ would be: ‘“ReD”=3000, “BluE”=4000’.
    +
    +
    output_table_size (optional)
    +

    INTEGER, default NULL. Desired size of the output data set. This parameter is ignored if ‘class_size’ parameter is set to either ‘oversample’ or ‘undersample’ since output table size is already determined. If NULL, the resulting output table size will depend on the settings for the ‘class_size’ parameter (see table below for more details).

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. A single column or a list of comma-separated columns that defines the strata. When this parameter is NULL, no grouping is used so the sampling is non-stratified, that is, the whole table is treated as a single group.

    +
    Note
    The 'output_table_size' and the 'class_sizes' are defined for the whole table. When grouping is used, these parameters are split evenly for each group. Further, if a specific class value is specified in the 'class_sizes' parameter, that particular class value should be present in each group. If not, an error will be thrown.
    +
    +
    with_replacement (optional)
    +

    BOOLEAN, default FALSE. Determines whether to sample with replacement or without replacement (default). With replacement means that it is possible that the same row may appear in the sample set more than once. Without replacement means a given row can be selected only once. This parameter affects undersampling only since oversampling is always done with replacement.

    +

    +
    +
    keep_null (optional)
    +
    BOOLEAN, default FALSE. Determines whether to sample rows whose class values are NULL. By default, all rows with NULL class values are ignored. If this is set to TRUE, then NULL is treated as another class value.
    +
    +

    How Output Table Size is Determined

    +

    The rule of thumb is that if you specify a value for 'output_table_size', then you will generally get an output table of that size, with some minor rounding variations. If you set 'output_table_size' to NULL, then the size of the output table will be calculated depending on what you put for the 'class_size' parameter. The following table shows how the parameters 'class_size' and 'output_table_size' work together:

    + + + + + + + + + + + + + + + + + + + +
    Case 'class_size' 'output_table_size' Result
    1 'uniform' NULL Resample for uniform class size with output size = input size (i.e., balanced).
    2 'uniform' 10000 Resample for uniform class size with output size = 10K (i.e., balanced).
    3 NULL NULL Resample for uniform class size with output size = input size (i.e., balanced). Class_size=NULL has same behavior as ‘uniform’.
    4 NULL 10000 Resample for uniform class size with output size = 10K (i.e., balanced). Class_size=NULL has same behavior as ‘uniform’.
    5 'undersample' n/a Undersample such that all class values end up with the same number of observations as the minority.
    6 'oversample' n/a Oversample with replacement (always) such that all class values end up with the same number of observations as the majority.
    7 'red=3000' NULL Resample red to 3K, leave rest of the class values (blue, green, etc.) as is.
    8 'red=3000, blue=4000' 10000 Resample red to 3K and blue to 4K, divide remaining class values evenly 3K/(n-2) each, where n=number of class values. Note that if red and blue are the only class values, then output table size will be 7K not 10K. (This is the only case where specifying a value for 'output_table_size' may not actually result in an output table of that size.)
    +

    Examples
    +

    Note that due to the random nature of sampling, your results may look different from those below.

    +
      +
    1. Create an input table using part of the flags data set from https://archive.ics.uci.edu/ml/datasets/Flags : 
      +DROP TABLE IF EXISTS flags;
+CREATE TABLE flags (
+    id INTEGER,
+    name TEXT,
+    landmass INTEGER,
+    zone INTEGER,
+    area INTEGER,
+    population INTEGER,
+    language INTEGER,
+    colours INTEGER,
+    mainhue TEXT
+);
+INSERT INTO flags VALUES
+(1, 'Argentina', 2, 3, 2777, 28, 2, 2, 'blue'),
+(2, 'Australia', 6, 2, 7690, 15, 1, 3, 'blue'),
+(3, 'Austria', 3, 1, 84, 8, 4, 2, 'red'),
+(4, 'Brazil', 2, 3, 8512, 119, 6, 4, 'green'),
+(5, 'Canada', 1, 4, 9976, 24, 1, 2, 'red'),
+(6, 'China', 5, 1, 9561, 1008, 7, 2, 'red'),
+(7, 'Denmark', 3, 1, 43, 5, 6, 2, 'red'),
+(8, 'Greece', 3, 1, 132, 10, 6, 2, 'blue'),
+(9, 'Guatemala', 1, 4, 109, 8, 2, 2, 'blue'),
+(10, 'Ireland', 3, 4, 70, 3, 1, 3, 'white'),
+(11, 'Jamaica', 1, 4, 11, 2, 1, 3, 'green'),
+(12, 'Luxembourg', 3, 1, 3, 0, 4, 3, 'red'),
+(13, 'Mexico', 1, 4, 1973, 77, 2, 4, 'green'),
+(14, 'Norway', 3, 1, 324, 4, 6, 3, 'red'),
+(15, 'Portugal', 3, 4, 92, 10, 6, 5, 'red'),
+(16, 'Spain', 3, 4, 505, 38, 2, 2, 'red'),
+(17, 'Sweden', 3, 1, 450, 8, 6, 2, 'blue'),
+(18, 'Switzerland', 3, 1, 41, 6, 4, 2, 'red'),
+(19, 'UK', 3, 4, 245, 56, 1, 3, 'red'),
+(20, 'USA', 1, 4, 9363, 231, 1, 3, 'white'),
+(21, 'xElba', 3, 1, 1, 1, 6, NULL, NULL),
+(22, 'xPrussia', 3, 1, 249, 61, 4, NULL, NULL);
+
      2. +
    2. Uniform sampling. All class values will be resampled so that they have the same number of rows. The output data size will be the same as the input data size, ignoring NULL values. Uniform sampling is the default for the 'class_size' parameter so we do not need to explicitly set it: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue');          -- Class column
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+             5 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+             2 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+             3 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             4 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             1 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+            11 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            12 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            14 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            15 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            13 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             8 |  3 | Austria     |        3 |    1 |   84 |          8 |        4 |       2 | red
+            10 |  5 | Canada      |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             9 |  7 | Denmark     |        3 |    1 |   43 |          5 |        6 |       2 | red
+             6 | 15 | Portugal    |        3 |    4 |   92 |         10 |        6 |       5 | red
+             7 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+            19 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            20 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            18 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            16 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+            17 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(20 rows)
+
      Next we do uniform sampling again, but this time we specify a size for the output table: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                              'uniform',           -- Uniform sample
+                               12);                -- Desired output table size
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |   name    | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-----------+----------+------+------+------------+----------+---------+---------
+            10 |  1 | Argentina |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            12 |  2 | Australia |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+            11 |  8 | Greece    |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             2 |  4 | Brazil    |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             3 | 11 | Jamaica   |        1 |    4 |   11 |          2 |        1 |       3 | green
+             1 | 13 | Mexico    |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             5 |  7 | Denmark   |        3 |    1 |   43 |          5 |        6 |       2 | red
+             6 | 14 | Norway    |        3 |    1 |  324 |          4 |        6 |       3 | red
+             4 | 15 | Portugal  |        3 |    4 |   92 |         10 |        6 |       5 | red
+             9 | 10 | Ireland   |        3 |    4 |   70 |          3 |        1 |       3 | white
+             7 | 20 | USA       |        1 |    4 | 9363 |        231 |        1 |       3 | white
+             8 | 20 | USA       |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(12 rows)
+
      3. +
    3. Oversampling. Oversample with replacement such that all class values except NULLs end up with the same number of observations as the majority class. Countries with red flags is the majority class with 10 observations, so other class values will be oversampled to 10 observations: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                              'oversample');       -- Oversample
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+            35 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            33 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            37 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            34 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            36 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            32 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            31 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+            39 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+            38 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+            40 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+            19 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            20 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            12 | 11 | Jamaica     |        1 |    4 |   11 |          2 |        1 |       3 | green
+            11 | 11 | Jamaica     |        1 |    4 |   11 |          2 |        1 |       3 | green
+            13 | 11 | Jamaica     |        1 |    4 |   11 |          2 |        1 |       3 | green
+            17 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            15 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            16 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            18 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            14 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             9 |  3 | Austria     |        3 |    1 |   84 |          8 |        4 |       2 | red
+             8 |  5 | Canada      |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             1 |  6 | China       |        5 |    1 | 9561 |       1008 |        7 |       2 | red
+            10 |  7 | Denmark     |        3 |    1 |   43 |          5 |        6 |       2 | red
+             2 | 12 | Luxembourg  |        3 |    1 |    3 |          0 |        4 |       3 | red
+             4 | 14 | Norway      |        3 |    1 |  324 |          4 |        6 |       3 | red
+             6 | 15 | Portugal    |        3 |    4 |   92 |         10 |        6 |       5 | red
+             3 | 16 | Spain       |        3 |    4 |  505 |         38 |        2 |       2 | red
+             5 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+             7 | 19 | UK          |        3 |    4 |  245 |         56 |        1 |       3 | red
+            22 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            26 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            24 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            21 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            27 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            25 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            23 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            29 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+            30 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+            28 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(40 rows)
+
      4. +
    4. Undersampling. Undersample such that all class values except NULLs end up with the same number of observations as the minority class. Countries with white flags is the minority class with 2 observations, so other class values will be undersampled to 2 observations: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                              'undersample');      -- Undersample
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+             1 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+             2 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+             4 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             3 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             5 | 16 | Spain       |        3 |    4 |  505 |         38 |        2 |       2 | red
+             6 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+             8 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+             7 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(8 rows)
+
      We may also want to undersample with replacement, so we set the 'with_replacement' parameter to TRUE: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                              'undersample',       -- Undersample
+                               NULL,               -- Output table size will be calculated
+                               NULL,               -- No grouping
+                              'TRUE');             -- Sample with replacement
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |   name    | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-----------+----------+------+------+------------+----------+---------+---------
+             2 |  9 | Guatemala |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             1 |  9 | Guatemala |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             3 |  4 | Brazil    |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             4 | 13 | Mexico    |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             6 |  5 | Canada    |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             5 | 19 | UK        |        3 |    4 |  245 |         56 |        1 |       3 | red
+             7 | 20 | USA       |        1 |    4 | 9363 |        231 |        1 |       3 | white
+             8 | 20 | USA       |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(8 rows)
+
      Note above that some rows may appear multiple times above since we sampled with replacement.
      5. +
    5. Setting class size by count. Here we set the number of rows for red and blue flags, and leave green and white flags unchanged: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                              'red=7, blue=7');    -- Want 7 reds and 7 blues
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |    name    | landmass | zone | area | population | language | colours | mainhue
+---------------+----+------------+----------+------+------+------------+----------+---------+---------
+             5 |  2 | Australia  |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+             7 |  8 | Greece     |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             6 |  8 | Greece     |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             1 |  9 | Guatemala  |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             3 | 17 | Sweden     |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             2 | 17 | Sweden     |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             4 | 17 | Sweden     |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             8 |  4 | Brazil     |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            18 | 11 | Jamaica    |        1 |    4 |   11 |          2 |        1 |       3 | green
+            19 | 13 | Mexico     |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            13 |  3 | Austria    |        3 |    1 |   84 |          8 |        4 |       2 | red
+            14 |  5 | Canada     |        1 |    4 | 9976 |         24 |        1 |       2 | red
+            17 |  6 | China      |        5 |    1 | 9561 |       1008 |        7 |       2 | red
+            15 | 12 | Luxembourg |        3 |    1 |    3 |          0 |        4 |       3 | red
+            16 | 14 | Norway     |        3 |    1 |  324 |          4 |        6 |       3 | red
+            11 | 15 | Portugal   |        3 |    4 |   92 |         10 |        6 |       5 | red
+            12 | 16 | Spain      |        3 |    4 |  505 |         38 |        2 |       2 | red
+             9 | 10 | Ireland    |        3 |    4 |   70 |          3 |        1 |       3 | white
+            10 | 20 | USA        |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(19 rows)
+
      Next we set the number of rows for red and blue flags, and also set an output table size. This means that green and white flags will be uniformly sampled to get to the desired output table size: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                              'red=7, blue=7',     -- Want 7 reds and 7 blues
+                               22);                -- Desired output table size
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+            16 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            20 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+            21 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+            22 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+            18 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+            19 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+            17 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             9 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            10 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             8 | 11 | Jamaica     |        1 |    4 |   11 |          2 |        1 |       3 | green
+            11 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             6 |  3 | Austria     |        3 |    1 |   84 |          8 |        4 |       2 | red
+             7 |  5 | Canada      |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             2 |  7 | Denmark     |        3 |    1 |   43 |          5 |        6 |       2 | red
+             1 | 12 | Luxembourg  |        3 |    1 |    3 |          0 |        4 |       3 | red
+             3 | 15 | Portugal    |        3 |    4 |   92 |         10 |        6 |       5 | red
+             5 | 16 | Spain       |        3 |    4 |  505 |         38 |        2 |       2 | red
+             4 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+            14 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            13 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            15 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            12 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+(22 rows)
+
      6. +
    6. To make NULL a valid class value, set the parameter to keep NULLs: 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+                              'flags',             -- Source table
+                              'output_table',      -- Output table
+                              'mainhue',           -- Class column
+                               NULL,               -- Uniform
+                               NULL,               -- Output table size
+                               NULL,               -- No grouping
+                               NULL,               -- Sample without replacement
+                              'TRUE');             -- Make NULLs a valid class value
+SELECT * FROM output_table ORDER BY mainhue, name;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+            25 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+            22 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+            24 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+            21 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+            23 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             7 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             6 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+            10 | 11 | Jamaica     |        1 |    4 |   11 |          2 |        1 |       3 | green
+             8 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             9 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             3 |  3 | Austria     |        3 |    1 |   84 |          8 |        4 |       2 | red
+             1 |  5 | Canada      |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             2 | 16 | Spain       |        3 |    4 |  505 |         38 |        2 |       2 | red
+             4 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+             5 | 19 | UK          |        3 |    4 |  245 |         56 |        1 |       3 | red
+            13 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            11 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            14 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            12 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+            15 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+            17 | 21 | xElba       |        3 |    1 |    1 |          1 |        6 |         |
+            18 | 21 | xElba       |        3 |    1 |    1 |          1 |        6 |         |
+            16 | 21 | xElba       |        3 |    1 |    1 |          1 |        6 |         |
+            20 | 22 | xPrussia    |        3 |    1 |  249 |         61 |        4 |         |
+            19 | 22 | xPrussia    |        3 |    1 |  249 |         61 |        4 |         |
+(25 rows)
+
      7. +
    7. To perform the balance sampling for independent groups, use the 'grouping_cols' parameter. Note below that each group (zone) has a different count of the classes (mainhue), with some groups not containing some class values. 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+    'flags',          -- Source table
+    'output_table',   -- Output table
+    'mainhue',        -- Class column
+    NULL,             -- Uniform
+    NULL,             -- Output table size
+    'zone'            -- Grouping by zone
+);
+SELECT * FROM output_table ORDER BY zone, mainhue;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+             6 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             5 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             8 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             7 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             2 |  7 | Denmark     |        3 |    1 |   43 |          5 |        6 |       2 | red
+             1 |  6 | China       |        5 |    1 | 9561 |       1008 |        7 |       2 | red
+             4 | 12 | Luxembourg  |        3 |    1 |    3 |          0 |        4 |       3 | red
+             3 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+             1 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+             1 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+             2 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             6 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             5 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             4 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+            12 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            10 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+            11 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             1 | 19 | UK          |        3 |    4 |  245 |         56 |        1 |       3 | red
+             3 |  5 | Canada      |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             2 | 15 | Portugal    |        3 |    4 |   92 |         10 |        6 |       5 | red
+             8 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+             7 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+             9 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+(23 rows)
+
      8. +
    8. Grouping can be used with class size specification as well. Note below that 'blue=<Integer>' is the only valid class value since 'blue' is the only class value that is present in each group. Further, 'blue=8' will be split between the four groups, resulting in two blue rows for each group. 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.balance_sample(
+    'flags',          -- Source table
+    'output_table',   -- Output table
+    'mainhue',        -- Class column
+    'blue=8',         -- Specified class value size. Rest of the values are outputed as is.
+    NULL,             -- Output table size
+    'zone'            -- Group by zone
+);
+SELECT * FROM output_table ORDER BY zone, mainhue;
+
      + __madlib_id__ | id |    name     | landmass | zone | area | population | language | colours | mainhue
+---------------+----+-------------+----------+------+------+------------+----------+---------+---------
+             2 | 17 | Sweden      |        3 |    1 |  450 |          8 |        6 |       2 | blue
+             1 |  8 | Greece      |        3 |    1 |  132 |         10 |        6 |       2 | blue
+             3 |  3 | Austria     |        3 |    1 |   84 |          8 |        4 |       2 | red
+             5 |  7 | Denmark     |        3 |    1 |   43 |          5 |        6 |       2 | red
+             4 |  6 | China       |        5 |    1 | 9561 |       1008 |        7 |       2 | red
+             8 | 18 | Switzerland |        3 |    1 |   41 |          6 |        4 |       2 | red
+             7 | 14 | Norway      |        3 |    1 |  324 |          4 |        6 |       3 | red
+             6 | 12 | Luxembourg  |        3 |    1 |    3 |          0 |        4 |       3 | red
+             1 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+             2 |  2 | Australia   |        6 |    2 | 7690 |         15 |        1 |       3 | blue
+             1 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+             2 |  1 | Argentina   |        2 |    3 | 2777 |         28 |        2 |       2 | blue
+             3 |  4 | Brazil      |        2 |    3 | 8512 |        119 |        6 |       4 | green
+             2 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             1 |  9 | Guatemala   |        1 |    4 |  109 |          8 |        2 |       2 | blue
+             5 | 11 | Jamaica     |        1 |    4 |   11 |          2 |        1 |       3 | green
+             6 | 13 | Mexico      |        1 |    4 | 1973 |         77 |        2 |       4 | green
+             3 |  5 | Canada      |        1 |    4 | 9976 |         24 |        1 |       2 | red
+             7 | 15 | Portugal    |        3 |    4 |   92 |         10 |        6 |       5 | red
+             8 | 16 | Spain       |        3 |    4 |  505 |         38 |        2 |       2 | red
+             9 | 19 | UK          |        3 |    4 |  245 |         56 |        1 |       3 | red
+            10 | 20 | USA         |        1 |    4 | 9363 |        231 |        1 |       3 | white
+             4 | 10 | Ireland     |        3 |    4 |   70 |          3 |        1 |       3 | white
+(23 rows)
+
      9. +
    +

    Literature
    +

    [1] Object naming in PostgreSQL https://www.postgresql.org/docs/current/static/sql-syntax-lexical.html#SQL-SYNTAX-IDENTIFIERS

    +

    Related Topics
    +

    File balance_sample.sql_in for list of functions and usage.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__bayes.html b/docs/docs/v2.1.0/group__grp__bayes.html new file mode 100644 index 00000000..949f5b79 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__bayes.html @@ -0,0 +1,479 @@ + + + + + + + + +MADlib: Naive Bayes Classification + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Naive Bayes Classification
    Early Stage Development
    +
    +
    +
    Contents +
    Warning
    This MADlib method is still in early stage development. Interface and implementation are subject to change.
    +

    Naive Bayes refers to a stochastic model where all independent variables \( a_1, \dots, a_n \) (often referred to as attributes in this context) independently contribute to the probability that a data point belongs to a certain class \( c \).

    +

    Naives Bayes classification estimates feature probabilities and class priors using maximum likelihood or Laplacian smoothing. For numeric attributes, Gaussian smoothing can be used to estimate the feature probabilities.These parameters are then used to classify new data.

    +

    Training Function(s)
    +

    For data with only categorical attributes, precompute feature probabilities and class priors using the following function:

    +
    +create_nb_prepared_data_tables ( trainingSource,
+                                 trainingClassColumn,
+                                 trainingAttrColumn,
+                                 numAttrs,
+                                 featureProbsName,
+                                 classPriorsName
+                               )
+

    For data containing both categorical and numeric attributes, use the following form to precompute the Gaussian parameters (mean and variance) for numeric attributes alongside the feature probabilities for categorical attributes and class priors.

    +
    +create_nb_prepared_data_tables ( trainingSource,
+                                 trainingClassColumn,
+                                 trainingAttrColumn,
+                                 numericAttrsColumnIndices,
+                                 numAttrs,
+                                 featureProbsName,
+                                 numericAttrParamsName,
+                                 classPriorsName
+                               )
+

    The trainingSource is expected to be of the following form: 

    {TABLE|VIEW} trainingSource (
+    ...
+    trainingClassColumn INTEGER,
+    trainingAttrColumn INTEGER[] OR NUMERIC[] OR FLOAT8[],
+    ...
+)

    numericAttrsColumnIndices should be of type TEXT, specified as an array of indices (starting from 1) in the trainingAttrColumn attributes-array that correspond to numeric attributes.

    +

    The two output tables are:

      +
    • featureProbsName – stores feature probabilities
      • +
    • classPriorsName – stores the class priors
      • +
    +

    In addition to the above, if the function specifying numeric attributes is used, an additional table numericAttrParamsName is created which stores the Gaussian parameters for the numeric attributes.

    +

    Classify Function(s)
    +

    Perform Naive Bayes classification: 

    +create_nb_classify_view ( featureProbsName,
+                          classPriorsName,
+                          classifySource,
+                          classifyKeyColumn,
+                          classifyAttrColumn,
+                          numAttrs,
+                          destName
+                        )
+

    For data with numeric attributes, use the following version:

    +
    +create_nb_classify_view ( featureProbsName,
+                          classPriorsName,
+                          classifySource,
+                          classifyKeyColumn,
+                          classifyAttrColumn,
+                          numAttrs,
+                          numericAttrParamsName,
+                          destName
+                        )
+

    The data to classify is expected to be of the following form: 

    {TABLE|VIEW} classifySource (
+    ...
+    classifyKeyColumn ANYTYPE,
+    classifyAttrColumn INTEGER[],
+    ...
+)

    This function creates the view destName mapping classifyKeyColumn to the Naive Bayes classification. 

    +key | nb_classification
+ ---+------------------
+...
+

    Probabilities Function(s)
    +

    Compute Naive Bayes probabilities. 

    +create_nb_probs_view( featureProbsName,
+                      classPriorsName,
+                      classifySource,
+                      classifyKeyColumn,
+                      classifyAttrColumn,
+                      numAttrs,
+                      destName
+                    )
+

    For data with numeric attributes , use the following version:

    +
    +create_nb_probs_view( featureProbsName,
+                      classPriorsName,
+                      classifySource,
+                      classifyKeyColumn,
+                      classifyAttrColumn,
+                      numAttrs,
+                      numericAttrParamsName,
+                      destName
+                    )
+

    This creates the view destName mapping classifyKeyColumn and every single class to the Naive Bayes probability: 

    +key | class | nb_prob
+ ---+-------+--------
+...
+

    Ad Hoc Computation Function
    +

    With ad hoc execution (no precomputation), the functions create_nb_classify_view() and create_nb_probs_view() can be used in an ad-hoc fashion without the precomputation step. In this case, replace the function arguments

    +
    'featureProbsName', 'classPriorsName'

    with 

    'trainingSource', 'trainingClassColumn', 'trainingAttrColumn'

    for data without any any numeric attributes and with 

    'trainingSource', 'trainingClassColumn', 'trainingAttrColumn', 'numericAttrsColumnIndices'

    for data containing numeric attributes as well.

    +

    Implementation Notes
      +
    • The probabilities computed on the platforms of PostgreSQL and Greenplum database have a small difference due to the nature of floating point computation. Usually this is not important. However, if a data point has

      +\[ P(C=c_i \mid A) \approx P(C=c_j \mid A) \] +

      + for two classes, this data point might be classified into diferent classes on PostgreSQL and Greenplum. This leads to the differences in classifications on PostgreSQL and Greenplum for some data sets, but this should not affect the quality of the results.
      • +
    • When two classes have equal and highest probability among all classes, the classification result is an array of these two classes, but the order of the two classes is random.
      • +
    • The current implementation of Naive Bayes classification is suitable for discontinuous (categorial) attributes as well as continuous (numeric) attributes.
      +For continuous data, a typical assumption, usually used for small datasets, is that the continuous values associated with each class are distributed according to a Gaussian distribution, and the probabilities \( P(A_i = a \mid C=c) \) are estimated using the Gaussian Distribution formula:

      +\[ P(A_i=a \mid C=c) = \frac{1}{\sqrt{2\pi\sigma^{2}_c}}exp\left(-\frac{(a-\mu_c)^{2}}{2\sigma^{2}_c}\right) \] +

      + where \(\mu_c\) and \(\sigma^{2}_c\) are the population mean and variance of the attribute for the class \(c\).
      +Another common technique for handling continuous values, which is better for large data sets, is to use binning to discretize the values, and convert the continuous data into categorical bins. This approach is currently not implemented.
      • +
    • One can provide floating point data to the Naive Bayes classification function. If the corresponding attribute index is not specified in numericAttrsColumnIndices, floating point numbers will be used as symbolic substitutions for categorial data. In this case, the classification would work best if there are sufficient data points for each floating point attribute. However, if floating point numbers are used as continuous data without the attribute being marked as of type numeric in numericAttrsColumnIndices, no warning is raised and the result may not be as expected.
      • +
    +
    +

    Examples
    +

    The following is an extremely simplified example of the above option #1 which can by verified by hand.

    +
      +
    1. The training and the classification data. 
      +SELECT * FROM training;
+
      Result: 
      + id | class | attributes
+ ---+-------+------------
+  1 |     1 | {1,2,3}
+  2 |     1 | {1,2,1}
+  3 |     1 | {1,4,3}
+  4 |     2 | {1,2,2}
+  5 |     2 | {0,2,2}
+  6 |     2 | {0,1,3}
+(6 rows)
+
      +SELECT * FROM toclassify;
+
      Result: 
      + id | attributes
+ ---+------------
+  1 | {0,2,1}
+  2 | {1,2,3}
+(2 rows)
+
      2. +
    2. Precompute feature probabilities and class priors. 
      +SELECT madlib.create_nb_prepared_data_tables( 'training',
+                                              'class',
+                                              'attributes',
+                                              3,
+                                              'nb_feature_probs',
+                                              'nb_class_priors'
+                                            );
+
      3. +
    3. Optionally check the contents of the precomputed tables. 
      +SELECT * FROM nb_class_priors;
+
      Result: 
      + class | class_cnt | all_cnt
+ ------+-----------+---------
+     1 |         3 |       6
+     2 |         3 |       6
+(2 rows)
+
      +SELECT * FROM nb_feature_probs;
+
      Result: 
      + class | attr | value | cnt | attr_cnt
+ ------+------+-------+-----+----------
+     1 |    1 |     0 |   0 |        2
+     1 |    1 |     1 |   3 |        2
+     1 |    2 |     1 |   0 |        3
+     1 |    2 |     2 |   2 |        3
+...
+
      4. +
    4. Create the view with Naive Bayes classification and check the results. 
      +SELECT madlib.create_nb_classify_view( 'nb_feature_probs',
+                                       'nb_class_priors',
+                                       'toclassify',
+                                       'id',
+                                       'attributes',
+                                       3,
+                                       'nb_classify_view_fast'
+                                     );
+ 
+SELECT * FROM nb_classify_view_fast;
+
      Result: 
      + key | nb_classification
+ ----+-------------------
+   1 | {2}
+   2 | {1}
+(2 rows)
+
      5. +
    5. Look at the probabilities for each class (note that we use "Laplacian smoothing"), 
      +SELECT madlib.create_nb_probs_view( 'nb_feature_probs',
+                                    'nb_class_priors',
+                                    'toclassify',
+                                    'id',
+                                    'attributes',
+                                    3,
+                                    'nb_probs_view_fast'
+                                  );
+ 
+SELECT * FROM nb_probs_view_fast;
+
      Result: 
      + key | class | nb_prob
+ ----+-------+---------
+   1 |     1 |     0.4
+   1 |     2 |     0.6
+   2 |     1 |    0.75
+   2 |     2 |    0.25
+(4 rows)
+
      6. +
    +

    The following is an example of using a dataset with both numeric and categorical attributes

    +
      +
    1. The training and the classification data. Attributes {height(numeric),weight(numeric),shoe size(categorical)}, Class{sex(1=male,2=female)} 
      +SELECT * FROM gaussian_data;
+
      Result: 
      + id | sex |  attributes
+ ----+-----+---------------
+  1 |   1 | {6,180,12}
+  2 |   1 | {5.92,190,12}
+  3 |   1 | {5.58,170,11}
+  4 |   1 | {5.92,165,11}
+  5 |   2 | {5,100,6}
+  6 |   2 | {5.5,150,6}
+  7 |   2 | {5.42,130,7}
+  8 |   2 | {5.75,150,8}
+(8 rows)
+
      +SELECT * FROM gaussian_test;
+
      Result: 
      + id | sex |  attributes
+----+-----+--------------
+  9 |   1 | {5.8,180,11}
+ 10 |   2 | {5,160,6}
+(2 rows)
+
      2. +
    2. Precompute feature probabilities and class priors. 
      +SELECT madlib.create_nb_prepared_data_tables( 'gaussian_data',
+                                              'sex',
+                                              'attributes',
+                                              'ARRAY[1,2]',
+                                              3,
+                                              'categ_feature_probs',
+                                              'numeric_attr_params',
+                                              'class_priors'
+                                            );
+
      3. +
    3. Optionally check the contents of the precomputed tables. 
      +SELECT * FROM class_priors;
+
      Result: 
      +class | class_cnt | all_cnt
+ -------+-----------+---------
+     1 |         4 |       8
+     2 |         4 |       8
+(2 rows)
+
      +SELECT * FROM categ_feature_probs;
+
      Result: 
      + class | attr | value | cnt | attr_cnt
+-------+------+-------+-----+----------
+     2 |    3 |     6 |   2 |        5
+     1 |    3 |    12 |   2 |        5
+     2 |    3 |     7 |   1 |        5
+     1 |    3 |    11 |   2 |        5
+     2 |    3 |     8 |   1 |        5
+     2 |    3 |    12 |   0 |        5
+     1 |    3 |     6 |   0 |        5
+     2 |    3 |    11 |   0 |        5
+     1 |    3 |     8 |   0 |        5
+     1 |    3 |     7 |   0 |        5
+(10 rows)
+
      +SELECT * FROM numeric_attr_params;
+
      Result: 
      +class | attr |      attr_mean       |        attr_var
+-------+------+----------------------+------------------------
+     1 |    1 |   5.8550000000000000 | 0.03503333333333333333
+     1 |    2 | 176.2500000000000000 |   122.9166666666666667
+     2 |    1 |   5.4175000000000000 | 0.09722500000000000000
+     2 |    2 | 132.5000000000000000 |   558.3333333333333333
+(4 rows)
+
      4. +
    4. Create the view with Naive Bayes classification and check the results. 
      +SELECT madlib.create_nb_classify_view( 'categ_feature_probs',
+                                       'class_priors',
+                                       'gaussian_test',
+                                       'id',
+                                       'attributes',
+                                       3,
+                                       'numeric_attr_params',
+                                       'classify_view'
+                                     );
+ 
+SELECT * FROM classify_view;
+
      Result: 
      + key | nb_classification
+ ----+-------------------
+   9 | {1}
+   10 | {2}
+(2 rows)
+
      5. +
    5. Look at the probabilities for each class 
      +SELECT madlib.create_nb_probs_view( 'categ_feature_probs',
+                                       'class_priors',
+                                       'gaussian_test',
+                                       'id',
+                                       'attributes',
+                                       3,
+                                       'numeric_attr_params',
+                                       'probs_view'
+                                  );
+ 
+SELECT * FROM probs_view;
+
      Result: 
      + key | class |       nb_prob
+-----+-------+----------------------
+   9 |     1 |    0.993556745948775
+   9 |     2 |  0.00644325405122553
+  10 |     1 | 5.74057538627122e-05
+  10 |     2 |    0.999942594246137
+(4 rows)
+
      6. +
    +

    Technical Background
    +

    In detail, Bayes' theorem states that

    +\[ \Pr(C = c \mid A_1 = a_1, \dots, A_n = a_n) = \frac{\Pr(C = c) \cdot \Pr(A_1 = a_1, \dots, A_n = a_n \mid C = c)} {\Pr(A_1 = a_1, \dots, A_n = a_n)} \,, \] +

    +

    and the naive assumption is that

    +\[ \Pr(A_1 = a_1, \dots, A_n = a_n \mid C = c) = \prod_{i=1}^n \Pr(A_i = a_i \mid C = c) \,. \] +

    +

    Naives Bayes classification estimates feature probabilities and class priors using maximum likelihood or Laplacian smoothing. These parameters are then used to classifying new data.

    +

    A Naive Bayes classifier computes the following formula:

    +\[ \text{classify}(a_1, ..., a_n) = \arg\max_c \left\{ \Pr(C = c) \cdot \prod_{i=1}^n \Pr(A_i = a_i \mid C = c) \right\} \] +

    +

    where \( c \) ranges over all classes in the training data and probabilites are estimated with relative frequencies from the training set. There are different ways to estimate the feature probabilities \( P(A_i = a \mid C = c) \). The maximum likelihood estimate takes the relative frequencies. That is:

    +\[ P(A_i = a \mid C = c) = \frac{\#(c,i,a)}{\#c} \] +

    +

    where

      +
    • \( \#(c,i,a) \) denotes the # of training samples where attribute \( i \) is \( a \) and class is \( c \)
      • +
    • \( \#c \) denotes the # of training samples where class is \( c \).
      • +
    +

    Since the maximum likelihood sometimes results in estimates of "0", you might want to use a "smoothed" estimate. To do this, you add a number of "virtual" samples and make the assumption that these samples are evenly distributed among the values assumed by attribute \( i \) (that is, the set of all values observed for attribute \( a \) for any class):

    +

    +\[ P(A_i = a \mid C = c) = \frac{\#(c,i,a) + s}{\#c + s \cdot \#i} \] +

    +

    where

      +
    • \( \#i \) denotes the # of distinct values for attribute \( i \) (for all classes)
      • +
    • \( s \geq 0 \) denotes the smoothing factor.
      • +
    +

    The case \( s = 1 \) is known as "Laplace smoothing". The case \( s = 0 \) trivially reduces to maximum-likelihood estimates.

    +

    Literature
    +

    [1] Tom Mitchell: Machine Learning, McGraw Hill, 1997. Book chapter Generativ and Discriminative Classifiers: Naive Bayes and Logistic Regression available at: http://www.cs.cmu.edu/~tom/NewChapters.html

    +

    [2] Wikipedia, Naive Bayes classifier, http://en.wikipedia.org/wiki/Naive_Bayes_classifier

    +

    Related Topics
    File bayes.sql_in documenting the SQL functions.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__bfs.html b/docs/docs/v2.1.0/group__grp__bfs.html new file mode 100644 index 00000000..bc95cfd7 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__bfs.html @@ -0,0 +1,408 @@ + + + + + + + + +MADlib: Breadth-First Search + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    Breadth-First Search
    Graph
    +
    +
    +
    Contents +

    Given a graph and a source vertex, the breadth-first search (BFS) algorithm finds all nodes reachable from the source vertex by searching / traversing the graph in a breadth-first manner.

    +

    BFS
    +graph_bfs( vertex_table,
+           vertex_id,
+           edge_table,
+           edge_args,
+           source_vertex,
+           out_table,
+           max_distance,
+           directed,
+           grouping_cols
+          )
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    +
    +
    vertex_id
    +

    TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous.

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex and destination vertex. Column naming convention is described below in the 'edge_args' parameter. In addition to vertex columns, if grouping is used then the columns specified in the 'grouping_cols' parameter must be present.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'. (This is not to be confused with the 'source_vertex' argument passed to the BFS function.)
      • +
    • dest (INTEGER or BIGINT): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    +

    +
    +
    source_vertex
    +

    INTEGER or BIGINT. The source vertex id for the algorithm to start. This vertex id must exist in the 'vertex_id' column of 'vertex_table'.

    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the result of BFS. It contains a row for every vertex that is reachable from the source_vertex. In the presence of grouping columns, only those edges are used for which there are no NULL values in any grouping column. The output table will have the following columns (in addition to the grouping columns):

      +
    • vertex_id : The id for any node reachable from source_vertex in addition to the source_vertex. Will use the input parameter 'vertex_id' for column naming.
      • +
    • dist : The distance in number of edges (or hops) from the source_vertex to where this vertex is located.
      • +
    • parent : The parent of this vertex in BFS traversal of the graph from source_vertex. Will use 'parent' for column naming. For the case where vertex_id = source_vertex, the value for parent is NULL.
      • +
    +

    A summary table named <out_table>_summary is also created. This is an internal table that keeps a record of the input parameters.

    +

    +
    +
    max_distance (optional)
    +

    INT, default = NULL. Maximum distance to traverse from the source vertex. When this value is null, traverses until reaches leaf node. E.g., if set to 1 will return only adjacent vertices, if set to 7 will return vertices up to a maximum distance of 7 vertices away.

    +

    +
    +
    directed (optional)
    +

    BOOLEAN, default = FALSE. If TRUE the graph will be treated as directed, else it will be treated as an undirected graph.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default = NULL. A comma-separated list of columns used to group the input into discrete subgraphs. These columns must exist in the edge table. When this value is NULL, no grouping is used and a single BFS result is generated.
    Note
    Expressions are not currently supported for 'grouping_cols'.
    +
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER
+        );
+CREATE TABLE edge(
+        src INTEGER,
+        dest INTEGER
+        );
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6),
+(7),
+(8),
+(9),
+(10),
+(11)
+;
+INSERT INTO edge VALUES
+(0, 5),
+(1, 0),
+(1, 3),
+(2, 6),
+(3, 4),
+(3, 5),
+(4, 2),
+(8, 9),
+(9, 10),
+(9, 11),
+(10, 8);
+
      2. +
    2. Traverse undirected graph from vertex 3: 
      +DROP TABLE IF EXISTS out, out_summary;
+SELECT madlib.graph_bfs(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         3,             -- Source vertex for BFS
+                         'out');        -- Output table of nodes reachable from source_vertex
+                         -- Default values used for the other arguments
+SELECT * FROM out ORDER BY dist,id;
+
      + id | dist | parent
+----+------+--------
+  3 |    0 |      3
+  1 |    1 |      3
+  4 |    1 |      3
+  5 |    1 |      3
+  0 |    2 |      1
+  2 |    2 |      4
+  6 |    3 |      2
+(7 rows)
+
      +SELECT * FROM out_summary;
+
      + vertex_table | vertex_id | edge_table | edge_args | source_vertex | out_table | max_distance | directed | grouping_cols
+--------------+-----------+------------+-----------+---------------+-----------+--------------+----------+---------------
+ vertex       | NULL      | edge       | NULL      |             3 | out       |              |          | NULL
+(1 row)
+
      3. +
    3. In this example, we use max_distance to limit the search distance. 
      +DROP TABLE IF EXISTS out_max, out_max_summary;
+SELECT madlib.graph_bfs(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         3,             -- Source vertex for BFS
+                         'out_max',     -- Output table of nodes reachable from source_vertex
+                         2);            -- Maximum distance to traverse from source_vertex
+                         -- Default values used for the other arguments
+SELECT * FROM out_max ORDER BY dist,id;
+
      + id | dist | parent
+----+------+--------
+  3 |    0 |      3
+  1 |    1 |      3
+  4 |    1 |      3
+  5 |    1 |      3
+  0 |    2 |      1
+  2 |    2 |      4
+(6 rows)
+
      4. +
    4. Now let's do an example using different column names in the tables (i.e., not the defaults). Create the vertex and edge tables: 
      +DROP TABLE IF EXISTS vertex_alt, edge_alt;
+CREATE TABLE vertex_alt AS SELECT id AS v_id FROM vertex;
+CREATE TABLE edge_alt AS SELECT src AS n1, dest AS n2 FROM edge;
+
      5. +
    5. Run BFS from vertex 8: 
      +DROP TABLE IF EXISTS out_alt, out_alt_summary;
+SELECT madlib.graph_bfs(
+                         'vertex_alt',                  -- Vertex table
+                         'v_id',                        -- Vertex id column (NULL means use default naming)
+                         'edge_alt',                    -- Edge table
+                         'src=n1, dest=n2',             -- Edge arguments (NULL means use default naming)
+                         8,                             -- Source vertex for BFS
+                         'out_alt');                    -- Output table of nodes reachable from source_vertex
+SELECT * FROM out_alt ORDER BY v_id;
+
      + v_id | dist | parent
+------+------+--------
+    8 |    0 |      8
+    9 |    1 |      8
+   10 |    1 |      8
+   11 |    2 |      9
+
      6. +
    6. Now we show an example where the graph is treated as a directed graph. 
      +DROP TABLE IF EXISTS out_alt_dir, out_alt_dir_summary;
+SELECT madlib.graph_bfs(
+                         'vertex_alt',                  -- Vertex table
+                         'v_id',                        -- Vertex id column (NULL means use default naming)
+                         'edge_alt',                    -- Edge table
+                         'src=n1, dest=n2',             -- Edge arguments (NULL means use default naming)
+                         8,                             -- Source vertex for BFS
+                         'out_alt_dir',                 -- Output table of nodes reachable from source_vertex
+                         NULL,                          -- Maximum distance to traverse from source_vertex
+                         TRUE);                         -- Flag for specifying directed graph
+SELECT * FROM out_alt_dir ORDER BY v_id;
+
      + v_id | dist | parent
+------+------+--------
+    8 |    0 |      8
+    9 |    1 |      8
+   10 |    2 |      9
+   11 |    2 |      9
+(4 rows)
+
      Notice that, with the graph being treated as directed, the parent of v_id=10 is now vertex 9 and not 8 as in the undirected case.
      7. +
    7. Create a graph with 2 groups: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr(
+                  g1 INTEGER,
+                  g2 TEXT,
+                  src INTEGER,
+                  dest INTEGER
+                );
+INSERT INTO edge_gr VALUES
+(100, 'a', 0, 5),
+(100, 'a', 1, 0),
+(100, 'a', 1, 3),
+(100, 'a', 2, 6),
+(100, 'a', 3, 4),
+(100, 'a', 3, 5),
+(100, 'a', 4, 2),
+(100, 'a', 8, 9),
+(100, 'a', 9, 10),
+(100, 'a', 9, 11),
+(100, 'a', 10, 8),
+(202, 'c', 8, 9),
+(202, 'c', 9, 10),
+(202, 'c', 9, 11),
+(202, 'c', 10, 8)
+;
+
      8. +
    8. Run BFS for all groups from a given source_vertex. 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_bfs(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         8,             -- Source vertex for BFS
+                         'out_gr',      -- Output table of nodes reachable from source_vertex
+                         NULL,          -- Maximum distance to traverse from source_vertex
+                         NULL,          -- Flag for specifying directed graph
+                         'g1,g2'        -- Grouping columns
+);
+SELECT * FROM out_gr ORDER BY g1,g2,dist,id;
+
      + g1  | g2 | id | dist | parent
+-----+----+----+------+--------
+ 100 | a  |  8 |    0 |      8
+ 100 | a  |  9 |    1 |      8
+ 100 | a  | 10 |    1 |      8
+ 100 | a  | 11 |    2 |      9
+ 202 | c  |  8 |    0 |      8
+ 202 | c  |  9 |    1 |      8
+ 202 | c  | 10 |    1 |      8
+ 202 | c  | 11 |    2 |      9
+(8 rows)
+
      If source_vertex is not present in a group, then that group will not appear in the output table. 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_bfs(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         3,             -- Source vertex for BFS
+                         'out_gr',      -- Output table of nodes reachable from source_vertex
+                         NULL,          -- Maximum distance to traverse from source_vertex
+                         NULL,          -- Flag for specifying directed graph
+                         'g1,g2'        -- Grouping columns
+);
+SELECT * FROM out_gr ORDER BY g1,g2,dist,id;
+
      + g1  | g2 | id | dist | parent
+-----+----+----+------+--------
+ 100 | a  |  3 |    0 |      3
+ 100 | a  |  1 |    1 |      3
+ 100 | a  |  4 |    1 |      3
+ 100 | a  |  5 |    1 |      3
+ 100 | a  |  0 |    2 |      1
+ 100 | a  |  2 |    2 |      4
+ 100 | a  |  6 |    3 |      2
+(7 rows)
+
      9. +
    +

    Notes
    +
      +
    1. On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance.
      2. +
    2. The graph_bfs function is a SQL implementation of the well-known breadth-first search algorithm [1] modified appropriately for a relational database. It will find any node in the graph reachable from the 'source_vertex' only once. If a node is reachable by many different paths from the 'source_vertex' (i.e. has more than one parent), then only one of those parents is present in the output table. The BFS result will, in general, be different for different choices of 'source_vertex'.
      3. +
    +

    Literature
    +

    [1] Breadth-first Search algorithm. https://en.wikipedia.org/wiki/Breadth-first_search

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__cg.html b/docs/docs/v2.1.0/group__grp__cg.html new file mode 100644 index 00000000..5786e83e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__cg.html @@ -0,0 +1,176 @@ + + + + + + + + +MADlib: Conjugate Gradient + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    +
    Conjugate Gradient
    Early Stage Development
    +
    +
    +
    Contents +
    Warning
    This MADlib method is still in early stage development. Interface and implementation are subject to change.
    +

    This function uses the iterative conjugate gradient method [1] to find a solution to the function:

    +\[ \boldsymbol Ax = \boldsymbol b \] +

    +

    where \( \boldsymbol A \) is a symmetric, positive definite matrix and \(x\) and \( \boldsymbol b \) are vectors.

    +

    Function Syntax
    Conjugate gradient returns x as an array. It has the following syntax.
    +
    +conjugate_gradient( table_name,
+                    name_of_row_values_col,
+                    name_of_row_number_col,
+                    aray_of_b_values,
+                    desired_precision
+                  )
+

    Matrix \( \boldsymbol A \) is assumed to be stored in a table where each row consists of at least two columns: array containing values of a given row, row number: 

    {TABLE|VIEW} matrix_A (
+    row_number FLOAT,
+    row_values FLOAT[],
+)

    The number of elements in each row should be the same.

    +

    \( \boldsymbol b \) is passed as a FLOAT[] to the function.

    +

    Examples
      +
    1. Construct matrix A according to structure. 
      +SELECT * FROM data;
+
      Result: 
      + row_num | row_val
+ --------+---------
+       1 | {2,1}
+       2 | {1,4}
+(2 rows)
+
      2. +
    2. Call the conjugate gradient function. 
      +SELECT conjugate_gradient( 'data',
+                           'row_val',
+                           'row_num',
+                           '{2,1}',
+                           1E-6,1
+                         );
+
      +INFO:  COMPUTE RESIDUAL ERROR 14.5655661859659
+INFO:  ERROR 0.144934004246004
+INFO:  ERROR 3.12963615962926e-31
+INFO:  TEST FINAL ERROR 2.90029642185163e-29
+    conjugate_gradient
+ --------------------------
+ {1,-1.31838984174237e-15}
+(1 row)
+
      3. +
    +
    +

    Literature
    [1] "Conjugate gradient method" Wikipedia - http://en.wikipedia.org/wiki/Conjugate_gradient_method
    +

    Related Topics
    File conjugate_gradient.sql_in documenting the SQL function.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__clustered__errors.html b/docs/docs/v2.1.0/group__grp__clustered__errors.html new file mode 100644 index 00000000..22ef335d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__clustered__errors.html @@ -0,0 +1,525 @@ + + + + + + + + +MADlib: Clustered Variance + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    Clustered Variance
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    The Clustered Variance module adjusts standard errors for clustering. For example, replicating a dataset 100 times should not increase the precision of parameter estimates, but performing this procedure with the IID assumption will actually do this. Another example is in economics of education research, it is reasonable to expect that the error terms for children in the same class are not independent. Clustering standard errors can correct for this.

    +

    The MADlib Clustered Variance module includes functions to calculate linear, logistic, and multinomial logistic regression problems.

    +

    Clustered Variance Linear Regression Training Function
    +

    The clustered variance linear regression training function has the following syntax. 

    +clustered_variance_linregr ( source_table,
+                             out_table,
+                             dependent_varname,
+                             independent_varname,
+                             clustervar,
+                             grouping_cols
+                           )
+

    Arguments

    +
    source_table
    +

    TEXT. The name of the table containing the input data.

    +

    +
    +
    out_table
    +

    VARCHAR. Name of the generated table containing the output model. The output table contains the following columns.

    + + + + + + + + +
    coef DOUBLE PRECISION[]. Vector of the coefficients of the regression.
    std_err DOUBLE PRECISION[]. Vector of the standard error of the coefficients.
    t_stats DOUBLE PRECISION[]. Vector of the t-stats of the coefficients.
    p_values DOUBLE PRECISION[]. Vector of the p-values of the coefficients.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by linregr_train function. Please refer to the documentation for linear regression for details.

    +

    +

    +
    +
    dependent_varname
    +
    TEXT. An expression to evaluate for the dependent variable.
    +
    independent_varname
    +
    TEXT. An Expression to evalue for the independent variables.
    +
    clustervar
    +
    TEXT. A comma-separated list of the columns to use as cluster variables.
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. Not currently implemented. Any non-NULL value is ignored. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL GROUP BY clause. When this value is null, no grouping is used and a single result model is generated.
    +
    +

    Clustered Variance Logistic Regression Training Function
    +

    The clustered variance logistic regression training function has the following syntax. 

    +clustered_variance_logregr( source_table,
+                            out_table,
+                            dependent_varname,
+                            independent_varname,
+                            clustervar,
+                            grouping_cols,
+                            max_iter,
+                            optimizer,
+                            tolerance,
+                            verbose_mode
+                          )
+

    Arguments

    +
    source_table
    +
    TEXT. The name of the table containing the input data.
    +
    out_table
    +

    VARCHAR. Name of the generated table containing the output model. The output table has the following columns:

    + + + + + + + + +
    coef Vector of the coefficients of the regression.
    std_err Vector of the standard error of the coefficients.
    z_stats Vector of the z-stats of the coefficients.
    p_values Vector of the p-values of the coefficients.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by logregr_train function. Please refer to the documentation for logistic regression for details.

    +

    +
    +
    dependent_varname
    +
    TEXT. An expression to evaluate for the dependent variable.
    +
    independent_varname
    +
    TEXT. An expression to evaluate for the independent variable.
    +
    clustervar
    +
    TEXT. A comma-separated list of columns to use as cluster variables.
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. Not yet implemented. Any non-NULL values are ignored. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL GROUP BY clause. When this value is NULL, no grouping is used and a single result model is generated.
    +
    max_iter (optional)
    +
    INTEGER, default: 20. The maximum number of iterations that are allowed.
    +
    optimizer (optional)
    +
    TEXT, default: 'irls'. The name of the optimizer to use:
      +
    • +'newton' or 'irls': Iteratively reweighted least squares
      • +
    • +'cg': conjugate gradient
      • +
    • +'igd': incremental gradient descent.
      • +
    +
    +
    tolerance (optional)
    +
    FLOAT8, default: 0.0001 The difference between log-likelihood values in successive iterations that should indicate convergence. A zero disables the convergence criterion, so that execution stops after n Iterations have completed.
    +
    verbose_mode (optional)
    +
    BOOLEAN, default FALSE. Provides verbose_mode output of the results of training.
    +
    +

    Clustered Variance Multinomial Logistic Regression Training Function
    +
    +clustered_variance_mlogregr( source_table,
+                             out_table,
+                             dependent_varname,
+                             independent_varname,
+                             cluster_varname,
+                             ref_category,
+                             grouping_cols,
+                             optimizer_params,
+                             verbose_mode
+                           )
+

    Arguments

    +
    source_table
    +
    TEXT. The name of the table containing the input data.
    +
    out_table
    +

    TEXT. The name of the table where the regression model will be stored. The output table has the following columns:

    + + + + + + + + + + + + +
    category The category.
    ref_category The refererence category used for modeling.
    coef Vector of the coefficients of the regression.
    std_err Vector of the standard error of the coefficients.
    z_stats Vector of the z-stats of the coefficients.
    p_values Vector of the p-values of the coefficients.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by mlogregr_train function. Please refer to the documentation for multinomial logistic regression for details.

    +
    +
    dependent_varname
    +
    TEXT. An expression to evaluate for the dependent variable.
    +
    independent_varname
    +
    TEXT. An expression to evaluate for the independent variable.
    +
    cluster_varname
    +
    TEXT. A comma-separated list of columns to use as cluster variables.
    +
    ref_category (optional)
    +
    INTEGER. Reference category in the range [0, num_category).
    +
    groupingvarng_cols (optional)
    +
    TEXT, default: NULL. Not yet implemented. Any non-NULL values are ignored. A comma-separated list of columns to use as grouping variables.
    +
    optimizer_params (optional)
    +
    TEXT, default: NULL, which uses the default values of optimizer parameters: max_iter=20, optimizer='newton', tolerance=1e-4. It should be a string that contains pairs of 'key=value' separated by commas.
    +
    verbose_mode (optional)
    +
    BOOLEAN, default FALSE. If TRUE, detailed information is printed when computing logistic regression.
    +
    +

    Clustered Variance for Cox Proportional Hazards model
    +

    The clustered robust variance estimator function for the Cox Proportional Hazards model has the following syntax. 

    +clustered_variance_coxph(model_table, output_table, clustervar)
+

    Arguments

    +
    model_table
    +
    TEXT. The name of the model table, which is exactaly the same as the 'output_table' parameter of coxph_train() function.
    +
    output_table
    +
    TEXT. The name of the table where the output is saved. It has the following columns: + + + + + + + + + + + + + + + + +
    coef FLOAT8[]. Vector of the coefficients.
    loglikelihood FLOAT8. Log-likelihood value of the MLE estimate.
    std_err FLOAT8[]. Vector of the standard error of the coefficients.
    clustervar TEXT. A comma-separated list of columns to use as cluster variables.
    clustered_se FLOAT8[]. Vector of the robust standard errors of the coefficients.
    clustered_z FLOAT8[]. Vector of the robust z-stats of the coefficients.
    clustered_p FLOAT8[]. Vector of the robust p-values of the coefficients.
    hessian FLOAT8[]. The Hessian matrix.
    +
    +
    clustervar
    +
    TEXT. A comma-separated list of columns to use as cluster variables.
    +
    +

    Examples
    +
      +
    1. Create a testing data table 
      +CREATE TABLE abalone (
+    id integer,
+    sex text,
+    length double precision,
+    diameter double precision,
+    height double precision,
+    whole double precision,
+    shucked double precision,
+    viscera double precision,
+    shell double precision,
+    rings integer
+);
+INSERT INTO abalone VALUES
+(3151, 'F', 0.655000000000000027, 0.505000000000000004, 0.165000000000000008, 1.36699999999999999, 0.583500000000000019, 0.351499999999999979, 0.396000000000000019, 10),
+(2026, 'F', 0.550000000000000044, 0.469999999999999973, 0.149999999999999994, 0.920499999999999985, 0.381000000000000005, 0.243499999999999994, 0.267500000000000016, 10),
+(3751, 'I', 0.434999999999999998, 0.375, 0.110000000000000001, 0.41549999999999998, 0.170000000000000012, 0.0759999999999999981, 0.14499999999999999, 8),
+(720, 'I', 0.149999999999999994, 0.100000000000000006, 0.0250000000000000014, 0.0149999999999999994, 0.00449999999999999966, 0.00400000000000000008, 0.0050000000000000001, 2),
+(1635, 'F', 0.574999999999999956, 0.469999999999999973, 0.154999999999999999, 1.1160000000000001, 0.509000000000000008, 0.237999999999999989, 0.340000000000000024, 10),
+(2648, 'I', 0.5, 0.390000000000000013, 0.125, 0.582999999999999963, 0.293999999999999984, 0.132000000000000006, 0.160500000000000004, 8),
+(1796, 'F', 0.57999999999999996, 0.429999999999999993, 0.170000000000000012, 1.47999999999999998, 0.65349999999999997, 0.32400000000000001, 0.41549999999999998, 10),
+(209, 'F', 0.525000000000000022, 0.41499999999999998, 0.170000000000000012, 0.832500000000000018, 0.275500000000000023, 0.168500000000000011, 0.309999999999999998, 13),
+(1451, 'I', 0.455000000000000016, 0.33500000000000002, 0.135000000000000009, 0.501000000000000001, 0.274000000000000021, 0.0995000000000000051, 0.106499999999999997, 7),
+(1108, 'I', 0.510000000000000009, 0.380000000000000004, 0.115000000000000005, 0.515499999999999958, 0.214999999999999997, 0.113500000000000004, 0.166000000000000009, 8),
+(3675, 'F', 0.594999999999999973, 0.450000000000000011, 0.165000000000000008, 1.08099999999999996, 0.489999999999999991, 0.252500000000000002, 0.279000000000000026, 12),
+(2108, 'F', 0.675000000000000044, 0.550000000000000044, 0.179999999999999993, 1.68849999999999989, 0.562000000000000055, 0.370499999999999996, 0.599999999999999978, 15),
+(3312, 'F', 0.479999999999999982, 0.380000000000000004, 0.135000000000000009, 0.507000000000000006, 0.191500000000000004, 0.13650000000000001, 0.154999999999999999, 12),
+(882, 'M', 0.655000000000000027, 0.520000000000000018, 0.165000000000000008, 1.40949999999999998, 0.585999999999999965, 0.290999999999999981, 0.405000000000000027, 9),
+(3402, 'M', 0.479999999999999982, 0.395000000000000018, 0.149999999999999994, 0.681499999999999995, 0.214499999999999996, 0.140500000000000014, 0.2495, 18),
+(829, 'I', 0.409999999999999976, 0.325000000000000011, 0.100000000000000006, 0.394000000000000017, 0.20799999999999999, 0.0655000000000000027, 0.105999999999999997, 6),
+(1305, 'M', 0.535000000000000031, 0.434999999999999998, 0.149999999999999994, 0.716999999999999971, 0.347499999999999976, 0.14449999999999999, 0.194000000000000006, 9),
+(3613, 'M', 0.599999999999999978, 0.46000000000000002, 0.179999999999999993, 1.1399999999999999, 0.422999999999999987, 0.257500000000000007, 0.364999999999999991, 10),
+(1068, 'I', 0.340000000000000024, 0.265000000000000013, 0.0800000000000000017, 0.201500000000000012, 0.0899999999999999967, 0.0475000000000000006, 0.0550000000000000003, 5),
+(2446, 'M', 0.5, 0.380000000000000004, 0.135000000000000009, 0.583500000000000019, 0.22950000000000001, 0.126500000000000001, 0.179999999999999993, 12),
+(1393, 'M', 0.635000000000000009, 0.474999999999999978, 0.170000000000000012, 1.19350000000000001, 0.520499999999999963, 0.269500000000000017, 0.366499999999999992, 10),
+(359, 'M', 0.744999999999999996, 0.584999999999999964, 0.214999999999999997, 2.49900000000000011, 0.92649999999999999, 0.471999999999999975, 0.699999999999999956, 17),
+(549, 'F', 0.564999999999999947, 0.450000000000000011, 0.160000000000000003, 0.79500000000000004, 0.360499999999999987, 0.155499999999999999, 0.23000000000000001, 12),
+(1154, 'F', 0.599999999999999978, 0.474999999999999978, 0.160000000000000003, 1.02649999999999997, 0.484999999999999987, 0.2495, 0.256500000000000006, 9),
+(1790, 'F', 0.54500000000000004, 0.385000000000000009, 0.149999999999999994, 1.11850000000000005, 0.542499999999999982, 0.244499999999999995, 0.284499999999999975, 9),
+(3703, 'F', 0.665000000000000036, 0.540000000000000036, 0.195000000000000007, 1.76400000000000001, 0.850500000000000034, 0.361499999999999988, 0.469999999999999973, 11),
+(1962, 'F', 0.655000000000000027, 0.515000000000000013, 0.179999999999999993, 1.41199999999999992, 0.619500000000000051, 0.248499999999999999, 0.496999999999999997, 11),
+(1665, 'I', 0.604999999999999982, 0.469999999999999973, 0.14499999999999999, 0.802499999999999991, 0.379000000000000004, 0.226500000000000007, 0.220000000000000001, 9),
+(635, 'M', 0.359999999999999987, 0.294999999999999984, 0.100000000000000006, 0.210499999999999993, 0.0660000000000000031, 0.0524999999999999981, 0.0749999999999999972, 9),
+(3901, 'M', 0.445000000000000007, 0.344999999999999973, 0.140000000000000013, 0.475999999999999979, 0.205499999999999988, 0.101500000000000007, 0.108499999999999999, 15),
+(2734, 'I', 0.41499999999999998, 0.33500000000000002, 0.100000000000000006, 0.357999999999999985, 0.169000000000000011, 0.067000000000000004, 0.104999999999999996, 7),
+(3856, 'M', 0.409999999999999976, 0.33500000000000002, 0.115000000000000005, 0.440500000000000003, 0.190000000000000002, 0.0850000000000000061, 0.135000000000000009, 8),
+(827, 'I', 0.395000000000000018, 0.28999999999999998, 0.0950000000000000011, 0.303999999999999992, 0.127000000000000002, 0.0840000000000000052, 0.076999999999999999, 6),
+(3381, 'I', 0.190000000000000002, 0.130000000000000004, 0.0449999999999999983, 0.0264999999999999993, 0.00899999999999999932, 0.0050000000000000001, 0.00899999999999999932, 5),
+(3972, 'I', 0.400000000000000022, 0.294999999999999984, 0.0950000000000000011, 0.252000000000000002, 0.110500000000000001, 0.0575000000000000025, 0.0660000000000000031, 6),
+(1155, 'M', 0.599999999999999978, 0.455000000000000016, 0.170000000000000012, 1.1915, 0.695999999999999952, 0.239499999999999991, 0.239999999999999991, 8),
+(3467, 'M', 0.640000000000000013, 0.5, 0.170000000000000012, 1.4544999999999999, 0.642000000000000015, 0.357499999999999984, 0.353999999999999981, 9),
+(2433, 'F', 0.609999999999999987, 0.484999999999999987, 0.165000000000000008, 1.08699999999999997, 0.425499999999999989, 0.232000000000000012, 0.380000000000000004, 11),
+(552, 'I', 0.614999999999999991, 0.489999999999999991, 0.154999999999999999, 0.988500000000000045, 0.41449999999999998, 0.195000000000000007, 0.344999999999999973, 13),
+(1425, 'F', 0.729999999999999982, 0.57999999999999996, 0.190000000000000002, 1.73750000000000004, 0.678499999999999992, 0.434499999999999997, 0.520000000000000018, 11),
+(2402, 'F', 0.584999999999999964, 0.41499999999999998, 0.154999999999999999, 0.69850000000000001, 0.299999999999999989, 0.145999999999999991, 0.195000000000000007, 12),
+(1748, 'F', 0.699999999999999956, 0.535000000000000031, 0.174999999999999989, 1.77299999999999991, 0.680499999999999994, 0.479999999999999982, 0.512000000000000011, 15),
+(3983, 'I', 0.57999999999999996, 0.434999999999999998, 0.149999999999999994, 0.891499999999999959, 0.362999999999999989, 0.192500000000000004, 0.251500000000000001, 6),
+(335, 'F', 0.739999999999999991, 0.599999999999999978, 0.195000000000000007, 1.97399999999999998, 0.597999999999999976, 0.408499999999999974, 0.709999999999999964, 16),
+(1587, 'I', 0.515000000000000013, 0.349999999999999978, 0.104999999999999996, 0.474499999999999977, 0.212999999999999995, 0.122999999999999998, 0.127500000000000002, 10),
+(2448, 'I', 0.275000000000000022, 0.204999999999999988, 0.0800000000000000017, 0.096000000000000002, 0.0359999999999999973, 0.0184999999999999991, 0.0299999999999999989, 6),
+(1362, 'F', 0.604999999999999982, 0.474999999999999978, 0.174999999999999989, 1.07600000000000007, 0.463000000000000023, 0.219500000000000001, 0.33500000000000002, 9),
+(2799, 'M', 0.640000000000000013, 0.484999999999999987, 0.149999999999999994, 1.09800000000000009, 0.519499999999999962, 0.222000000000000003, 0.317500000000000004, 10),
+(1413, 'F', 0.67000000000000004, 0.505000000000000004, 0.174999999999999989, 1.01449999999999996, 0.4375, 0.271000000000000019, 0.3745, 10),
+(1739, 'F', 0.67000000000000004, 0.540000000000000036, 0.195000000000000007, 1.61899999999999999, 0.739999999999999991, 0.330500000000000016, 0.465000000000000024, 11),
+(1152, 'M', 0.584999999999999964, 0.465000000000000024, 0.160000000000000003, 0.955500000000000016, 0.45950000000000002, 0.235999999999999988, 0.265000000000000013, 7),
+(2427, 'I', 0.564999999999999947, 0.434999999999999998, 0.154999999999999999, 0.782000000000000028, 0.271500000000000019, 0.16800000000000001, 0.284999999999999976, 14),
+(1777, 'M', 0.484999999999999987, 0.369999999999999996, 0.154999999999999999, 0.967999999999999972, 0.418999999999999984, 0.245499999999999996, 0.236499999999999988, 9),
+(3294, 'M', 0.574999999999999956, 0.455000000000000016, 0.184999999999999998, 1.15599999999999992, 0.552499999999999991, 0.242999999999999994, 0.294999999999999984, 13),
+(1403, 'M', 0.650000000000000022, 0.510000000000000009, 0.190000000000000002, 1.54200000000000004, 0.715500000000000025, 0.373499999999999999, 0.375, 9),
+(2256, 'M', 0.510000000000000009, 0.395000000000000018, 0.14499999999999999, 0.61850000000000005, 0.215999999999999998, 0.138500000000000012, 0.239999999999999991, 12),
+(3984, 'F', 0.584999999999999964, 0.450000000000000011, 0.125, 0.873999999999999999, 0.354499999999999982, 0.20749999999999999, 0.225000000000000006, 6),
+(1116, 'M', 0.525000000000000022, 0.405000000000000027, 0.119999999999999996, 0.755499999999999949, 0.3755, 0.155499999999999999, 0.201000000000000012, 9),
+(1366, 'M', 0.609999999999999987, 0.474999999999999978, 0.170000000000000012, 1.02649999999999997, 0.434999999999999998, 0.233500000000000013, 0.303499999999999992, 10),
+(3759, 'I', 0.525000000000000022, 0.400000000000000022, 0.140000000000000013, 0.605500000000000038, 0.260500000000000009, 0.107999999999999999, 0.209999999999999992, 9);
+
      2. +
    2. Run the linear regression function and view the results. 
      +\x on
+DROP TABLE IF EXISTS out_table, out_table_summary;
+SELECT madlib.clustered_variance_linregr( 'abalone',
+                                          'out_table',
+                                          'rings',
+                                          'ARRAY[1, diameter, length, height]',
+                                          'sex',
+                                          NULL
+                                        );
+SELECT * FROM out_table;
+
      Result: 
      +-[ RECORD 1 ]-----------------------------------------------------------------------
+coef     | {2.53526184512177,14.1959262629025,-17.4142205261305,73.9536825412142}
+std_err  | {2.08204036310278,10.1218601277935,16.350795118006,17.7971852600971}
+t_stats  | {1.21768141004893,1.40250172237829,-1.06503814649071,4.15535835922465}
+p_values | {0.22845116414893,0.166285056923658,0.2914293364465,0.000112184340238519}
+
      3. +
    3. Run the logistic regression function and view the results. 
      +DROP TABLE IF EXISTS out_table, out_table_summary;
+SELECT madlib.clustered_variance_logregr( 'abalone',
+                                          'out_table',
+                                          'rings < 10',
+                                          'ARRAY[1, diameter, length, height]',
+                                          'sex'
+                                        );
+SELECT * FROM out_table;
+
      Result: 
      +-[ RECORD 1 ]----------------------------------------------------------------------------
+coef     | {7.03525620439852,5.16355730320515,-4.03125518391448,-47.5439002903374}
+std_err  | {2.69860857119167,21.4303882155136,16.6528594816461,5.89094595954187}
+z_stats  | {2.60699394476904,0.240945579299736,-0.242075854201348,-8.0706733038907}
+p_values | {0.00913409755638422,0.809597295390548,0.808721387408619,6.99115526001629e-16}
+
      4. +
    4. Run the multinomial logistic regression and view the results. 
      +DROP TABLE IF EXISTS out_table, out_table_summary;
+SELECT madlib.clustered_variance_mlogregr( 'abalone',
+                                           'out_table',
+                                           'CASE WHEN rings < 10 THEN 1 ELSE 0 END',
+                                           'ARRAY[1, diameter, length, height]',
+                                           'sex',
+                                           0
+                                         );
+SELECT * FROM out_table;
+
      Result: 
      +-[ RECORD 1 ]+-------------------------------------------------------------------------------
+category     | 1
+ref_category | 0
+coef         | {7.03525620439846,5.16355730320138,-4.03125518391122,-47.5439002903385}
+std_err      | {2.69860857119169,21.4303882155156,16.6528594816446,5.89094595954797}
+z_stats      | {2.606993944769,0.240945579299537,-0.242075854201173,-8.07067330388254}
+p_values     | {0.00913409755638535,0.809597295390702,0.808721387408754,6.99115526048361e-16}
+
      5. +
    5. Run the Cox Proportional Hazards regression and compute the clustered robust estimator. 
      +DROP TABLE IF EXISTS sample_data;
+CREATE TABLE sample_data (
+    id INTEGER NOT NULL,
+    grp DOUBLE PRECISION,
+    wbc DOUBLE PRECISION,
+    timedeath INTEGER,
+    status BOOLEAN,
+    sex TEXT
+);
+COPY sample_data FROM STDIN WITH DELIMITER '|';
+  0 |   0 | 1.45 |        35 | t |   'M'
+  1 |   0 | 1.47 |        34 | t |   'M'
+  3 |   0 |  2.2 |        32 | t |   'M'
+  4 |   0 | 1.78 |        25 | t |   'M'
+  5 |   0 | 2.57 |        23 | t |   'M'
+  6 |   0 | 2.32 |        22 | t |   'M'
+  7 |   0 | 2.01 |        20 | t |   'M'
+  8 |   0 | 2.05 |        19 | t |   'M'
+  9 |   0 | 2.16 |        17 | t |   'M'
+ 10 |   0 |  3.6 |        16 | t |   'M'
+ 11 |   1 |  2.3 |        15 | t |   'M'
+ 12 |   0 | 2.88 |        13 | t |   'I'
+ 13 |   1 |  1.5 |        12 | t |   'I'
+ 14 |   0 |  2.6 |        11 | t |   'I'
+ 15 |   0 |  2.7 |        10 | t |   'I'
+ 16 |   0 |  2.8 |         9 | t |   'I'
+ 17 |   1 | 2.32 |         8 | t |   'F'
+ 18 |   0 | 4.43 |         7 | t |   'F'
+ 19 |   0 | 2.31 |         6 | t |   'F'
+ 20 |   1 | 3.49 |         5 | t |   'F'
+ 21 |   1 | 2.42 |         4 | t |   'F'
+ 22 |   1 | 4.01 |         3 | t |   'F'
+ 23 |   1 | 4.91 |         2 | t |   'F'
+ 24 |   1 |    5 |         1 | t |   'F'
+\.
+DROP TABLE IF EXISTS sample_cox, sample_cox_summary, sample_cox_cl;
+SELECT madlib.coxph_train( 'sample_data',
+                           'sample_cox',
+                           'timedeath',
+                           'ARRAY[grp,wbc]',
+                           'status'
+                         );
+SELECT madlib.clustered_variance_coxph('sample_cox',
+                                       'sample_cox_cl',
+                                       'sex');
+SELECT * FROM sample_cox_cl;
+
      Result: 
      +-[ RECORD 1 ]-+----------------------------------------------------------------------------
+coef          | {2.54407073265254,1.67172094779487}
+loglikelihood | -37.8532498733
+std_err       | {0.677180599295183,0.387195514577697}
+clustervar    | sex
+clustered_se  | {0.545274710867954,0.228046806400425}
+clustered_z   | {4.6656679320465,7.33060451133666}
+clustered_p   | {3.07616143241047e-06,2.29116873819977e-13}
+hessian       | {{2.78043065745617,-2.25848560642761},{-2.25848560642761,8.50472838284472}}
+
      Notes
      +
      6. +
    +
      +
    • Note that we need to manually include an intercept term in the independent variable expression. The NULL value of groupingvar means that there is no grouping in the calculation.
      • +
    +

    Technical Background
    +

    Assume that the data can be separated into \(m\) clusters. Usually this can be done by grouping the data table according to one or multiple columns.

    +

    The estimator has a similar form to the usual sandwich estimator

    +\[ S(\vec{c}) = B(\vec{c}) M(\vec{c}) B(\vec{c}) \] +

    +

    The bread part is the same as Huber-White sandwich estimator

    +\begin{eqnarray} B(\vec{c}) & = & \left(-\sum_{i=1}^{n} H(y_i, \vec{x}_i, \vec{c})\right)^{-1}\\ & = & \left(-\sum_{i=1}^{n}\frac{\partial^2 l(y_i, \vec{x}_i, \vec{c})}{\partial c_\alpha \partial c_\beta}\right)^{-1} \end{eqnarray} +

    +

    where \(H\) is the hessian matrix, which is the second derivative of the target function

    +\[ L(\vec{c}) = \sum_{i=1}^n l(y_i, \vec{x}_i, \vec{c})\ . \] +

    +

    The meat part is different

    +\[ M(\vec{c}) = \bf{A}^T\bf{A} \] +

    +

    where the \(m\)-th row of \(\bf{A}\) is

    +\[ A_m = \sum_{i\in G_m}\frac{\partial l(y_i,\vec{x}_i,\vec{c})}{\partial \vec{c}} \] +

    +

    where \(G_m\) is the set of rows that belong to the same cluster.

    +

    We can compute the quantities of \(B\) and \(A\) for each cluster during one scan through the data table in an aggregate function. Then sum over all clusters to the full \(B\) and \(A\) in the outside of the aggregate function. At last, the matrix mulplitications are done in a separate function on the master node.

    +

    When multinomial logistic regression is computed before the multinomial clustered variance calculation, it uses a default reference category of zero and the regression coefficients are included in the output table. The regression coefficients in the output are in the same order as multinomial logistic regression function, which is described below. For a problem with \( K \) dependent variables \( (1, ..., K) \) and \( J \) categories \( (0, ..., J-1) \), let \( {m_{k,j}} \) denote the coefficient for dependent variable \( k \) and category \( j \). The output is \( {m_{k_1, j_0}, m_{k_1, j_1} \ldots m_{k_1, j_{J-1}}, m_{k_2, j_0}, m_{k_2, j_1} \ldots m_{k_K, j_{J-1}}} \). The order is NOT CONSISTENT with the multinomial regression marginal effect calculation with function marginal_mlogregr. This is deliberate because the interfaces of all multinomial regressions (robust, clustered, ...) will be moved to match that used in marginal.

    +

    Literature
    +

    [1] Standard, Robust, and Clustered Standard Errors Computed in R, http://diffuseprior.wordpress.com/2012/06/15/standard-robust-and-clustered-standard-errors-computed-in-r/

    +

    Related Topics
    File clustered_variance.sql_in documenting the clustered variance SQL functions.
    +

    File clustered_variance_coxph.sql_in documenting the clustered variance for Cox proportional hazards SQL functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__clustering.html b/docs/docs/v2.1.0/group__grp__clustering.html new file mode 100644 index 00000000..b43f750e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__clustering.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: Clustering + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    +Modules
    +
    +
    Clustering
    Unsupervised Learning
    +
    +
    +

    Detailed Description

    +

    Methods for clustering data.

    + + + + + +

    +Modules

     k-Means Clustering
     Partitions a set of observations into clusters by finding centroids that minimize the sum of observations' distances from their closest centroid.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__clustering.js b/docs/docs/v2.1.0/group__grp__clustering.js new file mode 100644 index 00000000..61858da9 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__clustering.js @@ -0,0 +1,4 @@ +var group__grp__clustering = +[ + [ "k-Means Clustering", "group__grp__kmeans.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__cols2vec.html b/docs/docs/v2.1.0/group__grp__cols2vec.html new file mode 100644 index 00000000..8fbabadb --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__cols2vec.html @@ -0,0 +1,391 @@ + + + + + + + + +MADlib: Columns to Vector + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    Columns to Vector
    Utilities
    +
    +
    +
    Contents +
    About
    Convert feature columns in a table into an array in a single column.
    +

    Given a table with a number of feature columns, this function will create an output table that contains the feature columns in an array. A summary table will also be created that contains the names of the features combined into array, so that this process can be reversed using the function vec2cols.

    +

    Usage
    +
    +cols2vec(
+    source_table,
+    output_table,
+    list_of_features,
+    list_of_features_to_exclude,
+    cols_to_output
+)
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the source data.

    +

    +
    +
    output_table
    +

    TEXT. Name of the generated table containing the output.

    +

    +
    +
    list_of_features
    +

    TEXT. Comma-separated string of column names or expressions to put into feature array. Can also be '*' implying all columns are to be put into feature array (except for the ones included in the next argument that lists exclusions). Type casting will be done as per the regular type casting rules of the underlying database. Array columns in the source table are not supported in the 'list_of_features' parameter. Also, all of the features to be included must be of the same type and must not have null values.

    +

    +
    +
    list_of_features_to_exclude (optional)
    +

    TEXT. Default NULL. Comma-separated string of column names to exclude from the feature array. Typically used when 'list_of_features' is set to '*'.

    +

    +
    +
    cols_to_output (optional)
    +
    TEXT. Default NULL. Comma-separated string of column names from the source table to keep in the output table, in addition to the feature array. To keep all columns from the source table, use '*' for this parameter.
    +
    +

    Output table
    + The output table produced by the cols2vec function contains the following columns:

    + + + + +
    <...> Columns from source table, depending on which ones are kept (if any).
    feature_vector Column that contains the feature array.
    +

    Output summary table
    + A summary table named <output_table>_summary is also created that contains:

    + + + + + + + + +
    source_table Name of the table containing the source data.
    list_of_features List of features to put in vector.
    list_of_features_to_exclude Features specified by the user to exclude from 'list_of_features'.
    feature_names Names of the features that were nested (converted to a vector) in the output table.
    +

    Examples
    +
      +
    1. Load sample data: 
      +DROP TABLE IF EXISTS golf CASCADE;
+CREATE TABLE golf (
+    id integer NOT NULL,
+    "OUTLOOK" text,
+    temperature double precision,
+    humidity double precision,
+    "Temp_Humidity" double precision[],
+    clouds_airquality text[],
+    windy boolean,
+    class text,
+    observation_weight double precision
+);
+INSERT INTO golf VALUES
+(1,'sunny', 85, 85, ARRAY[85, 85],ARRAY['none', 'unhealthy'], 'false','Don''t Play', 5.0),
+(2, 'sunny', 80, 90, ARRAY[80, 90], ARRAY['none', 'moderate'], 'true', 'Don''t Play', 5.0),
+(3, 'overcast', 83, 78, ARRAY[83, 78], ARRAY['low', 'moderate'], 'false', 'Play', 1.5),
+(4, 'rain', 70, 96, ARRAY[70, 96], ARRAY['low', 'moderate'], 'false', 'Play', 1.0),
+(5, 'rain', 68, 80, ARRAY[68, 80], ARRAY['medium', 'good'], 'false', 'Play', 1.0),
+(6, 'rain', 65, 70, ARRAY[65, 70], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play', 1.0),
+(7, 'overcast', 64, 65, ARRAY[64, 65], ARRAY['medium', 'moderate'], 'true', 'Play', 1.5),
+(8, 'sunny', 72, 95, ARRAY[72, 95], ARRAY['high', 'unhealthy'], 'false', 'Don''t Play', 5.0),
+(9, 'sunny', 69, 70, ARRAY[69, 70], ARRAY['high', 'good'], 'false', 'Play', 5.0),
+(10, 'rain', 75, 80, ARRAY[75, 80], ARRAY['medium', 'good'], 'false', 'Play', 1.0),
+(11, 'sunny', 75, 70, ARRAY[75, 70], ARRAY['none', 'good'], 'true', 'Play', 5.0),
+(12, 'overcast', 72, 90, ARRAY[72, 90], ARRAY['medium', 'moderate'], 'true', 'Play', 1.5),
+(13, 'overcast', 81, 75, ARRAY[81, 75], ARRAY['medium', 'moderate'], 'false', 'Play', 1.5),
+(14, 'rain', 71, 80, ARRAY[71, 80], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play', 1.0);
+
      2. +
    2. Run cols2vec to combine the temperature and humidity columns into a single array feature. 
      +DROP TABLE IF EXISTS cols2vec_result, cols2vec_result_summary;
+SELECT madlib.cols2vec(
+    'golf',
+    'cols2vec_result',
+    'temperature, humidity'
+);
+SELECT * FROM cols2vec_result;
+
      + feature_vector
+----------------+
+ {85,85}
+ {80,90}
+ {83,78}
+ {70,96}
+ {68,80}
+ {65,70}
+ {64,65}
+ {72,95}
+ {69,70}
+ {75,80}
+ {75,70}
+ {72,90}
+ {81,75}
+ {71,80}
+(14 rows)
+
      View the summary table: 
      +\x on
+SELECT * FROM cols2vec_result_summary;
+\x off
+
      +-[ RECORD 1 ]---------------+----------------------------------------------------------------
+source_table                | golf
+list_of_features            | temperature, humidity
+list_of_features_to_exclude | None
+feature_names               | {temperature,humidity}
+
      3. +
    3. Combine the temperature and humidity columns and keep 2 other columns from source_table. 
      +DROP TABLE IF EXISTS cols2vec_result, cols2vec_result_summary;
+SELECT madlib.cols2vec(
+    'golf',
+    'cols2vec_result',
+    'temperature, humidity',
+    NULL,
+    'id, "OUTLOOK"'
+);
+SELECT * FROM cols2vec_result ORDER BY id;
+
      + id | OUTLOOK  | feature_vector
+----+----------+----------------
+  1 | sunny    | {85,85}
+  2 | sunny    | {80,90}
+  3 | overcast | {83,78}
+  4 | rain     | {70,96}
+  5 | rain     | {68,80}
+  6 | rain     | {65,70}
+  7 | overcast | {64,65}
+  8 | sunny    | {72,95}
+  9 | sunny    | {69,70}
+ 10 | rain     | {75,80}
+ 11 | sunny    | {75,70}
+ 12 | overcast | {72,90}
+ 13 | overcast | {81,75}
+ 14 | rain     | {71,80}
+(14 rows)
+
      View the summary table: 
      +\x on
+SELECT * FROM cols2vec_result_summary;
+\x off
+
      +-[ RECORD 1 ]---------------+----------------------------------------------------------------
+source_table                | golf
+list_of_features            | temperature, humidity
+list_of_features_to_exclude | None
+feature_names               | {temperature,humidity}
+
      4. +
    4. Combine all columns, excluding all columns that are not of type double precision. 
      +DROP TABLE IF EXISTS cols2vec_result, cols2vec_result_summary;
+SELECT madlib.cols2vec(
+    'golf',
+    'cols2vec_result',
+    '*',
+    '"OUTLOOK", "Temp_Humidity", clouds_airquality, windy, class, id',
+    'id, "OUTLOOK"'
+);
+SELECT * FROM cols2vec_result ORDER BY id;
+
      + id | OUTLOOK  | feature_vector
+----+----------+----------------
+  1 | sunny    | {85,85,5}
+  2 | sunny    | {80,90,5}
+  3 | overcast | {83,78,1.5}
+  4 | rain     | {70,96,1}
+  5 | rain     | {68,80,1}
+  6 | rain     | {65,70,1}
+  7 | overcast | {64,65,1.5}
+  8 | sunny    | {72,95,5}
+  9 | sunny    | {69,70,5}
+ 10 | rain     | {75,80,1}
+ 11 | sunny    | {75,70,5}
+ 12 | overcast | {72,90,1.5}
+ 13 | overcast | {81,75,1.5}
+ 14 | rain     | {71,80,1}
+(14 rows)
+
      View summary table: 
      +\x on
+SELECT * FROM cols2vec_result_summary;
+\x off
+
      +-[ RECORD 1 ]---------------+----------------------------------------------------------------
+source_table                | golf
+list_of_features            | *
+list_of_features_to_exclude | "OUTLOOK", "Temp_Humidity", clouds_airquality, windy, class, id
+feature_names               | {temperature,humidity,observation_weight}
+
      5. +
    5. Combine the temperature and humidity columns, exclude windy, and keep all of the columns from the source table. 
      +DROP TABLE IF EXISTS cols2vec_result, cols2vec_result_summary;
+SELECT madlib.cols2vec(
+    'golf',
+    'cols2vec_result',
+    'windy, temperature, humidity',
+    'windy',
+    '*'
+);
+SELECT * FROM cols2vec_result ORDER BY id;
+
      + id | OUTLOOK  | temperature | humidity | Temp_Humidity | clouds_airquality | windy |   class    | observation_weight | feature_vector
+----+----------+-------------+----------+---------------+-------------------+-------+------------+--------------------+----------------
+  1 | sunny    |          85 |       85 | {85,85}       | {none,unhealthy}  | f     | Don't Play |                  5 | {85,85}
+  2 | sunny    |          80 |       90 | {80,90}       | {none,moderate}   | t     | Don't Play |                  5 | {80,90}
+  3 | overcast |          83 |       78 | {83,78}       | {low,moderate}    | f     | Play       |                1.5 | {83,78}
+  4 | rain     |          70 |       96 | {70,96}       | {low,moderate}    | f     | Play       |                  1 | {70,96}
+  5 | rain     |          68 |       80 | {68,80}       | {medium,good}     | f     | Play       |                  1 | {68,80}
+  6 | rain     |          65 |       70 | {65,70}       | {low,unhealthy}   | t     | Don't Play |                  1 | {65,70}
+  7 | overcast |          64 |       65 | {64,65}       | {medium,moderate} | t     | Play       |                1.5 | {64,65}
+  8 | sunny    |          72 |       95 | {72,95}       | {high,unhealthy}  | f     | Don't Play |                  5 | {72,95}
+  9 | sunny    |          69 |       70 | {69,70}       | {high,good}       | f     | Play       |                  5 | {69,70}
+ 10 | rain     |          75 |       80 | {75,80}       | {medium,good}     | f     | Play       |                  1 | {75,80}
+ 11 | sunny    |          75 |       70 | {75,70}       | {none,good}       | t     | Play       |                  5 | {75,70}
+ 12 | overcast |          72 |       90 | {72,90}       | {medium,moderate} | t     | Play       |                1.5 | {72,90}
+ 13 | overcast |          81 |       75 | {81,75}       | {medium,moderate} | f     | Play       |                1.5 | {81,75}
+ 14 | rain     |          71 |       80 | {71,80}       | {low,unhealthy}   | t     | Don't Play |                  1 | {71,80}
+(14 rows)
+
      View the summary table: 
      +\x on
+SELECT * FROM cols2vec_result_summary;
+\x off
+
      +-[ RECORD 1 ]---------------+-----------------------------
+source_table                | golf
+list_of_features            | windy, temperature, humidity
+list_of_features_to_exclude | windy
+feature_names               | {temperature,humidity}
+
      This also shows that you can exclude features in 'list_of_features_to_exclude' that are in the list of 'list_of_features'. This can be useful if the 'list_of_features' is generated from an expression or subquery.
      6. +
    6. Type casting works as per regular rules of the underlying database. E.g, combining integer and double precisions columns will create a double precision feature vector. For Boolean, do an explicit cast to the target type: 
      +DROP TABLE IF EXISTS cols2vec_result, cols2vec_result_summary;
+SELECT madlib.cols2vec(
+    'golf',
+    'cols2vec_result',
+    'windy::TEXT, class',
+    NULL,
+    'id'
+);
+SELECT * FROM cols2vec_result ORDER BY id;
+
      + id |    feature_vector
+-—+-------------------—
+  1 | {false,"Don't Play"}
+  2 | {true,"Don't Play"}
+  3 | {false,Play}
+  4 | {false,Play}
+  5 | {false,Play}
+  6 | {true,"Don't Play"}
+  7 | {true,Play}
+  8 | {false,"Don't Play"}
+  9 | {false,Play}
+ 10 | {false,Play}
+ 11 | {true,Play}
+ 12 | {true,Play}
+ 13 | {false,Play}
+ 14 | {true,"Don't Play"}
+(14 rows)
+
      7. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__correlation.html b/docs/docs/v2.1.0/group__grp__correlation.html new file mode 100644 index 00000000..5e6f1521 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__correlation.html @@ -0,0 +1,382 @@ + + + + + + + + +MADlib: Covariance and Correlation + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    +
    Covariance and Correlation
    Statistics » Descriptive Statistics
    +
    +
    +
    Contents +

    A correlation function is the degree and direction of association of two variables—how well one random variable can be predicted from the other. It is a normalized version of covariance. The Pearson correlation coefficient is used here, which has a value between -1 and 1, where 1 implies total positive linear correlation, 0 means no linear correlation, and -1 means total negative linear correlation.

    +

    This function generates an \(N\)x \(N\) cross correlation matrix for pairs of numeric columns in a source_table. It is square symmetrical with the \( (i,j) \)th element equal to the correlation coefficient between the \(i\)th and the \(j\)th variable. The diagonal elements (correlations of variables with themselves) are always equal to 1.0.

    +

    We also provide a covariance function which is similar in nature to correlation, and is a measure of the joint variability of two random variables.

    +

    Covariance and Correlation Functions
    +

    The correlation function has the following syntax: 

    +correlation( source_table,
+             output_table,
+             target_cols,
+             verbose,
+             grouping_cols,
+             n_groups_per_run
+           )
+

    The covariance function has a similar syntax: 

    +covariance( source_table,
+            output_table,
+            target_cols,
+            verbose,
+            grouping_cols,
+            n_groups_per_run
+          )
+
    +
    source_table
    +

    TEXT. Name of the table containing the input data.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table containing the cross correlation matrix. The output table has N rows, where N is the number of 'target_cols' in the 'source_table' for which correlation or covariance is being computed. It has the following columns:

    + + + + + + + + +
    column_position An automatically generated sequential counter indicating the order of the variable in the 'output_table'.
    variable Contains the row header for the variables of interest.
    grouping_cols Contains the grouping columns, if any.
    <...> The remainder of the table is the NxN correlation matrix for the pairs of variables of interest.
    +

    The output table is arranged as a lower-triangular matrix with the upper triangle set to NULL and the diagonal elements set to 1.0. To obtain the result from the 'output_table' order by 'column_position': 

    +SELECT * FROM output_table ORDER BY column_position;
+

    In addition to output table, a summary table named <output_table>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + +
    method'Correlation' or 'Covariance'
    source_tableVARCHAR. Data source table name.
    output_tableVARCHAR. Output table name.
    column_namesVARCHAR. Column names used for correlation computation, as a comma-separated string.
    grouping_cols Contains the grouping columns, if any.
    mean_vectorFLOAT8[]. Mean value of column for variables of interest.
    total_rows_processed BIGINT. Total numbers of rows processed.
    +

    +
    +
    target_cols (optional)
    +

    TEXT, default: '*'. A comma-separated list of the columns to correlate. If NULL or '*', results are produced for all numeric columns.

    +

    +
    +
    verbose (optional)
    +

    BOOLEAN, default: FALSE. Print verbose information if TRUE.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. A comma-separated list of the columns to group by.

    +

    +
    +
    n_groups_per_run (optional)
    +
    INTEGER, default: 10. Number of groups to process at a time. This parameter is ignored if 'grouping_cols' is not specified. Generally the default value will work fine, but there may be cases (see below) where you will want to experiment with it to reduce execution time and memory usage.
    Note
    This is a lower level parameter that can potentially be used to improve performance, but should be used with caution. It is designed to handle the case where you have a large number of groups. In general, increasing 'n_groups_per_run' means we construct a larger 'UNION ALL' query which uses more memory and may slow down execution if it gets too big. If you have a large number of groups and a smaller data size, there may be benefits to increasing this value. Conversely, decreasing 'n_groups_per_run' means we issue more 'plpy.execute' commands. This increases overhead and can modestly affect the execution time.
    +
    +
    +

    Examples
    +
      +
    1. Create an input dataset. 
      +DROP TABLE IF EXISTS example_data CASCADE;
+CREATE TABLE example_data(
+    id SERIAL,
+    outlook TEXT,
+    temperature FLOAT8,
+    humidity FLOAT8,
+    windy TEXT,
+    class TEXT,
+    day TEXT
+);
+INSERT INTO example_data VALUES
+(1, 'sunny', 85, 85, 'false', 'Dont Play', 'Mon'),
+(2, 'sunny', 80, 90, 'true', 'Dont Play', 'Mon'),
+(3, 'overcast', 83, 78, 'false', 'Play', 'Mon'),
+(4, 'rain', 70, 96, 'false', 'Play', 'Mon'),
+(5, 'rain', 68, 80, 'false', 'Play', 'Mon'),
+(6, 'rain', 65, 70, 'true', 'Dont Play', 'Mon'),
+(7, 'overcast', 64, 65, 'true', 'Play', 'Mon'),
+(8, 'sunny', 72, 95, 'false', 'Dont Play', 'Mon'),
+(9, 'sunny', 69, 70, 'false', 'Play', 'Mon'),
+(10, 'rain', 75, 80, 'false', 'Play', 'Mon'),
+(11, 'sunny', 75, 70, 'true', 'Play', 'Mon'),
+(12, 'overcast', 72, 90, 'true', 'Play', 'Mon'),
+(13, 'overcast', 81, 75, 'false', 'Play', 'Mon'),
+(14, 'rain', 71, 80, 'true', 'Dont Play', 'Mon'),
+(15, NULL, 100, 100, 'true', NULL, 'Mon'),
+(16, NULL, 110, 100, 'true', NULL, 'Mon'),
+(101, 'sunny', 85, 85, 'false', 'Dont Play', 'Tues'),
+(102, 'sunny', 80, 90, 'true', 'Dont Play', 'Tues'),
+(103, 'overcast', 83, 78, 'false', 'Play', 'Tues'),
+(104, 'rain', 70, 96, 'false', 'Play', 'Tues'),
+(105, 'rain', 68, 80, 'false', 'Play', 'Tues'),
+(106, 'rain', 65, 70, 'true', 'Dont Play', 'Tues'),
+(107, 'overcast', 64, 65, 'true', 'Play', 'Tues'),
+(108, 'sunny', 72, 95, 'false', 'Dont Play', 'Tues'),
+(109, 'sunny', 69, 70, 'false', 'Play', 'Tues'),
+(110, 'rain', 75, 80, 'false', 'Play', 'Tues'),
+(111, 'sunny', 75, 70, 'true', 'Play', 'Tues'),
+(112, 'overcast', 72, 90, 'true', 'Play', 'Tues'),
+(113, 'overcast', 81, 75, 'false', 'Play', 'Tues'),
+(114, 'rain', 71, 80, 'true', 'Dont Play', 'Tues'),
+(115, NULL, 100, 100, 'true', NULL, 'Tues'),
+(116, NULL, 110, 100, 'true', NULL, 'Tues'),
+(201, 'sunny', 85, 85, 'false', 'Dont Play', 'Wed'),
+(202, 'sunny', 80, 90, 'true', 'Dont Play', 'Wed'),
+(203, 'overcast', 83, 78, 'false', 'Play', 'Wed'),
+(204, 'rain', 70, 96, 'false', 'Play', 'Wed'),
+(205, 'rain', 68, 80, 'false', 'Play', 'Wed'),
+(206, 'rain', 65, 70, 'true', 'Dont Play', 'Wed'),
+(207, 'overcast', 64, 65, 'true', 'Play', 'Wed'),
+(208, 'sunny', 7, 95, 'false', 'Dont Play', 'Wed'),
+(209, 'sunny', 6, 70, 'false', 'Play', 'Wed'),
+(210, 'rain', 7, 80, 'false', 'Play', 'Wed'),
+(211, 'sunny', 75, 70, 'true', 'Play', 'Wed'),
+(212, 'overcast', 72, 90, 'true', 'Play', 'Wed'),
+(213, 'overcast', 81, 75, 'false', 'Play', 'Wed'),
+(214, 'rain', 71, 80, 'true', 'Dont Play', 'Wed'),
+(215, NULL, 10, 100, 'true', NULL, 'Wed'),
+(216, NULL, 10, 100, 'true', NULL, 'Wed'),
+(217, 'sunny', 85, 85, 'false', 'Dont Play', 'Wed'),
+(218, 'sunny', 80, 9, 'true', 'Dont Play', 'Wed'),
+(219, 'overcast', 83, 78, 'false', 'Play', 'Wed'),
+(220, 'rain', 70, 9, 'false', 'Play', 'Wed'),
+(221, 'rain', 68, 80, 'false', 'Play', 'Wed');
+
      2. +
    2. Get correlation between temperature and humidity: 
      +DROP TABLE IF EXISTS example_data_output, example_data_output_summary;
+SELECT madlib.correlation( 'example_data',
+                           'example_data_output',
+                           'temperature, humidity'
+                         );
+
      View the correlation matrix: 
      +SELECT * FROM example_data_output ORDER BY column_position;
+
      + column_position |  variable   |     temperature     | humidity
+-----------------+-------------+---------------------+----------
+               1 | temperature |                   1 |
+               2 | humidity    | 0.00607993890408995 |        1
+(2 rows)
+
      View the summary table: 
      +\x on
+SELECT * FROM example_data_output_summary;
+
      +-[ RECORD 1 ]--------+-----------------------------------
+method               | Correlation
+source               | example_data
+output_table         | example_data_output
+column_names         | {temperature,humidity}
+mean_vector          | {70.188679245283,79.8679245283019}
+total_rows_processed | 53
+
      3. +
    3. Correlation with grouping by day: 
      +\x off
+DROP TABLE IF EXISTS example_data_output, example_data_output_summary;
+SELECT madlib.correlation( 'example_data',
+                           'example_data_output',
+                           'temperature, humidity',
+                           FALSE,
+                           'day'
+                         );
+
      View the correlation matrix by group: 
      +SELECT * FROM example_data_output ORDER BY day, column_position;
+
      + column_position |  variable   | day  |    temperature    | humidity
+-----------------+-------------+------+-------------------+----------
+               1 | temperature | Mon  |                 1 |
+               2 | humidity    | Mon  | 0.616876934548786 |        1
+               1 | temperature | Tues |                 1 |
+               2 | humidity    | Tues | 0.616876934548786 |        1
+               1 | temperature | Wed  |                 1 |
+               2 | humidity    | Wed  | -0.28969669368457 |        1
+(6 rows)
+
      View the summary table: 
      +\x on
+SELECT * FROM example_data_output_summary ORDER BY day;
+
      +-[ RECORD 1 ]--------+------------------------------------
+method               | Correlation
+source               | example_data
+output_table         | example_data_output
+column_names         | {temperature,humidity}
+day                  | Mon
+mean_vector          | {77.5,82.75}
+total_rows_processed | 16
+-[ RECORD 2 ]--------+------------------------------------
+method               | Correlation
+source               | example_data
+output_table         | example_data_output
+column_names         | {temperature,humidity}
+day                  | Tues
+mean_vector          | {77.5,82.75}
+total_rows_processed | 16
+-[ RECORD 3 ]--------+------------------------------------
+method               | Correlation
+source               | example_data
+output_table         | example_data_output
+column_names         | {temperature,humidity}
+day                  | Wed
+mean_vector          | {59.0476190476191,75.4761904761905}
+total_rows_processed | 21
+
      4. +
    4. Get covariance between temperature and humidity: 
      +\x off
+DROP TABLE IF EXISTS example_data_output, example_data_output_summary;
+SELECT madlib.covariance( 'example_data',
+                          'example_data_output',
+                          'temperature, humidity'
+                         );
+
      View the covariance matrix: 
      +SELECT * FROM example_data_output ORDER BY column_position;
+
      + column_position |  variable   |   temperature    |     humidity
+-----------------+-------------+------------------+------------------
+               1 | temperature | 507.926664293343 |
+               2 | humidity    | 2.40227839088644 | 307.359914560342
+(2 rows)
+
      View the summary table: 
      +\x on
+SELECT * FROM example_data_output_summary;
+
      +-[ RECORD 1 ]--------+-----------------------------------
+method               | Covariance
+source               | example_data
+output_table         | example_data_output
+column_names         | {temperature,humidity}
+mean_vector          | {70.188679245283,79.8679245283019}
+total_rows_processed | 53
+
      5. +
    +
    Notes
    +

    Null values will be replaced by the mean of their respective columns (mean imputation/substitution). Mean imputation is a method in which the missing value on a certain variable is replaced by the mean of the available cases. This method maintains the sample size and is easy to use, but the variability in the data is reduced, so the standard deviations and the variance estimates tend to be underestimated. Please refer to [1] and [2] for details.

    +

    If the mean imputation method is not suitable for the target use case, it is advised to employ a view that handles the NULL values prior to calling the correlation/covariance functions.

    +

    Literature
    +

    [1] https://en.wikipedia.org/wiki/Imputation_(statistics)

    +

    [2] https://www.iriseekhout.com/missing-data/missing-data-methods/imputation-methods/

    +

    Related Topics
    +

    File correlation.sql_in documenting the SQL functions

    +

    Summary for general descriptive statistics for a table

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__countmin.html b/docs/docs/v2.1.0/group__grp__countmin.html new file mode 100644 index 00000000..6514ee41 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__countmin.html @@ -0,0 +1,232 @@ + + + + + + + + +MADlib: CountMin (Cormode-Muthukrishnan) + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    CountMin (Cormode-Muthukrishnan)
    Statistics » Descriptive Statistics » Cardinality Estimators
    +
    +
    +
    Contents +

    This module implements Cormode-Muthukrishnan CountMin sketches on integer values, implemented as a user-defined aggregate. It also provides scalar functions over the sketches to produce approximate counts, order statistics, and histograms.

    +

    Syntax
      +
    • Get a sketch of a selected column specified by col_name. 
      +cmsketch( col_name )
+
      • +
    • Get the number of rows where col_name = p, computed from the sketch obtained from cmsketch. 
      +cmsketch_count( cmsketch,
+                p )
+
      • +
    • Get the number of rows where col_name is between m and n inclusive. 
      +cmsketch_rangecount( cmsketch,
+                     m,
+                     n )
+
      • +
    • Get the kth percentile of col_name where count specifies number of rows. k should be an integer between 1 to 99. 
      +cmsketch_centile( cmsketch,
+                  k,
+                  count )
+
      • +
    • Get the median of col_name where count specifies number of rows. This is equivalent to cmsketch_centile(cmsketch,50,count). 
      +cmsketch_median( cmsketch,
+                 count )
+
      • +
    • Get an n-bucket histogram for values between min and max for the column where each bucket has approximately the same width. The output is a text string containing triples {lo, hi, count} representing the buckets; counts are approximate. 
      +cmsketch_width_histogram( cmsketch,
+                          min,
+                          max,
+                          n )
+
      • +
    • Get an n-bucket histogram for the column where each bucket has approximately the same count. The output is a text string containing triples {lo, hi, count} representing the buckets; counts are approximate. Note that an equi-depth histogram is equivalent to a spanning set of equi-spaced centiles. 
      +cmsketch_depth_histogram( cmsketch,
+                          n )
+
      • +
    +
    +
    Note
    This is a User Defined Aggregate which returns the results when used in a query. Use "CREATE TABLE AS ", with the UDA as subquery if the results are to be stored. This is unlike the usual MADlib stored procedure interface which places the results in a table instead of returning it.
    +

    Examples
    +
      +
    1. Generate some data. 
      +CREATE TABLE data(class INT, a1 INT);
+INSERT INTO data SELECT 1,1 FROM generate_series(1,10000);
+INSERT INTO data SELECT 1,2 FROM generate_series(1,15000);
+INSERT INTO data SELECT 1,3 FROM generate_series(1,10000);
+INSERT INTO data SELECT 2,5 FROM generate_series(1,1000);
+INSERT INTO data SELECT 2,6 FROM generate_series(1,1000);
+
      2. +
    2. Count number of rows where a1 = 2 in each class. Store results in a table. 
      +CREATE TABLE sketch_count AS
+SELECT class,
+       cmsketch_count( cmsketch( a1 ), 2 )
+FROM data GROUP BY data.class;
+SELECT * FROM sketch_count;
+
      Result: 
      + class | cmsketch_count
+ ------+----------------
+     2 |              0
+     1 |          15000
+(2 rows)
+
      3. +
    3. Count number of rows where a1 is between 3 and 6. 
      +SELECT class,
+       cmsketch_rangecount( cmsketch(a1), 3, 6 )
+FROM data GROUP BY data.class;
+
      Result: 
      + class | cmsketch_rangecount
+ ------+---------------------
+     2 |                2000
+     1 |               10000
+(2 rows)
+
      4. +
    4. Compute the 90th percentile of all of a1. 
      +SELECT cmsketch_centile( cmsketch( a1 ), 90, count(*) )
+FROM data;
+
      Result: 
      + cmsketch_centile
+ -----------------
+                3
+(1 row)
+
      5. +
    5. Produce an equi-width histogram with 2 bins between 0 and 10. 
      +SELECT cmsketch_width_histogram( cmsketch( a1 ), 0, 10, 2 )
+FROM data;
+
      Result: 
      +      cmsketch_width_histogram
+ -----------------------------------
+ [[0L, 4L, 35000], [5L, 10L, 2000]]
+(1 row)
+
      6. +
    6. Produce an equi-depth histogram of a1 with 2 bins of approximately equal depth. 
      +SELECT cmsketch_depth_histogram( cmsketch( a1 ), 2 )
+FROM data;
+
      Result: 
      +                       cmsketch_depth_histogram
+ ----------------------------------------------------------------------
+ [[-9223372036854775807L, 1, 10000], [2, 9223372036854775807L, 27000]]
+(1 row)
+
      7. +
    +

    Literature
    +

    [1] G. Cormode and S. Muthukrishnan. An improved data stream summary: The count-min sketch and its applications. LATIN 2004, J. Algorithm 55(1): 58-75 (2005) . http://dimacs.rutgers.edu/~graham/pubs/html/CormodeMuthukrishnan04CMLatin.html

    +

    [2] G. Cormode. Encyclopedia entry on 'Count-Min Sketch'. In L. Liu and M. T. Ozsu, editors, Encyclopedia of Database Systems, pages 511-516. Springer, 2009. http://dimacs.rutgers.edu/~graham/pubs/html/Cormode09b.html

    +

    File sketch.sql_in documenting the SQL functions.

    +

    Module grp_quantile for a different implementation of quantile function.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__cox__prop__hazards.html b/docs/docs/v2.1.0/group__grp__cox__prop__hazards.html new file mode 100644 index 00000000..2e5d29c1 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__cox__prop__hazards.html @@ -0,0 +1,468 @@ + + + + + + + + +MADlib: Cox-Proportional Hazards Regression + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    +
    Cox-Proportional Hazards Regression
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    Proportional-Hazard models enable the comparison of various survival models. These survival models are functions describing the probability of a one-item event (prototypically, this event is death) with respect to time. The interval of time before the occurrence of death can be called the survival time. Let T be a random variable representing the survival time, with a cumulative probability function P(t). Informally, P(t) is the probability that death has happened before time t.

    +

    Training Function
    +

    Following is the syntax for the coxph_train() training function: 

    +coxph_train( source_table,
+             output_table,
+             dependent_variable,
+             independent_variable,
+             right_censoring_status,
+             strata,
+             optimizer_params
+           )
+

    Arguments

    +
    source_table
    +
    TEXT. The name of the table containing input data.
    +
    output_table
    +

    TEXT. The name of the table where the output model is saved. The output is saved in the table named by the output_table argument. It has the following columns:

    + + + + + + + + + + + + + + +
    coef FLOAT8[]. Vector of the coefficients.
    loglikelihood FLOAT8. Log-likelihood value of the MLE estimate.
    std_err FLOAT8[]. Vector of the standard error of the coefficients.
    stats FLOAT8[]. Vector of the statistics of the coefficients.
    p_values FLOAT8[]. Vector of the p-values of the coefficients.
    hessian FLOAT8[]. The Hessian matrix computed using the final solution.
    num_iterations INTEGER. The number of iterations performed by the optimizer.
    +

    Additionally, a summary output table is generated that contains a summary of the parameters used for building the Cox model. It is stored in a table named <output_table>_summary. It has the following columns:

    + + + + + + + + + + + + + + +
    source_table The source table name.
    dependent_variable The dependent variable name.
    independent_variable The independent variable name.
    right_censoring_status The right censoring status
    strata The stratification columns
    num_processed The number of rows that were actually used in the computation.
    num_missing_rows_skipped The number of rows that were skipped in the computation due to NULL values in them.
    +

    +
    +
    dependent_variable
    +
    TEXT. A string containing the name of a column that contains an array of numeric values, or a string expression in the format 'ARRAY[1, x1, x2, x3]', where x1, x2 and x3 are column names. Dependent variables refer to the time of death. There is no need to pre-sort the data.
    +
    independent_variable
    +
    TEXT. The name of the independent variable.
    +
    right_censoring_status (optional)
    +
    TEXT, default: TRUE for all observations. A string containing an expression that evaluates to the right-censoring status for the observation—TRUE if the observation is not censored and FALSE if the observation is censored. The string could contain the name of the column containing the right-censoring status, a fixed Boolean expression (i.e., 'true', 'false', '0', '1') that applies to all observations, or a Boolean expression such as 'column_name < 10' that can be evaluated for each observation.
    +
    strata (optional)
    +
    VARCHAR, default: NULL, which does not do any stratifications. A string of comma-separated column names that are the strata ID variables used to do stratification.
    +
    optimizer_params (optional)
    +

    VARCHAR, default: NULL, which uses the default values of optimizer parameters: max_iter=100, optimizer=newton, tolerance=1e-8, array_agg_size=10000000, sample_size=1000000. It should be a string that contains 'key=value' pairs separated by commas. The meanings of these parameters are:

    +
      +
    • max_iter — The maximum number of iterations. The computation stops if the number of iterations exceeds this, which usually means that there is no convergence.
      • +
    • optimizer — The optimization method. Right now, "newton" is the only one supported.
      • +
    • tolerance — The stopping criteria. When the difference between the log-likelihoods of two consecutive iterations is smaller than this number, the computation has already converged and stops.
      • +
    • array_agg_size — To speed up the computation, the original data table is cut into multiple pieces, and each pieces of the data is aggregated into one big row. In the process of computation, the whole big row is loaded into memory and thus speed up the computation. This parameter controls approximately how many numbers we want to put into one big row. Larger value of array_agg_size may speed up more, but the size of the big row cannot exceed 1GB due to the restriction of PostgreSQL databases.
      • +
    • sample_size — To cut the data into approximate equal pieces, we first sample the data, and then find out the break points using this sampled data. A larger sample_size produces more accurate break points.
      • +
    +
    +
    +

    Proportional Hazards Assumption Test Function
    +

    The cox_zph() function tests the proportional hazards assumption (PHA) of a Cox regression.

    +

    Proportional-hazard models enable the comparison of various survival models. These PH models, however, assume that the hazard for a given individual is a fixed proportion of the hazard for any other individual, and the ratio of the hazards is constant across time. MADlib does not currently have support for performing any transformation of the time to compute the correlation.

    +

    The cox_zph() function is used to test this assumption by computing the correlation of the residual of the coxph_train() model with time.

    +

    Following is the syntax for the cox_zph() function: 

    +cox_zph(cox_model_table, output_table)
+

    Arguments

    +
    cox_model_table
    +

    TEXT. The name of the table containing the Cox Proportional-Hazards model.

    +

    +
    +
    output_table
    +
    TEXT. The name of the table where the test statistics are saved. The output table is named by the output_table argument and has the following columns: + + + + + + + + +
    covariate TEXT. The independent variables.
    rho FLOAT8[]. Vector of the correlation coefficients between survival time and the scaled Schoenfeld residuals.
    chi_square FLOAT8[]. Chi-square test statistic for the correlation analysis.
    p_value FLOAT8[]. Two-side p-value for the chi-square statistic.
    +
    +
    +

    Additionally, the residual values are outputted to the table named output_table_residual. The table contains the following columns:

    + + + + + + +
    <dep_column_name> FLOAT8. Time values (dependent variable) present in the original source table.
    residual FLOAT8[]. Difference between the original covariate values and the expectation of the covariates obtained from the coxph_train model.
    scaled_residual Residual values scaled by the variance of the coefficients.
    +

    Notes
    +
      +
    • Table names can be optionally schema qualified (current_schemas() is used if a schema name is not provided) and table and column names should follow case-sensitivity and quoting rules per the database. For instance, 'mytable' and 'MyTable' both resolve to the same entity—'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"'.
      • +
    • The cox_prop_hazards_regr() and cox_prop_hazards() functions have been deprecated; coxph_train() should be used instead.
      • +
    +

    Prediction Function
    The prediction function is provided to calculate the linear predictionors, risk or the linear terms for the given prediction data. It has the following syntax: 
    +coxph_predict(model_table,
+              source_table,
+              id_col_name,
+              output_table,
+              pred_type,
+              reference)
+
    +

    Arguments

    +
    model_table
    +

    TEXT. Name of the table containing the cox model.

    +

    +
    +
    source_table
    +

    TEXT. Name of the table containing the prediction data.

    +

    +
    +
    id_col_name
    +

    TEXT. Name of the id column in the source table.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table to store the prediction results in. The output table is named by the output_table argument and has the following columns:

    + + + + +
    id TEXT. The id column name from the source table.
    predicted_result DOUBLE PRECISION. Result of prediction based of the value of the prediction type parameter.
    +

    +
    +
    pred_type
    +

    TEXT, OPTIONAL. Type of prediction. This can be one of 'linear_predictors', 'risk', or 'terms'. DEFAULT='linear_predictors'.

      +
    • 'linear_predictors' calculates the dot product of the independent variables and the coefficients.
      • +
    • 'risk' is the exponentiated value of the linear prediction.
      • +
    • 'terms' correspond to the linear terms obtained by multiplying the independent variables with their corresponding coefficients values (without further calculating the sum of these terms)
      • +
    +

    +
    +
    reference
    +
    TEXT, OPTIONAL. Reference level to use for centering predictions. Can be one of 'strata', 'overall'. DEFAULT='strata'. Note that R uses 'sample' instead of 'overall' when referring to the overall mean value of the covariates as being the reference level.
    +
    +

    Examples
    +
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS sample_data;
+CREATE TABLE sample_data (
+    id INTEGER NOT NULL,
+    grp DOUBLE PRECISION,
+    wbc DOUBLE PRECISION,
+    timedeath INTEGER,
+    status BOOLEAN
+);
+COPY sample_data FROM STDIN WITH DELIMITER '|';
+  0 |   0 | 1.45 |        35 | t
+  1 |   0 | 1.47 |        34 | t
+  3 |   0 |  2.2 |        32 | t
+  4 |   0 | 1.78 |        25 | t
+  5 |   0 | 2.57 |        23 | t
+  6 |   0 | 2.32 |        22 | t
+  7 |   0 | 2.01 |        20 | t
+  8 |   0 | 2.05 |        19 | t
+  9 |   0 | 2.16 |        17 | t
+ 10 |   0 |  3.6 |        16 | t
+ 11 |   1 |  2.3 |        15 | t
+ 12 |   0 | 2.88 |        13 | t
+ 13 |   1 |  1.5 |        12 | t
+ 14 |   0 |  2.6 |        11 | t
+ 15 |   0 |  2.7 |        10 | t
+ 16 |   0 |  2.8 |         9 | t
+ 17 |   1 | 2.32 |         8 | t
+ 18 |   0 | 4.43 |         7 | t
+ 19 |   0 | 2.31 |         6 | t
+ 20 |   1 | 3.49 |         5 | t
+ 21 |   1 | 2.42 |         4 | t
+ 22 |   1 | 4.01 |         3 | t
+ 23 |   1 | 4.91 |         2 | t
+ 24 |   1 |    5 |         1 | t
+\.
+
      2. +
    2. Run the Cox regression function. 
      +DROP TABLE IF EXISTS sample_cox, sample_cox_summary;
+SELECT madlib.coxph_train( 'sample_data',
+                           'sample_cox',
+                           'timedeath',
+                           'ARRAY[grp,wbc]',
+                           'status'
+                         );
+
      3. +
    3. View the results of the regression. 
      +\x on
+SELECT * FROM sample_cox;
+
      Results: 
      +-[ RECORD 1 ]--+----------------------------------------------------------------------------
+coef           | {2.54407073265254,1.67172094779487}
+loglikelihood  | -37.8532498733
+std_err        | {0.677180599294897,0.387195514577534}
+z_stats        | {3.7568570855419,4.31751114064138}
+p_values       | {0.000172060691513886,1.5779844638453e-05}
+hessian        | {{2.78043065745617,-2.25848560642414},{-2.25848560642414,8.50472838284472}}
+num_iterations | 5
+
      4. +
    4. Computing predictions using cox model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used.) 
      +\x off
+-- Display the linear predictors for the original dataset
+DROP TABLE IF EXISTS sample_pred;
+SELECT madlib.coxph_predict('sample_cox',
+                            'sample_data',
+                            'id',
+                            'sample_pred');
+SELECT * FROM sample_pred;
+
      + id |  predicted_value
+----+--------------------
+  0 |  -2.97110918125034
+  4 |  -2.41944126847803
+  6 |   -1.5167119566688
+  8 |  -1.96807661257341
+ 10 |  0.623090856508638
+ 12 |  -0.58054822590367
+ 14 |  -1.04863009128623
+ 16 | -0.714285901727259
+ 18 |   2.01061924317838
+ 20 |   2.98327228490375
+ 22 |   3.85256717775708
+ 24 |     5.507570916074
+  1 |  -2.93767476229444
+  3 |  -1.71731847040418
+  5 |  -1.09878171972008
+  7 |  -2.03494545048521
+  9 |  -1.78418730831598
+ 15 | -0.881457996506747
+ 19 |  -1.53342916614675
+ 11 |  0.993924357027849
+ 13 | -0.343452401208048
+ 17 |   1.02735877598375
+ 21 |   1.19453087076323
+ 23 |   5.35711603077246
+(24 rows)
+
      +-- Display the relative risk for the original dataset
+DROP TABLE IF EXISTS sample_pred;
+SELECT madlib.coxph_predict('sample_cox',
+                            'sample_data',
+                            'id',
+                            'sample_pred',
+                            'risk');
+SELECT * FROM sample_pred;
+
      + id |  predicted_value
+ ----+--------------------
+  1 | 0.0529887971503509
+  3 |  0.179546963459175
+  5 |   0.33327686110022
+  7 |  0.130687611255372
+  9 |  0.167933483703554
+ 15 |  0.414178600294289
+ 19 |  0.215794402223054
+ 11 |   2.70181658768287
+ 13 |  0.709317242984782
+ 17 |   2.79367735395696
+ 21 |   3.30200833843654
+ 23 |   212.112338046551
+  0 | 0.0512464372091503
+  4 | 0.0889713146524469
+  6 |  0.219432204682557
+  8 |  0.139725343898993
+ 10 |   1.86468261037506
+ 12 |  0.559591499901241
+ 14 |  0.350417460388247
+ 16 |  0.489541567796517
+ 18 |   7.46794038691975
+ 20 |   19.7523463121038
+ 22 |   47.1138577624204
+ 24 |   246.551504798816
+(24 rows)
+
      5. +
    5. Run the test for Proportional Hazards assumption to obtain correlation between residuals and time. 
      +SELECT madlib.cox_zph( 'sample_cox',
+                       'sample_zph_output'
+                     );
+
      6. +
    6. View results of the PHA test. 
      +\x on
+SELECT * FROM sample_zph_output;
+
      Results: 
      +-[ RECORD 1 ]-----------------------------------------
+covariate  | ARRAY[grp,wbc]
+rho        | {0.00237308357328641,0.0375600568840431}
+chi_square | {0.000100675718191977,0.0232317400546175}
+p_value    | {0.991994376850758,0.878855984657948}
+
      7. +
    +

    Technical Background
    +

    Generally, proportional-hazard models start with a list of \( \boldsymbol n \) observations, each with \( \boldsymbol m \) covariates and a time of death. From this \( \boldsymbol n \times m \) matrix, we would like to derive the correlation between the covariates and the hazard function. This amounts to finding the parameters \( \boldsymbol \beta \) that best fit the model described below.

    +

    Let us define:

      +
    • \( \boldsymbol t \in \mathbf R^{m} \) denote the vector of observed dependent variables, with \( n \) rows.
      • +
    • \( X \in \mathbf R^{m} \) denote the design matrix with \( m \) columns and \( n \) rows, containing all observed vectors of independent variables \( \boldsymbol x_i \) as rows.
      • +
    • \( R(t_i) \) denote the set of observations still alive at time \( t_i \)
      • +
    +

    Note that this model does not include a constant term, and the data cannot contain a column of 1s.

    +

    By definition,

    +\[ P[T_k = t_i | \boldsymbol R(t_i)] = \frac{e^{\beta^T x_k} }{ \sum_{j \in R(t_i)} e^{\beta^T x_j}}. \,. \] +

    +

    The partial likelihood function can now be generated as the product of conditional probabilities:

    +\[ \mathcal L = \prod_{i = 1}^n \left( \frac{e^{\beta^T x_i}}{ \sum_{j \in R(t_i)} e^{\beta^T x_j}} \right). \] +

    +

    The log-likelihood form of this equation is

    +\[ L = \sum_{i = 1}^n \left[ \beta^T x_i - \log\left(\sum_{j \in R(t_i)} e^{\beta^T x_j }\right) \right]. \] +

    +

    Using this score function and Hessian matrix, the partial likelihood can be maximized using the Newton-Raphson algorithm. Breslow's method is used to resolved tied times of deaths. The time of death for two records are considered "equal" if they differ by less than 1.0e-6

    +

    The inverse of the Hessian matrix, evaluated at the estimate of \( \boldsymbol \beta \), can be used as an approximate variance-covariance matrix for the estimate, and used to produce approximate standard errors for the regression coefficients.

    +

    +\[ \mathit{se}(c_i) = \left( (H)^{-1} \right)_{ii} \,. \] +

    +

    The Wald z-statistic is

    +\[ z_i = \frac{c_i}{\mathit{se}(c_i)} \,. \] +

    +

    The Wald \( p \)-value for coefficient \( i \) gives the probability (under the assumptions inherent in the Wald test) of seeing a value at least as extreme as the one observed, provided that the null hypothesis ( \( c_i = 0 \)) is true. Letting \( F \) denote the cumulative density function of a standard normal distribution, the Wald \( p \)-value for coefficient \( i \) is therefore

    +\[ p_i = \Pr(|Z| \geq |z_i|) = 2 \cdot (1 - F( |z_i| )) \] +

    +

    where \( Z \) is a standard normally distributed random variable.

    +

    The condition number is computed as \( \kappa(H) \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration). A large condition number (say, more than 1000) indicates the presence of significant multicollinearity.

    +

    Literature
    +

    A somewhat random selection of nice write-ups, with valuable pointers into further literature:

    +

    [1] John Fox: Cox Proportional-Hazards Regression for Survival Data, Appendix to An R and S-PLUS companion to Applied Regression Feb 2012, http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-cox-regression.pdf

    +

    [2] Stephen J Walters: What is a Cox model? http://www.medicine.ox.ac.uk/bandolier/painres/download/whatis/cox_model.pdf

    +

    Notes
    +

    If number of ties in the source table is very large, a memory allocation error may be raised. The limitation is about \((10^8 / m)\), where \(m\) is number of featrues. For instance, if there are 100 featrues, the number of ties should be fewer than 1 million.

    +

    Related Topics
    +

    File cox_prop_hazards.sql_in documenting the functions

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__crf.html b/docs/docs/v2.1.0/group__grp__crf.html new file mode 100644 index 00000000..7754403d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__crf.html @@ -0,0 +1,584 @@ + + + + + + + + +MADlib: Conditional Random Field + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Conditional Random Field
    Supervised Learning
    +
    +
    +
    Contents +

    A conditional random field (CRF) is a type of discriminative, undirected probabilistic graphical model. A linear-chain CRF is a special type of CRF that assumes the current state depends only on the previous state.

    +

    Feature extraction modules are provided for text-analysis tasks such as part-of-speech (POS) tagging and named-entity resolution (NER). Currently, six feature types are implemented:

    +
      +
    • Edge Feature: transition feature that encodes the transition feature weight from current label to next label.
      • +
    • Start Feature: fired when the current token is the first token in a sequence.
      • +
    • End Feature: fired when the current token is the last token in a sequence.
      • +
    • Word Feature: fired when the current token is observed in the trained dictionary.
      • +
    • Unknown Feature: fired when the current token is not observed in the trained dictionary for at least a certain number of times (default 1).
      • +
    • Regex Feature: fired when the current token can be matched by a regular expression.
      • +
    +

    A Viterbi implementation is also provided to get the best label sequence and the conditional probability \( \Pr( \text{best label sequence} \mid \text{sequence}) \).

    +

    Following steps are required for CRF Learning and Inference:

      +
    1. Training Feature Generation
      2. +
    2. CRF Training
      3. +
    3. Testing Feature Generation
      4. +
    4. Inference using Viterbi
      5. +
    +

    Training Feature Generation
    The function takes train_segment_tbl and regex_tbl as input and does feature generation generating three tables dictionary_tbl, train_feature_tbl and train_featureset_tbl, that are required as an input for CRF training. 
    +crf_train_fgen(train_segment_tbl,
+               regex_tbl,
+               label_tbl,
+               dictionary_tbl,
+               train_feature_tbl,
+               train_featureset_tbl)
+
    Arguments
    +
    train_segment_tbl
    +
    TEXT. Name of the training segment table. The table is expected to have the following columns: + + + + + + + + +
    doc_id INTEGER. Document id column
    start_pos INTEGER. Index of a particular term in the respective document
    seg_text TEXT. Term at the respective start_pos in the document
    label INTEGER. Label id for the term corresponding to the actual label from label_tbl
    +
    +
    regex_tbl
    +
    TEXT. Name of the regular expression table. The table is expected to have the following columns: + + + + +
    pattern TEXT. Regular Expression
    name TEXT. Regular Expression name
    +
    +
    label_tbl
    +
    TEXT. Name of the table containing unique labels and their id's. The table is expected to have the following columns: + + + + +
    id INTEGER. Unique label id. NOTE: Must range from 0 to total number of labels in the table - 1.
    label TEXT. Label name
    +
    +
    dictionary_tbl
    +
    TEXT. Name of the dictionary table to be created containing unique terms along with their counts. The table will have the following columns: + + + + +
    token TEXT. Contains all the unique terms found in train_segment_tbl
    total INTEGER. Respective counts for the terms
    +
    +
    train_feature_tbl
    +
    +
    +

    TEXT. Name of the training feature table to be created. The table will have the following columns:

    + + + + + + + + + + +
    doc_id INTEGER. Document id
    f_size INTEGER. Feature set size. This value will be same for all the tuples in the table
    sparse_r DOUBLE PRECISION[]. Array union of individual single state features (previous label, label, feature index, start position, training existance indicator), ordered by their start position.
    dense_m DOUBLE PRECISION[]. Array union of (previous label, label, feature index, start position, training existance indicator) of edge features ordered by start position.
    sparse_m DOUBLE PRECISION[]. Array union of (feature index, previous label, label) of edge features ordered by feature index.
    +

    +
    +
    train_featureset_tbl
    +
    TEXT. Name of the table to be created containing distinct featuresets generated from training feature extraction. The table will have the following columns: + + + + + + +
    f_index INTEGER. Column containing distinct featureset ids
    f_name TEXT. Feature name
    feature ARRAY. Feature value. The value is of the form [L1, L2]
    + - If L1 = -1: represents single state feature with L2 being the current label id.
    + - If L1 != -1: represents transition feature with L1 be the previous label and L2 be the current label.
    +
    +
    +
    +

    Linear Chain CRF Training Function
    The function takes train_feature_tbl and train_featureset_tbl tables generated in the training feature generation steps as input along with other required parameters and produces two output tables crf_stats_tbl and crf_weights_tbl.
    +
    +lincrf_train(train_feature_tbl,
+             train_featureset_tbl,
+             label_tbl,
+             crf_stats_tbl,
+             crf_weights_tbl
+             max_iterations
+            )
+

    Arguments

    +
    train_feature_tbl
    +

    TEXT. Name of the feature table generated during training feature generation

    +

    +
    +
    train_featureset_tbl
    +

    TEXT. Name of the featureset table generated during training feature generation

    +

    +
    +
    label_tbl
    +

    TEXT. Name of the label table used

    +

    +
    +
    crf_stats_table
    +
    TEXT. Name of the table to be created containing statistics for CRF training. The table has the following columns: + + + + + + +
    coef DOUBLE PRECISION[]. Array of coefficients
    log_likelihood DOUBLE. Log-likelihood
    num_iterations INTEGER. The number of iterations at which the algorithm terminated
    +
    +
    crf_weights_table
    +

    TEXT. Name of the table to be created creating learned feature weights. The table has the following columns:

    + + + + + + + + + + +
    id INTEGER. Feature set id
    name TEXT. Feature name
    prev_label_id INTEGER. Label for the previous token encountered
    label_id INTEGER. Label of the token with the respective feature
    weight DOUBLE PRECISION. Weight for the respective feature set
    +

    +
    +
    max_iterations
    +
    INTEGER. The maximum number of iterations
    +
    +

    Testing Feature Generation
    +
    +crf_test_fgen(test_segment_tbl,
+              dictionary_tbl,
+              label_tbl,
+              regex_tbl,
+              crf_weights_tbl,
+              viterbi_mtbl,
+              viterbi_rtbl
+             )
+

    Arguments

    +
    test_segment_tbl
    +

    TEXT. Name of the testing segment table. The table is expected to have the following columns:

    + + + + + + +
    doc_id INTEGER. Document id column
    start_pos INTEGER. Index of a particular term in the respective document
    seg_text TEXT. Term at the respective start_pos in the document
    +

    +
    +
    dictionary_tbl
    +

    TEXT. Name of the dictionary table created during training feature generation (crf_train_fgen)

    +

    +
    +
    label_tbl
    +

    TEXT. Name of the label table

    +

    +
    +
    regex_tbl
    +

    TEXT. Name of the regular expression table

    +

    +
    +
    crf_weights_tbl
    +

    TEXT. Name of the weights table generated during CRF training (lincrf_train)

    +

    +
    +
    viterbi_mtbl
    +

    TEXT. Name of the Viterbi M table to be created

    +

    +
    +
    viterbi_rtbl
    +
    TEXT. Name of the Viterbi R table to be created
    +
    +

    Inference using Viterbi
    +vcrf_label(test_segment_tbl,
+           viterbi_mtbl,
+           viterbi_rtbl,
+           label_tbl,
+           result_tbl)
+
    Arguments
    +
    test_segment_tbl
    +
    TEXT. Name of the testing segment table. For required table schema, please refer to arguments in previous section
    +
    viterbi_mtbl
    +
    TEXT. Name of the table viterbi_mtbl generated from testing feature generation crf_test_fgen.
    +
    viterbi_rtbl
    +
    TEXT. Name of the table viterbi_rtbl generated from testing feature generation crf_test_fgen.
    +
    label_tbl
    +
    TEXT. Name of the label table.
    +
    result_tbl
    +
    TEXT. Name of the result table to be created containing extracted best label sequences.
    +
    +
    +

    Using CRF
    +

    Generate text features, calculate their weights, and output the best label sequence for test data:
    +

      +
    1. Perform feature generation on training data i.e. train_segment_tbl generating train_feature_tbl and train_featureset_tbl. 
      SELECT madlib.crf_train_fgen(
+         'train_segment_tbl',
+         'regex_tbl',
+         'label_tbl',
+         'dictionary_tbl',
+         'train_feature_tbl',
+         'train_featureset_tbl');
      2. +
    2. Use linear-chain CRF for training providing train_feature_tbl and train_featureset_tbl generated from previous step as an input. 
      SELECT madlib.lincrf_train(
+         'train_feature_tbl',
+         'train_featureset_tbl',
+         'label_tbl',
+         'crf_stats_tbl',
+         'crf_weights_tbl',
+         max_iterations);
      3. +
    3. Perform feature generation on testing data test_segment_tbl generating viterbi_mtbl and viterbi_rtbl required for inferencing. 
      SELECT madlib.crf_test_fgen(
+         'test_segment_tbl',
+         'dictionary_tbl',
+         'label_tbl',
+         'regex_tbl',
+         'crf_weights_tbl',
+         'viterbi_mtbl',
+         'viterbi_rtbl');
      4. +
    4. Run the Viterbi function to get the best label sequence and the conditional probability \( \Pr( \text{best label sequence} \mid \text{sequence}) \). 
      SELECT madlib.vcrf_label(
+         'test_segment_tbl',
+         'viterbi_mtbl',
+         'viterbi_rtbl',
+         'label_tbl',
+         'result_tbl');
      5. +
    +

    Examples
    This example uses a trivial training and test data set.
    +
      +
    1. Load the label table, the regular expressions table, and the training segment table: 
      +CREATE TABLE crf_label (id integer,label character varying);
+INSERT INTO crf_label VALUES
+(0,'CC'),   (1,'CD'),  (2,'DT'),    (3,'EX'),   (4,'FW'),  (5,'IN'),   (6,'JJ'),  (7,'JJR'), (8,'JJS'),
+(9,'LS'),   (10,'MD'), (11,'NN'),   (12,'NNS'), (13,'NNP'),(14,'NNPS'),(15,'PDT'),(16,'POS'),(17,'PRP'),
+(18,'PRP$'),(19,'RB'), (20,'RBR'),  (21,'RBS'), (22,'RP'), (23,'SYM'), (24,'TO'), (25,'UH'), (26,'VB'),
+(27,'VBD'), (28,'VBG'),(29,'VBN'),  (30,'VBP'), (31,'VBZ'),(32,'WDT'), (33,'WP'), (34,'WP$'),(35,'WRB'),
+(36,'$'),   (37,'#'),  (38,''''''), (39,'``'),  (40,'('),  (41,')'),   (42,','),  (43,'.'),  (44,':');
+CREATE TABLE crf_regex (pattern text,name text);
+INSERT INTO crf_regex VALUES
+('^[A-Z][a-z]+$','InitCapital'), ('^[A-Z]+$','isAllCapital'), ('^.*[0-9]+.*$','containsDigit'),
+('^.+[.]$','endsWithDot'),       ('^.+[,]$','endsWithComma'), ('^.+er$','endsWithER'),
+('^.+est$','endsWithEst'),       ('^.+ed$','endsWithED'),     ('^.+s$','endsWithS'),
+('^.+ing$','endsWithIng'),       ('^.+ly$','endsWithly'),     ('^.+-.+$','isDashSeparatedWords'),
+('^.*.*$','isEmailId');
+CREATE TABLE train_segmenttbl(start_pos integer,doc_id integer,seg_text text,label integer,max_pos integer);
+INSERT INTO train_segmenttbl VALUES
+(0,1,'confidence',11,36),  (1,1,'in',5,36),         (2,1,'the',2,36),         (3,1,'pound',11,36),
+(4,1,'is',31,36),          (5,1,'widely',19,36),    (6,1,'expected',29,36),   (7,1,'to',24,36),
+(8,1,'take',26,36),        (9,1,'another',2,36),    (10,1,'sharp',6,36),      (11,1,'dive',11,36),
+(12,1,'if',5,36),          (13,1,'trade',11,36),    (14,1,'figures',12,36),   (15,1,'for',5,36),
+(16,1,'september',13,36),  (17,1,',',42,36),        (18,1,'due',6,36),        (19,1,'for',5,36),
+(20,1,'release',11,36),    (21,1,'tomorrow',11,36), (22,1,',',42,36),         (23,1,'fail',26,36),
+(24,1,'to',24,36),         (25,1,'show',26,36),     (26,1,'a',2,36),          (27,1,'substantial',6,36),
+(28,1,'improvement',11,36),(29,1,'from',5,36),      (30,1,'july',13,36),      (31,1,'and',0,36),
+(32,1,'august',13,36),     (33,1,'''s',16,36),      (34,1,'near-record',6,36),(35,1,'deficits',12,36),
+(36,1,'.',43,36),          (0,2,'chancellor',13,26),(1,2,'of',5,26),          (2,2,'the',2,26),
+(3,2,'exchequer',13,26),   (4,2,'nigel',13,26),     (5,2,'lawson',13,26),     (6,2,'''s',16,26),
+(7,2,'restated',29,26),    (8,2,'commitment',11,26),(9,2,'to',24,26),         (10,2,'a',2,26),
+(11,2,'firm',11,26),       (12,2,'monetary',6,26),  (13,2,'policy',11,26),    (14,2,'has',31,26),
+(15,2,'helped',29,26),     (16,2,'to',24,26),       (17,2,'prevent',26,26),   (18,2,'a',2,26),
+(19,2,'freefall',11,26),   (20,2,'in',5,26),        (21,2,'sterling',11,26),  (22,2,'over',5,26),
+(23,2,'the',2,26),         (24,2,'past',6,26),      (25,2,'week',11,26),      (26,2,'.',43,26);
+
      2. +
    2. Generate the training features: 
      +SELECT crf_train_fgen( 'train_segmenttbl',
+                       'crf_regex',
+                       'crf_label',
+                       'crf_dictionary',
+                       'train_featuretbl',
+                       'train_featureset'
+                     );
+SELECT * from crf_dictionary;
+
      Result: 
      +    token    | total
+ ------------+-------
+ a           |     3
+ and         |     1
+ august      |     1
+ chancellor  |     1
+ dive        |     1
+ exchequer   |     1
+...
+
      +SELECT * from train_featuretbl;
+
      Result: 
      + doc_id | f_size |            sparse_r          |              dense_m             |       sparse_m
+ -------+--------+------------------------------+----------------------------------+-----------------------
+      1 |    115 | {-1,11,82,0,1,-1,2,32,0,...} | {11,5,11,1,1,5,2,8,2,1,2,11,...} | {5,2,13,11,11,5,13,...}
+      2 |    115 | {-1,19,35,0,0,-1,26,38,0,..} | {13,5,66,1,1,5,2,8,2,1,2,13,...} | {5,2,13,11,11,5,13,...}
+
      +SELECT * from train_featureset;
+
      + f_index |    f_name     | feature
+ --------+---------------+---------
+       6 | W_the         | {-1,2}
+       9 | R_endsWithly  | {-1,19}
+      14 | W_figures     | {-1,12}
+      17 | W_helped      | {-1,29}
+      25 | W_show        | {-1,26}
+      28 | W_'s          | {-1,16}
+      33 | W_chancellor  | {-1,13}
+      43 | W_over        | {-1,5}
+      52 | W_trade       | {-1,11}
+      10 | W_july        | {-1,13}
+      21 | W_substantial | {-1,6}
+       5 | E.            | {2,13}
+...
+
      3. +
    3. Train using linear CRF: 
      +SELECT lincrf_train( 'train_featuretbl',
+                     'train_featureset',
+                     'crf_label',
+                     'crf_stats_tbl',
+                     'crf_weights_tbl',
+                     20
+             );
+
      +                                lincrf_train
+ -----------------------------------------------------------------------------------
+ CRF Train successful. Results stored in the specified CRF stats and weights table
+ lincrf
+
      View the feature weight table. 
      +SELECT * from crf_weights_tbl;
+
      Result: 
      +  id |     name      | prev_label_id | label_id |      weight
+ ----+---------------+---------------+----------+-------------------
+   4 | W_lawson      |            -1 |       13 |  1.73698153439171
+   3 | End.          |            -1 |       43 |   3.3198742329636
+   7 | W_has         |            -1 |       31 |  2.19831004450897
+  24 | W_tomorrow    |            -1 |       11 |  3.34106414300743
+  29 | W_.           |            -1 |       43 |   3.3198742329636
+  34 | W_from        |            -1 |        5 |  2.80284597986744
+  37 | W_august      |            -1 |       13 |  1.34455487966976
+  39 | W_due         |            -1 |        6 |  3.39258895715363
+  41 | W_exchequer   |            -1 |       13 |  1.82177698489335
+...
+
      4. +
    4. To find the best labels for a test set using the trained linear CRF model, repeat steps #1-2 and generate the test features, except instead of creating a new dictionary, use the dictionary generated from the training set. 
      +CREATE TABLE test_segmenttbl (start_pos integer,doc_id integer,seg_text text,max_pos integer);
+INSERT INTO test_segmenttbl VALUES
+(0,1,'chancellor',26),(1,1,'of',26),       (2,1,'the',26),      (3,1,'exchequer',26), (4,1,'nigel',26),
+(5,1,'lawson',26),    (6,1,'''s',26),      (7,1,'restated',26), (8,1,'commitment',26),(9,1,'to',26),
+(10,1,'a',26),        (11,1,'firm',26),    (12,1,'monetary',26),(13,1,'policy',26),   (14,1,'has',26),
+(15,1,'helped',26),   (16,1,'to',26),      (17,1,'prevent',26), (18,1,'a',26),        (19,1,'freefall',26),
+(20,1,'in',26),       (21,1,'sterling',26),(22,1,'over',26),    (23,1,'the',26),      (24,1,'past',26),
+(25,1,'week',26),     (26,1,'.',26),       (0,2,'but',28),      (1,2,'analysts',28),  (2,2,'reckon',28),
+(3,2,'underlying',28),(4,2,'support',28),  (5,2,'for',28),      (6,2,'sterling',28),  (7,2,'has',28),
+(8,2,'been',28),      (9,2,'eroded',28),   (10,2,'by',28),      (11,2,'the',28),      (12,2,'chancellor',28),
+(13,2,'''s',28),      (14,2,'failure',28), (15,2,'to',28),      (16,2,'announce',28), (17,2,'any',28),
+(18,2,'new',28),      (19,2,'policy',28),  (20,2,'measures',28),(21,2,'in',28),       (22,2,'his',28),
+(23,2,'mansion',28),  (24,2,'house',28),   (25,2,'speech',28),  (26,2,'last',28),     (27,2,'thursday',28),
+(28,2,'.',28),        (0,3,'his',4),       (1,3,'actions',4),   (2,3,'prevent',4),    (3,3,'disaster',4),
+(4,3,'.',4);
+
      +SELECT crf_test_fgen( 'test_segmenttbl',
+                      'crf_dictionary',
+                      'crf_label',
+                      'crf_regex',
+                      'crf_weights_tbl',
+                      'viterbi_mtbl',
+                      'viterbi_rtbl'
+                    );
+
      5. +
    5. Calculate the best label sequence and save in the table extracted_best_labels. 
      +SELECT vcrf_label( 'test_segmenttbl',
+                   'viterbi_mtbl',
+                   'viterbi_rtbl',
+                   'crf_label',
+                   'extracted_best_labels'
+                 );
+
      View the best labels. 
      +SELECT * FROM extracted_best_labels;
+
      Result: 
      + doc_id | start_pos |   seg_text    | label | id | max_pos |   prob
+ -------+-----------+---------------+-------+----+---------+----------
+      1 |         4 | nigel         | NNP   | 13 |      26 | 0.387118
+      1 |         5 | lawson        | NNP   | 13 |      26 | 0.387118
+      1 |         7 | restated      | VBN   | 29 |      26 | 0.387118
+      1 |         8 | commitment    | NN    | 11 |      26 | 0.387118
+...
+      3 |         0 | his           | NNP   | 13 |       4 | 0.047757
+      3 |         2 | prevent       | JJ    |  6 |       4 | 0.047757
+      3 |         4 | .             | .     | 43 |       4 | 0.047757
+...
+
      6. +
    +

    Technical Background
    +

    Specifically, a linear-chain CRF is a distribution defined by

    +\[ p_\lambda(\boldsymbol y | \boldsymbol x) = \frac{\exp{\sum_{m=1}^M \lambda_m F_m(\boldsymbol x, \boldsymbol y)}}{Z_\lambda(\boldsymbol x)} \,. \] +

    +

    where

      +
    • \( F_m(\boldsymbol x, \boldsymbol y) = \sum_{i=1}^n f_m(y_i,y_{i-1},x_i) \) is a global feature function that is a sum along a sequence \( \boldsymbol x \) of length \( n \)
      • +
    • \( f_m(y_i,y_{i-1},x_i) \) is a local feature function dependent on the current token label \( y_i \), the previous token label \( y_{i-1} \), and the observation \( x_i \)
      • +
    • \( \lambda_m \) is the corresponding feature weight
      • +
    • \( Z_\lambda(\boldsymbol x) \) is an instance-specific normalizer

      +\[ Z_\lambda(\boldsymbol x) = \sum_{\boldsymbol y'} \exp{\sum_{m=1}^M \lambda_m F_m(\boldsymbol x, \boldsymbol y')} \] +

      +
      • +
    +

    A linear-chain CRF estimates the weights \( \lambda_m \) by maximizing the log-likelihood of a given training set \( T=\{(x_k,y_k)\}_{k=1}^N \).

    +

    The log-likelihood is defined as

    +\[ \ell_{\lambda}=\sum_k \log p_\lambda(y_k|x_k) =\sum_k[\sum_{m=1}^M \lambda_m F_m(x_k,y_k) - \log Z_\lambda(x_k)] \] +

    +

    and the zero of its gradient

    +\[ \nabla \ell_{\lambda}=\sum_k[F(x_k,y_k)-E_{p_\lambda(Y|x_k)}[F(x_k,Y)]] \] +

    +

    is found since the maximum likelihood is reached when the empirical average of the global feature vector equals its model expectation. The MADlib implementation uses limited-memory BFGS (L-BFGS), a limited-memory variation of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) update, a quasi-Newton method for unconstrained optimization.

    +

    \(E_{p_\lambda(Y|x)}[F(x,Y)]\) is found by using a variant of the forward-backward algorithm:

    +\[ E_{p_\lambda(Y|x)}[F(x,Y)] = \sum_y p_\lambda(y|x)F(x,y) = \sum_i\frac{\alpha_{i-1}(f_i*M_i)\beta_i^T}{Z_\lambda(x)} \] +

    +

    +\[ Z_\lambda(x) = \alpha_n.1^T \] +

    +

    where \(\alpha_i\) and \( \beta_i\) are the forward and backward state cost vectors defined by

    +\[ \alpha_i = \begin{cases} \alpha_{i-1}M_i, & 0<i<=n\\ 1, & i=0 \end{cases}\\ \] +

    +

    +\[ \beta_i^T = \begin{cases} M_{i+1}\beta_{i+1}^T, & 1<=i<n\\ 1, & i=n \end{cases} \] +

    +

    To avoid overfitting, we penalize the likelihood with a spherical Gaussian weight prior:

    +\[ \ell_{\lambda}^\prime=\sum_k[\sum_{m=1}^M \lambda_m F_m(x_k,y_k) - \log Z_\lambda(x_k)] - \frac{\lVert \lambda \rVert^2}{2\sigma ^2} \] +

    +

    +\[ \nabla \ell_{\lambda}^\prime=\sum_k[F(x_k,y_k) - E_{p_\lambda(Y|x_k)}[F(x_k,Y)]] - \frac{\lambda}{\sigma ^2} \] +

    +
    Literature
    [1] F. Sha, F. Pereira. Shallow Parsing with Conditional Random Fields, http://www-bcf.usc.edu/~feisha/pubs/shallow03.pdf
    +

    [2] Wikipedia, Conditional Random Field, http://en.wikipedia.org/wiki/Conditional_random_field

    +

    [3] A. Jaiswal, S.Tawari, I. Mansuri, K. Mittal, C. Tiwari (2012), CRF, http://crf.sourceforge.net/

    +

    [4] D. Wang, ViterbiCRF, http://www.cs.berkeley.edu/~daisyw/ViterbiCRF.html

    +

    [5] Wikipedia, Viterbi Algorithm, http://en.wikipedia.org/wiki/Viterbi_algorithm

    +

    [6] J. Nocedal. Updating Quasi-Newton Matrices with Limited Storage (1980), Mathematics of Computation 35, pp. 773-782

    +

    [7] J. Nocedal, Software for Large-scale Unconstrained Optimization, http://users.eecs.northwestern.edu/~nocedal/lbfgs.html

    +

    Related Topics
    +

    File crf.sql_in crf_feature_gen.sql_in viterbi.sql_in (documenting the SQL functions)

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__custom__function.html b/docs/docs/v2.1.0/group__grp__custom__function.html new file mode 100644 index 00000000..0adc0986 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__custom__function.html @@ -0,0 +1,318 @@ + + + + + + + + +MADlib: Define Custom Functions + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
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    +
    Define Custom Functions
    Deep Learning » Model Preparation
    +
    +
    +
    Contents +
    Warning
    For security reasons there are controls on custom functions in MADlib. You must be a superuser to create custom functions because they could theoretically allow execution of any untrusted Python code. Regular users with MADlib USAGE permission can use existing custom functions but cannot create new ones or update existing ones. See references [1] and [2] for information on privileges in Greenplum and PostgreSQL.
    +

    This function loads custom Python functions into a table for use by deep learning algorithms.

    +

    Custom functions can be useful if, for example, you need loss functions or metrics that are not built into the standard libraries. The functions to be loaded must be in the form of serialized Python objects created using Dill, which extends Python's pickle module to the majority of the built-in Python types [3].

    +

    Custom functions can also be used to return top k categorical accuracy in the case that you want a different k value than the default from tensorflow.keras. This module includes a helper function to create the custom function automatically for a specified k.

    +

    There is also a utility function to delete a function from the table.

    +
    Note
    Do not specify a schema for the argument 'object_table' containing the Python objects, because the 'object_table' is automatically put in the MADlib schema. Also, any subsequent SQL queries on this table by regular users must specify '<madlib_schema>.object_table' in the usual way.
    +

    Load Function
    +
    +load_custom_function(
+    object_table,
+    object,
+    name,
+    description
+    )
+

    Arguments

    +
    object_table
    +

    VARCHAR. Table to load serialized Python objects. If this table does not exist, it will be created. If this table already exists, a new row is inserted into the existing table. Do not specify schema as part of the object table name, since it will be put in the MADlib schema automatically.

    +

    +
    +
    object
    +

    BYTEA. PostgreSQL binary data type of the Python object. Object must be created with the Dill package for serializing Python objects.

    +
    Note
    The Dill package must be installed on all segments of the database cluster [3].
    +
    +
    name
    +

    TEXT. Name of the object. Must be unique identifier in the table, since this name is used when passing the object to Keras.

    +

    +
    +
    description (optional)
    +

    TEXT, default: NULL. Free text string to provide a description, if desired.

    +

    +
    +
    +

    Output table
    + The output table contains the following columns:

    + + + + + + + + +
    id SERIAL. Object ID.
    name TEXT PRIMARY KEY. Name of the object.
    description TEXT. Description of the object (free text).
    object BYTEA. Serialized Python object stored as a PostgreSQL binary data type.
    +

    Delete Function
    +

    Delete by id: 

    +delete_custom_function(
+    object_table,
+    id
+)
+

    Or alternatively by name: 

    +delete_custom_function(
+    object_table,
+    name
+)
+

    Arguments

    +
    object_table
    +
    VARCHAR. Table containing Python object to be deleted. Do not specify schema as part of the object table name.
    +
    id
    +
    INTEGER. The id of the object to be deleted.
    +
    name
    +
    TEXT. Name of the object to be deleted.
    +
    +

    Top k Accuracy Function
    +

    Create and load a custom function for a specific k into the custom functions table. The Keras accuracy parameter 'top_k_categorical_accuracy' returns top 5 accuracy by default [4]. If you want a different top k value, use this helper function to create a custom Python function to compute the top k accuracy that you specify.

    +
    +load_top_k_accuracy_function(
+    object_table,
+    k
+    )
+

    Arguments

    +
    object_table
    +

    VARCHAR. Table to load serialized Python objects. If this table does not exist, it will be created. If this table already exists, a new row is inserted into the existing table. Do not specify schema as part of the object table name, since it will be put in the MADlib schema automatically.

    +

    +
    +
    k
    +

    INTEGER. k value for the top k accuracy that you want.

    +

    +
    +
    +

    Output table
    + The output table contains the following columns:

    + + + + + + + + +
    id SERIAL. Object ID.
    name TEXT PRIMARY KEY. Name of the object. Generated with the following pattern: top_(k)_accuracy.
    description TEXT. Description of the object.
    object BYTEA. Serialized Python object stored as a PostgreSQL binary data type.
    +

    Examples
      +
    1. Load object using psycopg2. Psycopg is a PostgreSQL database adapter for the Python programming language. Note need to use the psycopg2.Binary() method to pass as bytes. 
      +# import database connector psycopg2 and create connection cursor
+import psycopg2 as p2
+conn = p2.connect('postgresql://gpadmin:8000/madlib')
+cur = conn.cursor()
+# import Dill and define functions
+import dill
+# custom loss
+def squared_error(y_true, y_pred):
+    import keras.backend as K
+    return K.square(y_pred - y_true)
+pb_squared_error=dill.dumps(squared_error)
+# custom metric
+def rmse(y_true, y_pred):
+    import keras.backend as K
+    return K.sqrt(K.mean(K.square(y_pred - y_true), axis=-1))
+pb_rmse=dill.dumps(rmse)
+# call load function
+cur.execute("DROP TABLE IF EXISTS madlib.custom_function_table")
+cur.execute("SELECT madlib.load_custom_function('custom_function_table',  %s,'squared_error', 'squared error')", [p2.Binary(pb_squared_error)])
+cur.execute("SELECT madlib.load_custom_function('custom_function_table',  %s,'rmse', 'root mean square error')", [p2.Binary(pb_rmse)])
+conn.commit()
+
      List table to see objects: 
      +SELECT id, name, description FROM madlib.custom_function_table ORDER BY id;
+
      + id |     name      |      description
+----+---------------+------------------------
+  1 | squared_error | squared error
+  2 | rmse          | root mean square error
+
      2. +
    2. Load object using a PL/Python function. First define the objects: 
      +CREATE OR REPLACE FUNCTION custom_function_squared_error()
+RETURNS BYTEA AS
+$$
+import dill
+def squared_error(y_true, y_pred):
+    import keras.backend as K
+    return K.square(y_pred - y_true)
+pb_squared_error=dill.dumps(squared_error)
+return pb_squared_error
+$$ language plpython3u;
+CREATE OR REPLACE FUNCTION custom_function_rmse()
+RETURNS BYTEA AS
+$$
+import dill
+def rmse(y_true, y_pred):
+    import keras.backend as K
+    return K.sqrt(K.mean(K.square(y_pred - y_true), axis=-1))
+pb_rmse=dill.dumps(rmse)
+return pb_rmse
+$$ language plpython3u;
+
      Now call loader: 
      +DROP TABLE IF EXISTS madlib.custom_function_table;
+SELECT madlib.load_custom_function('custom_function_table',
+                                   custom_function_squared_error(),
+                                   'squared_error',
+                                   'squared error');
+SELECT madlib.load_custom_function('custom_function_table',
+                                   custom_function_rmse(),
+                                   'rmse',
+                                   'root mean square error');
+
      3. +
    3. Delete an object by id: 
      +SELECT madlib.delete_custom_function( 'custom_function_table', 1);
+SELECT id, name, description FROM madlib.custom_function_table ORDER BY id;
+
      + id | name |      description
+----+------+------------------------
+  2 | rmse | root mean square error
+
      Delete an object by name: 
      +SELECT madlib.delete_custom_function( 'custom_function_table', 'rmse');
+
      If all objects are deleted from the table using this function, the table itself will be dropped.
      4. +
    4. Load top 3 accuracy function followed by a top 10 accuracy function: 
      +DROP TABLE IF EXISTS custom_function_table;
+SELECT madlib.load_top_k_accuracy_function('custom_function_table',
+                                           3);
+SELECT madlib.load_top_k_accuracy_function('custom_function_table',
+                                           10);
+SELECT id, name, description FROM madlib.custom_function_table ORDER BY id;
+
      + id |      name       |       description
+----+-----------------+-------------------------
+  1 | top_3_accuracy  | returns top_3_accuracy
+  2 | top_10_accuracy | returns top_10_accuracy
+
      5. +
    +
    +
    Literature
    +

    [1] https://gpdb.docs.pivotal.io/latest/admin_guide/roles_privs.html

    +

    [2] https://www.postgresql.org/docs/current/ddl-priv.html

    +

    [3] Python catalog for Dill package https://pypi.org/project/dill/

    +

    [4] https://keras.io/api/metrics/accuracy_metrics/#topkcategoricalaccuracy-class

    +

    Related Topics
    +

    See madlib_keras_custom_function.sql_in

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__datatrans.html b/docs/docs/v2.1.0/group__grp__datatrans.html new file mode 100644 index 00000000..4e46cd09 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__datatrans.html @@ -0,0 +1,145 @@ + + + + + + + + +MADlib: Data Types and Transformations + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Data Types and Transformations
    +
    +
    +

    Detailed Description

    +

    Data types and operations that transform and shape data.

    + + + + + + + + + + + + + + + + + + + + +

    +Modules

     Arrays and Matrices
     Mathematical operations for arrays and matrices.
     
     Encoding Categorical Variables
     Functions to encode categorical variables to prepare data for input into predictive algorithms.
     
     Path
     A function to perform complex pattern matching across rows and extract useful information about the matches.
     
     Pivot
     Pivoting and data summarization tools for preparing data for modeling operations.
     
     Sessionize
     Session reconstruction of data consisting of a time stampled sequence of events.
     
     Stemming
     Provides porter stemmer operations supporting other MADlib modules.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__datatrans.js b/docs/docs/v2.1.0/group__grp__datatrans.js new file mode 100644 index 00000000..49004558 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__datatrans.js @@ -0,0 +1,9 @@ +var group__grp__datatrans = +[ + [ "Arrays and Matrices", "group__grp__arraysmatrix.html", "group__grp__arraysmatrix" ], + [ "Encoding Categorical Variables", "group__grp__encode__categorical.html", null ], + [ "Path", "group__grp__path.html", null ], + [ "Pivot", "group__grp__pivot.html", null ], + [ "Sessionize", "group__grp__sessionize.html", null ], + [ "Stemming", "group__grp__stemmer.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__dbscan.html b/docs/docs/v2.1.0/group__grp__dbscan.html new file mode 100644 index 00000000..45f16e6c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__dbscan.html @@ -0,0 +1,369 @@ + + + + + + + + +MADlib: DBSCAN + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
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    +
    DBSCAN
    Early Stage Development
    +
    +
    +
    Contents +
    Warning
    This MADlib method is still in early stage development. Interface and implementation are subject to change.
    +

    Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm designed to discover clusters of arbitrary shape [1,2]. It places minimum requirements on domain knowledge to determine input parameters and has good efficiency on large databases.

    +

    Given a set of points, DBSCAN groups together points that are closely packed with many nearby neighbors (core), and marks points that lie alone in low-density regions with few nearby neighbors (border). Other points in the dataset that are not core or border are considered as noise. This method tends to be good for data which contains clusters of similar density.

    +

    Currently only a brute force approach is implemented, suitable for small datasets. Other approaches for larger datasets will be implemented in a future release.

    +

    Clustering Function
    +
    +dbscan( source_table,
+        output_table,
+        id_column,
+        expr_point,
+        eps,
+        min_samples,
+        metric,
+        algorithm,
+        max_segmentation_depth
+      )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the input data points.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table containing the clustering results.

    +

    +
    +
    id
    +

    TEXT. Name of a column or expression containing a unique integer id for each training point.

    +

    +
    +
    point
    +

    TEXT. Name of the column with point coordinates in array form, or an expression that evaluates to an array of point coordinates.

    +

    +
    +
    eps
    +

    FLOAT8. Maximum distance between two samples for one to be considered in the neighborhood of the other. (Note this is not a maximum bound on the distances of points within a cluster.) This is an important parameter to choose appropriately and should consider both the nature of the data set and the distance function.

    +

    +
    +
    min_samples (optional)
    +

    INTEGER, default: 5. Number of samples in a neighborhood for a point to be considered as a core point. This includes the point itself. This parameter controls how tolerant the algorithm is towards noise, so on noisy data sets it may be useful to increase the magnitude of this parameter.

    +
    Note
    The parameters 'eps' and 'min_samples' together define the density of a cluster. A core point is where there exist 'min_samples' other points within a distance of 'eps', which are defined as neighbors of the core point. A higher value of 'min_samples' or a lower value of 'eps' indicate that higher density is needed to form a cluster.
    +
    +
    metric (optional)
    +
    TEXT, default: 'squared_dist_norm2'. The name of the function used to calculate the distance between data points. The following distance functions can be used:
      +
    • +dist_norm1: 1-norm/Manhattan (element-wise median). MADlib does not provide a median aggregate function for performance reasons.
      • +
    • +dist_norm2: 2-norm/Euclidean (element-wise mean)
      • +
    • +squared_dist_norm2: squared Euclidean distance (element-wise mean)
      • +
    • +dist_angle: angle (element-wise mean of normalized points)
      • +
    • +

      dist_tanimoto: tanimoto (element-wise mean of normalized points)

      +

      +
      • +
    +
    +
    algorithm (optional)
    +

    TEXT, default: 'optimized'. The name of the algorithm used to compute clusters.

      +
    • +

      brute_force: Brute force can be slow and should not be used for large datasets. However, it does have less initial setup overhead than the parllel-optimized algorithm, which may make it faster for some cases involving small datasets. You can also use a short form "b" or "brute" etc. to select brute force.

      +

      +
      • +
    • +

      optimized: This uses an rtree index to accelerate range_queries while performing the cluster detection. It is designed with gpdb in mind, in which case it intelligently partitions the space into a number of connected regions, runs DBSCAN in parallel on each region, and then merges the results together. By default, the maximum number of regions it will consider using is equal to the number of segments in the database, but if you suspect it may be spending too much time on the segmentation, this can be limited further by setting the max_segmentation_depth parameter to something lower. This should decrease the segmentation overhead, but will also decrease the amount of parallelism. If the dataset is relatively small, another option to consider is brute force, which has very little overhead but won't scale as well. For large enough datasets, and an appropriate choice of eps, this algorithm should be able to run in O((N/S) log N) time where N is the number of rows (points) in the input and S is the number of regions (often equal to the number of segments, but may be less). (Worst case for brute force is O(N^2).) eps should be chosen based on the density of the dataset, where DBSCAN works best for datasets where the clusters have a roughly uniform density. If eps is chosen too large, then the runtime will explode and nearly every point will be considered connected to every other point in one large cluster. Best practice is to start with a relatively small eps, so it can return the first result faster; if it looks like there are too many small clusters, increase eps and allow it to run for longer.

      +

      +
      • +
    +

    +
    +
    max_segmentation_depth (optional)
    +

    INTEGER, default: <number of="" segments>="">. The number of regions to segment the data. See optimized for usage.

    +

    +
    +
    +

    Output
    + The output table for DBSCAN module has the following columns:

    + + + + + + + + +
    id SMALLINT|INTEGER|BIGINT. A column or expression which specifies unique ids for each row in the training dataset. Must evaluate to an integer type.
    cluster_id INTEGER. The cluster id of each classified data point.
    is_core_point BOOLEAN. Indicates if the training data point is core If it is not a core point and listed in the output table, it is a border point. Noise points are not shown in this table.
    point TEXT. The coordinates of each point classified
    +

    Cluster Assignment
    +

    After clustering, the cluster assignment for each data point can be computed:

    +
    +dbscan_predict( dbscan_table,
+                source_table,
+                id,
+                point,
+                output_table
+                )
+

    Arguments

    +
    dbscan_table
    +

    TEXT. Name of the table created by running DBSCAN.

    +

    +
    +
    source_table
    +

    TEXT. Name of the table containing the input data points.

    +

    +
    +
    id
    +

    VARCHAR. A column name or expression which selects a unique integer id for each training point.

    +

    +
    +
    point
    +

    TEXT. Name of the column with point coordinates in array form, or an expression that evaluates to an array of point coordinates.

    +

    +
    +
    output_table
    +
    TEXT. Name of the table containing the clustering results.
    +
    +

    Output
    + The output is a table with the following columns:

    + + + + + + +
    id BIGINT. The unique id of each row, as it as passed in.
    cluster_id INTEGER. Cluster assignment (zero-based, i.e., 0,1,2...).
    distance DOUBLE PRECISION. Distance to the cluster centroid.
    +

    Examples
    +
      +
    1. Create input data: 
      +DROP TABLE IF EXISTS dbscan_train_data;
+CREATE TABLE dbscan_train_data (pid int, points double precision[]);
+INSERT INTO dbscan_train_data VALUES
+(1,  '{1, 1}'),
+(2,  '{2, 1}'),
+(3,  '{1, 2}'),
+(4,  '{2, 2}'),
+(5,  '{3, 5}'),
+(6,  '{3, 9}'),
+(7,  '{3, 10}'),
+(8,  '{4, 10}'),
+(9,  '{4, 11}'),
+(10,  '{5, 10}'),
+(11,  '{7, 10}'),
+(12,  '{10, 9}'),
+(13,  '{10, 6}'),
+(14,  '{9, 5}'),
+(15,  '{10, 5}'),
+(16,  '{11, 5}'),
+(17,  '{9, 4}'),
+(18,  '{10, 4}'),
+(19,  '{11, 4}'),
+(20,  '{10, 3}');
+CREATE TABLE dbscan_test_data (pid int, points double precision[]);
+INSERT INTO dbscan_test_data VALUES
+(1,  '{1, 2}'),
+(2,  '{2, 2}'),
+(3,  '{1, 3}'),
+(4,  '{2, 2}'),
+(10,  '{5, 11}'),
+(11,  '{7, 10}'),
+(12,  '{10, 9}'),
+(13,  '{10, 6}'),
+(14,  '{9, 5}'),
+(15,  '{10, 6}');
+
      2. +
    2. Run DBSCAN using the brute force method with a Euclidean distance function: 
      +DROP TABLE IF EXISTS dbscan_result, dbscan_result_summary;
+SELECT madlib.dbscan(
+                'dbscan_train_data',    -- source table
+                'dbscan_result',        -- output table
+                'pid',                  -- point id column
+                'points',               -- data point
+                 1.75,                  -- epsilon
+                 4,                     -- min samples
+                'dist_norm2',           -- metric
+                'brute_force');         -- algorithm
+SELECT * FROM dbscan_result ORDER BY pid;
+
      + pid | cluster_id | is_core_point | __points__
+-----+------------+---------------+------------
+   1 |          0 | t             | {1,1}
+   2 |          0 | t             | {2,1}
+   3 |          0 | t             | {1,2}
+   4 |          0 | t             | {2,2}
+   6 |          1 | f             | {3,9}
+   7 |          1 | t             | {3,10}
+   8 |          1 | t             | {4,10}
+   9 |          1 | t             | {4,11}
+  10 |          1 | f             | {5,10}
+  13 |          2 | t             | {10,6}
+  14 |          2 | t             | {9,5}
+  15 |          2 | t             | {10,5}
+  16 |          2 | t             | {11,5}
+  17 |          2 | t             | {9,4}
+  18 |          2 | t             | {10,4}
+  19 |          2 | t             | {11,4}
+  20 |          2 | t             | {10,3}
+(17 rows)
+
      There are three clusters created. All points are core points except for 6 and 10 which are border points. The noise points do not show up in the output table. If you want to see the noise points you can use a query like: 
      +SELECT l.* FROM dbscan_train_data l WHERE NOT EXISTS
+    (SELECT NULL FROM dbscan_result r WHERE r.pid = l.pid)
+    ORDER BY l.pid;
+
      + pid | points
+-----+--------
+   5 | {3,5}
+  11 | {7,10}
+  12 | {10,9}
+
      The summary table lists the 'eps' value and the distance metric used: 
      +SELECT * FROM dbscan_result_summary;
+
      + id | eps  |   metric
+-----------+------+------------
+ pid       | 1.75 | dist_norm2
+
      3. +
    3. Find the cluster assignment for the test data points: 
      +SELECT madlib.dbscan_predict(
+                        'dbscan_result',        -- from DBSCAN run
+                        'dbscan_test_data',     -- test dataset
+                        'pid',                  -- point id column
+                        'points',               -- data point
+                        'dbscan_predict_out'    -- output table
+                        );
+SELECT * FROM dbscan_predict_out ORDER BY pid;
+
      + pid | cluster_id | distance 
+-----+------------+----------
+   1 |          0 |        0
+   2 |          0 |        0
+   3 |          0 |        1
+   4 |          0 |        0
+  10 |          1 |        1
+  13 |          2 |        0
+  14 |          2 |        0
+  15 |          2 |        0
+(8 rows)
+
      4. +
    +

    Literature
    +

    [1] Martin Ester, Hans-Peter Kriegel, Jörg Sander, Xiaowei Xu, "A Density-Based Algorithm for Discovering Clusters +in Large Spatial Databases with Noise", KDD-96 Proceedings, https://www.aaai.org/Papers/KDD/1996/KDD96-037.pdf

    +

    [2] Erich Schubert, Jörg Sander, Martin Ester, Hans-Peter Kriegel, Xiaowei Xu, "DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN", ACM Transactions on Database Systems, July 2017, Article No. 19, https://dl.acm.org/doi/10.1145/3068335

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__decision__tree.html b/docs/docs/v2.1.0/group__grp__decision__tree.html new file mode 100644 index 00000000..85c0092c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__decision__tree.html @@ -0,0 +1,1162 @@ + + + + + + + + +MADlib: Decision Tree + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Decision Tree
    Supervised Learning » Tree Methods
    +
    +
    +
    Contents +

    A decision tree is a supervised learning method that can be used for classification and regression. It consists of a structure in which internal nodes represent tests on attributes, and the branches from nodes represent the result of those tests. Each leaf node is a class label and the paths from root to leaf nodes define the set of classification or regression rules.

    +

    Training Function
    We implement the decision tree using the CART algorithm introduced by Breiman et al. [1]. The training function has the following syntax: 
    +tree_train(
+    training_table_name,
+    output_table_name,
+    id_col_name,
+    dependent_variable,
+    list_of_features,
+    list_of_features_to_exclude,
+    split_criterion,
+    grouping_cols,
+    weights,
+    max_depth,
+    min_split,
+    min_bucket,
+    num_splits,
+    pruning_params,
+    null_handling_params,
+    verbosity
+    )
+
    Arguments
    +
    training_table_name
    +

    TEXT. Name of the table containing the training data.

    +

    +
    +
    output_table_name
    +

    TEXT. Name of the generated table containing the model. If a table with the same name already exists, an error will be returned. A summary table named <output_table_name>_summary is also created. A cross-validation table <output_table_name>_cv may also be created. These are described later on this page.

    +

    +
    +
    id_col_name
    +

    TEXT. Name of the column containing id information in the training data. This is a mandatory argument and is used for prediction and cross-validation. The values are expected to be unique for each row.

    +

    +
    +
    dependent_variable
    +

    TEXT. Name of the column that contains the output (response) for training. Boolean, integer and text types are considered to be classification outputs, while double precision values are considered to be regression outputs. The response variable for a classification tree can be multinomial, but the time and space complexity of the training function increases linearly as the number of response classes increases.

    +

    +
    +
    list_of_features
    +

    TEXT. Comma-separated string of column names or expressions to use as predictors. Can also be a '*' implying all columns are to be used as predictors (except for the ones included in the next argument that lists exclusions). The types of the features can be mixed: boolean, integer, and text columns are considered categorical and double precision columns are considered continuous. Categorical variables are not encoded and used as is in the training.

    +

    Array columns can also be included in the list, where the array is expanded to treat each element of the array as a feature.

    +

    Note that not every combination of the levels of a categorical variable is checked when evaluating a split. The levels of the non-integer categorical variable are ordered by the entropy of the variable in predicting the response. The split at each node is evaluated between these ordered levels. Integer categorical variables, however, are simply ordered by their value.

    +

    +
    +
    list_of_features_to_exclude (optional)
    +

    TEXT. Comma-separated string of column names to exclude from the predictors list. If the dependent_variable is an expression (including cast of a column name), then this list should include the columns present in the dependent_variable expression, otherwise those columns will be included in the features. The names in this parameter should be identical to the names used in the table and quoted appropriately.

    +

    +
    +
    split_criterion (optional)
    +

    TEXT, default = 'gini' for classification, 'mse' for regression. Impurity function to compute the feature to use to split a node. Supported criteria are 'gini', 'entropy', 'misclassification' for classification trees. For regression trees, split_criterion of 'mse' (mean-squared error) is always used, irrespective of the input for this argument. Refer to reference [1] for more information on impurity measures.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. Comma-separated list of column names to group the data by. This will produce multiple decision trees, one for each group.

    +

    +
    +
    weights (optional)
    +

    TEXT. Column name containing numerical weights for each observation. Can be any value greater than 0 (does not need to be an integer). This can be used to handle the case of unbalanced data sets. The weights are used to compute a weighted average in the output leaf node. For classification, the contribution of a row towards the vote of its corresponding level is multiplied by the weight (weighted mode). For regression, the output value of the row is multiplied by the weight (weighted mean).

    +

    +
    +
    max_depth (optional)
    +

    INTEGER, default: 7. Maximum depth of any node of the final tree, with the root node counted as depth 0. A deeper tree can lead to better prediction but will also result in longer processing time and higher memory usage. Current allowed maximum is 100.

    +

    +
    +
    min_split (optional)
    +

    INTEGER, default: 20. Minimum number of observations that must exist in a node for a split to be attempted. The best value for this parameter depends on the number of tuples in the dataset.

    +

    +
    +
    min_bucket (optional)
    +

    INTEGER, default: min_split/3. Minimum number of observations in any terminal node. If only one of min_bucket or min_split is specified, min_split is set to min_bucket*3 or min_bucket to min_split/3, as appropriate.

    +

    +
    +
    num_splits (optional)
    +

    INTEGER, default: 20. Continuous-valued features are binned into discrete quantiles to compute split boundaries. Uniform binning is used. This global parameter is used to compute the resolution of splits for continuous features. Higher number of bins will lead to better prediction, but will also result in longer processing time and higher memory usage.

    +

    +
    +
    pruning_params (optional)
    +

    TEXT. Comma-separated string of key-value pairs giving the parameters for pruning the tree.

    + + + + +
    cp

    Default: 0. Complexity parameter. A split on a node is attempted only if it decreases the overall lack of fit by a factor of 'cp', otherwise the split is pruned away. This value is used to create an initial tree before running cross-validation (see below).

    +

    +
    n_folds

    Default: 0 (i.e. no cross-validation). Number of cross-validation folds to use to compute the best value of cp. To perform cross-validation, a positive value of n_folds (2 or more) should be specified. An additional output table <model_table>_cv is created containing the values of evaluated cp and the cross-validation error statistics. The tree returned in the output table corresponds to the cp with the lowest cross-validation error (we pick the maximum cp if multiple values have same error).

    +

    The list of cp values is automatically computed by parsing through the tree initially trained on the complete dataset. The tree output is a subset of this initial tree corresponding to the best computed cp.

    +

    +
    +

    +
    +
    null_handling_params (optional)
    +

    TEXT. Comma-separated string of key-value pairs controlling the behavior of various features handling missing values. One of the following can be used if desired (not both):

    + + + + +
    max_surrogates Default: 0. Number of surrogates to store for each node. One approach to handling NULLs is to use surrogate splits for each node. A surrogate variable enables you to make better use of the data by using another predictor variable that is associated (correlated) with the primary split variable. The surrogate variable comes into use when the primary predictior value is NULL. Surrogate rules implemented here are based on reference [1].
    null_as_category

    Default: FALSE. Whether to treat NULL as a valid level for categorical features. FALSE means that NULL is not a valid level, which is probably the most common sitation.

    +

    If set to TRUE, NULL values are considered a categorical value and placed at the end of the ordering of categorical levels. Placing at the end ensures that NULL is never used as a value to split a node on. One reason to make NULL a category is that it allows you to predict on categorical levels that were not in the training data by lumping them into an "other bucket."

    +

    This parameter is ignored for continuous-valued features.

    +
    +

    +
    +
    verbosity (optional)
    +
    BOOLEAN, default: FALSE. Provides verbose output of the training result.
    +
    +
    +

    Output

    +
    +

    The model table produced by the training function contains the following columns:

    + + + + + + + + + + + + + + + +
    <...> Grouping columns, if provided as input, in the same types as the training table. This could be multiple columns depending on the grouping_cols input.
    tree BYTEA8. Trained decision tree model stored in binary format (not human readable).
    cat_levels_in_text TEXT[]. Ordered levels (values) of categorical variables corresponding to the categorical features in the 'list_of_features' argument above. Used to help interpret the trained decision tree. For example, if the categorical features specified are weather_outlook and windy in that order, then 'cat_levels_in_text' might be [overcast, rain, sunny, False, True].
    cat_n_levels INTEGER[]. Number of levels for each categorical variable. Used to help interpret the trained decision tree. In the example from above, 'cat_n_levels' would be [3, 2] since there are 3 levels for weather_outlook and 2 levels windy.
    impurity_var_importance

    DOUBLE PRECISION[]. Impurity importance of each variable. The order of the variables is the same as that of the 'independent_varnames' column in the summary table (see below).

    +

    The impurity importance of any feature is the decrease in impurity by a node containing the feature as a primary split, summed over the whole tree. If surrogates are used, then the importance value includes the impurity decrease scaled by the adjusted surrogate agreement. Importance values are displayed as raw values as per the 'split_criterion' parameter. To see importance values normalized to sum to 100 across all variables, use the importance display helper function described later on this page. Please refer to [1] for more information on variable importance.

    +

    +
    tree_depth

    INTEGER. The maximum depth the tree obtained after training (root has depth 0).

    +

    +
    pruning_cp

    DOUBLE PRECISION. The cost complexity parameter used for pruning the trained tree(s). This could be different than the cp value input using the pruning_params if cross-validation is used.

    +

    +
    +

    A summary table named <output_table_name>_summary is also created at the same time, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    method

    TEXT. 'tree_train'

    +

    +
    is_classification

    BOOLEAN. TRUE if the decision trees are for classification, FALSE if for regression.

    +

    +
    source_table

    TEXT. The data source table name.

    +

    +
    model_table

    TEXT. The model table name.

    +

    +
    id_col_name

    TEXT. The ID column name.

    +

    +
    list_of_features

    TEXT. The list_of_features inputed to the 'tree_train' procedure.

    +

    +
    list_of_features_to_exclude

    TEXT. The list_of_features_to_exclude inputed to the 'tree_train' procedure.

    +

    +
    dependent_varname

    TEXT. The dependent variable.

    +

    +
    independent_varnames

    TEXT. The independent variables. These are the features used in the training of the decision tree.

    +

    +
    cat_features

    TEXT. The list of categorical feature names as a comma-separated string.

    +

    +
    con_features

    TEXT. The list of continuous feature names as a comma-separated string.

    +

    +
    grouping_cols

    TEXT. Names of grouping columns.

    +

    +
    num_all_groups

    INTEGER. Number of groups in decision tree training.

    +

    +
    num_failed_groups

    INTEGER. Number of failed groups in decision tree training.

    +

    +
    total_rows_processed

    BIGINT. Total numbers of rows processed in all groups.

    +

    +
    total_rows_skipped

    BIGINT. Total numbers of rows skipped in all groups due to missing values or failures.

    +

    +
    dependent_var_levels

    TEXT. For classification, the distinct levels of the dependent variable.

    +

    +
    dependent_var_type

    TEXT. The type of dependent variable.

    +

    +
    input_cp

    DOUBLE PRECISION. The complexity parameter (cp) used for pruning the trained tree(s) before cross-validation is run. This is same as the cp value input using the pruning_params.

    +

    +
    independent_var_types

    TEXT. A comma separated string for the types of independent variables.

    +

    +
    n_folds

    BIGINT. Number of cross-validation folds used.

    +

    +
    null_proxy TEXT. Describes how NULLs are handled. If NULL is not treated as a separate categorical variable, this will be NULL. If NULL is treated as a separate categorical value, this will be set to "__NULL__"
    +

    A cross-validation table called <output_table_name>_cv is created if 'n_folds' is set in the 'pruning_params'. It has the following columns:

    + + + + + + +
    cp

    DOUBLE PRECISION. Complexity parameter.

    +

    +
    cv_error_avg

    DOUBLE PRECISION. Average error resulting from cp value.

    +

    +
    cv_error_stdev DOUBLE PRECISION. Standard deviation resulting from cp value.
    +
    Note
      +
    • Many of the parameters are designed to be similar to the popular R package 'rpart'. An important distinction between rpart and the MADlib function is that for both response and feature variables, MADlib considers integer values as categorical values, while rpart considers them as continuous. To use integers as continuous, cast them to double precision.
      • +
    • Integer values are ordered by value for computing the split boundaries. Cast to TEXT if the entropy-based ordering method is desired.
      • +
    • When cross-validation is not used (n_folds=0), each tree output is pruned by the input cost complexity (cp). With cross-validation, the input cp is the minimum value of all the explored values of 'cp'. During cross-validation, we train an initial tree using the provided cp and explore all possible sub-trees (up to a single-node tree) to compute the optimal sub-tree. The optimal sub-tree and the 'cp' corresponding to this optimal sub-tree is placed in the output_table, with the columns named as tree and pruning_cp respectively.
      • +
    +
    +

    Run-time and Memory Usage
    +

    The number of features and the number of class values per categorical feature have a direct impact on run-time and memory. In addition, here is a summary of the main parameters in the training function that affect run-time and memory:

    + + + + + + + + + + + +
    Parameter Run-time Memory Notes
    'max_depth' High High Deeper trees can take longer to run and use more memory.
    'min_split' No or little effect, unless very small. No or little effect, unless very small. If too small, can impact run-time by building trees that are very thick.
    'min_bucket' No or little effect, unless very small. No or little effect, unless very small. If too small, can impact run-time by building trees that are very thick.
    'num_splits' High High Depends on number of continuous variables. Effectively adds more features as the binning becomes more granular.
    +

    If you experience long run-times or are hitting memory limits, consider reducing one or more of these parameters. One approach when building a decision tree model is to start with a low maximum depth value and use suggested defaults for other parameters. This will give you a sense of run-time and test set accuracy. Then you can change maximum depth in a systematic way as required to improve accuracy.

    +

    Prediction Function
    The prediction function estimates the conditional mean given a new predictor. It has the following syntax: 
    +tree_predict(tree_model,
+             new_data_table,
+             output_table,
+             type)
+
    +

    Arguments

    +
    tree_model
    +

    TEXT. Name of the table containing the decision tree model. This should be the output table returned from tree_train.

    +

    +
    +
    new_data_table
    +

    TEXT. Name of the table containing prediction data. This table is expected to contain the same features that were used during training. The table should also contain id_col_name used for identifying each row.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table to output prediction results. If this table already exists, an error is returned. The table contains the id_col_name column giving the 'id' for each prediction and the prediction columns for the dependent variable.

    +

    If type = 'response', then the table has a single additional column with the prediction value of the response. The type of this column depends on the type of the response variable used during training.

    +

    If type = 'prob', then the table has multiple additional columns, one for each possible value of the response variable. The columns are labeled as 'estimated_prob_dep_value', where dep_value represents each value of the response variable.

    +

    +
    +
    type (optional)
    +
    TEXT, optional, default: 'response'. For regression trees, the output is always the predicted value of the dependent variable. For classification trees, the type variable can be 'response', giving the classification prediction as output, or 'prob', giving the class probabilities as output. For each value of the dependent variable, a column with the probabilities is added to the output table.
    +
    +

    Tree Display
    The display function outputs a graph representation of the decision tree. The output can either be in the popular 'dot' format that can be visualized using various programs including those in the GraphViz package, or in a simple text format. The details of the text format are output with the tree. 
    +tree_display(tree_model, dot_format, verbosity)
+
    +

    An additional display function is provided to output the surrogate splits chosen for each internal node: 

    +tree_surr_display(tree_model)
+

    This output contains the list of surrogate splits for each internal node. The nodes are sorted in ascending order by id. This is equivalent to viewing the tree in a breadth-first manner. For each surrogate, we output the surrogate split (variable and threshold) and also give the number of rows that were common between the primary split and the surrogate split. Finally, the number of rows present in the majority branch of the primary split is also shown. Only surrogates that perform better than this majority branch are included in the surrogate list. When the primary variable has a NULL value the surrogate variables are used in order to compute the split for that node. If all surrogates variables are NULL, then the majority branch is used to compute the split for a tuple.

    +

    Arguments

    +
    tree_model
    +
    TEXT. Name of the table containing the decision tree model.
    +
    dot_format (optional)
    +
    BOOLEAN, default = TRUE. Output can either be in a dot format or a text format. If TRUE, the result is in the dot format, else output is in text format.
    +
    verbosity (optional)
    +
    BOOLEAN, default = FALSE. If set to TRUE, the dot format output will contain additional information (impurity, sample size, number of weighted rows for each response variable, classification or prediction if the tree was pruned at this level)
    +
    +

    The output is always returned as a 'TEXT'. For the dot format, the output can be redirected to a file on the client side and then rendered using visualization programs.

    +

    To export the dot format result to an external file, use the method below. Please note that you should use unaligned table output mode for psql with '-A' flag, or else you may get an error when you try to convert the dot file to another format for viewing (e.g., PDF). And inside the psql client, both '\t' and '\o' should be used:

    +
    +> # under bash
+> psql -A my_database
+# -- in psql now
+# \t
+# \o test.dot -- export to a file
+# select madlib.tree_display('tree_out');
+# \o
+# \t
+

    After the dot file has been generated, use third-party plotting software to plot the trees in a nice format: 

    +> # under bash, convert the dot file into a PDF file
+> dot -Tpdf test.dot > test.pdf
+> xpdf test.pdf&
+

    Please see the examples below for more details on the contents of the tree output formats.

    +

    An additional display function is provided to output the surrogate splits chosen for each internal node: 

    +tree_surr_display(tree_model)
+

    Importance Display
    +

    This is a helper function that creates a table to more easily view impurity variable importance values for a given model table. This function rescales the importance values to represent them as percentages i.e. importance values are scaled to sum to 100.

    +
    +get_var_importance(model_table, output_table)
+

    Arguments

    +
    model_table
    +
    TEXT. Name of the table containing the decision tree model.
    +
    output_table
    +
    TEXT. Name of the table to create for importance values.
    +
    +

    The summary table generated by the tree_train function is necessary for this function to work.

    +

    Examples

    Decision Tree Classification Examples

    +
    +
      +
    1. Load input data set related to whether to play golf or not: 
      +DROP TABLE IF EXISTS dt_golf CASCADE;
+CREATE TABLE dt_golf (
+    id integer NOT NULL,
+    "OUTLOOK" text,
+    temperature double precision,
+    humidity double precision,
+    "Temp_Humidity" double precision[],
+    clouds_airquality text[],
+    windy boolean,
+    class text,
+    observation_weight double precision
+);
+INSERT INTO dt_golf VALUES
+(1,'sunny', 85, 85, ARRAY[85, 85],ARRAY['none', 'unhealthy'], 'false','Don''t Play', 5.0),
+(2, 'sunny', 80, 90, ARRAY[80, 90], ARRAY['none', 'moderate'], 'true', 'Don''t Play', 5.0),
+(3, 'overcast', 83, 78, ARRAY[83, 78], ARRAY['low', 'moderate'], 'false', 'Play', 1.5),
+(4, 'rain', 70, 96, ARRAY[70, 96], ARRAY['low', 'moderate'], 'false', 'Play', 1.0),
+(5, 'rain', 68, 80, ARRAY[68, 80], ARRAY['medium', 'good'], 'false', 'Play', 1.0),
+(6, 'rain', 65, 70, ARRAY[65, 70], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play', 1.0),
+(7, 'overcast', 64, 65, ARRAY[64, 65], ARRAY['medium', 'moderate'], 'true', 'Play', 1.5),
+(8, 'sunny', 72, 95, ARRAY[72, 95], ARRAY['high', 'unhealthy'], 'false', 'Don''t Play', 5.0),
+(9, 'sunny', 69, 70, ARRAY[69, 70], ARRAY['high', 'good'], 'false', 'Play', 5.0),
+(10, 'rain', 75, 80, ARRAY[75, 80], ARRAY['medium', 'good'], 'false', 'Play', 1.0),
+(11, 'sunny', 75, 70, ARRAY[75, 70], ARRAY['none', 'good'], 'true', 'Play', 5.0),
+(12, 'overcast', 72, 90, ARRAY[72, 90], ARRAY['medium', 'moderate'], 'true', 'Play', 1.5),
+(13, 'overcast', 81, 75, ARRAY[81, 75], ARRAY['medium', 'moderate'], 'false', 'Play', 1.5),
+(14, 'rain', 71, 80, ARRAY[71, 80], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play', 1.0);
+
      2. +
    2. Run the decision tree training function: 
      +DROP TABLE IF EXISTS train_output, train_output_summary;
+SELECT madlib.tree_train('dt_golf',         -- source table
+                         'train_output',    -- output model table
+                         'id',              -- id column
+                         'class',           -- response
+                         '"OUTLOOK", temperature, windy',   -- features
+                         NULL::text,        -- exclude columns
+                         'gini',            -- split criterion
+                         NULL::text,        -- no grouping
+                         NULL::text,        -- no weights, all observations treated equally
+                         5,                 -- max depth
+                         3,                 -- min split
+                         1,                 -- min bucket
+                         10                 -- number of bins per continuous variable
+                         );
+
      View the output table (excluding the tree which is in binary format): 
      +\x on
+SELECT pruning_cp, cat_levels_in_text, cat_n_levels, impurity_var_importance, tree_depth FROM train_output;
+
      +-[ RECORD 1 ]-----------+--------------------------------------
+pruning_cp              | 0
+cat_levels_in_text      | {overcast,rain,sunny,False,True}
+cat_n_levels            | {3,2}
+impurity_var_importance | {0.102040816326531,0,0.85905612244898}
+tree_depth              | 5
+
      View the summary table: 
      +\x on
+SELECT * FROM train_output_summary;
+
      +-[ RECORD 1 ]---------------+--------------------------------
+method                      | tree_train
+is_classification           | t
+source_table                | dt_golf
+model_table                 | train_output
+id_col_name                 | id
+list_of_features            | "OUTLOOK", temperature, windy
+list_of_features_to_exclude | None
+dependent_varname           | class
+independent_varnames        | "OUTLOOK",windy,temperature
+cat_features                | "OUTLOOK",windy
+con_features                | temperature
+grouping_cols               |
+num_all_groups              | 1
+num_failed_groups           | 0
+total_rows_processed        | 14
+total_rows_skipped          | 0
+dependent_var_levels        | "Don't Play","Play"
+dependent_var_type          | text
+input_cp                    | 0
+independent_var_types       | text, boolean, double precision
+n_folds                     | 0
+null_proxy                  |
+
      View the normalized impurity importance table using the helper function: 
      +\x off
+DROP TABLE IF EXISTS imp_output;
+SELECT madlib.get_var_importance('train_output','imp_output');
+SELECT * FROM imp_output;
+
      +   feature   | impurity_var_importance
+-------------+-------------------------
+ "OUTLOOK"   |        10.6171090593052
+ windy       |                       0
+ temperature |         89.382786893026
+
      3. +
    3. Predict output categories. For the purpose of this example, we use the same data that was used for training: 
      +\x off
+DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.tree_predict('train_output',          -- tree model
+                           'dt_golf',               -- new data table
+                           'prediction_results',    -- output table
+                           'response');             -- show response
+SELECT g.id, class, estimated_class FROM prediction_results p,
+dt_golf g WHERE p.id = g.id ORDER BY g.id;
+
      + id |   class    | estimated_class
+----+------------+-----------------
+  1 | Don't Play | Don't Play
+  2 | Don't Play | Don't Play
+  3 | Play       | Play
+  4 | Play       | Play
+  5 | Play       | Play
+  6 | Don't Play | Don't Play
+  7 | Play       | Play
+  8 | Don't Play | Don't Play
+  9 | Play       | Play
+ 10 | Play       | Play
+ 11 | Play       | Play
+ 12 | Play       | Play
+ 13 | Play       | Play
+ 14 | Don't Play | Don't Play
+(14 rows)
+
      To display the probabilities associated with each value of the dependent variable, set the 'type' parameter to 'prob': 
      +DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.tree_predict('train_output',          -- tree model
+                           'dt_golf',               -- new data table
+                           'prediction_results',    -- output table
+                           'prob');                 -- show probability
+SELECT g.id, class, "estimated_prob_Don't Play",  "estimated_prob_Play"
+FROM prediction_results p, dt_golf g WHERE p.id = g.id ORDER BY g.id;
+
      + id |   class    | estimated_prob_Don't Play | estimated_prob_Play
+----+------------+---------------------------+---------------------
+  1 | Don't Play |                         1 |                   0
+  2 | Don't Play |                         1 |                   0
+  3 | Play       |                         0 |                   1
+  4 | Play       |                         0 |                   1
+  5 | Play       |                         0 |                   1
+  6 | Don't Play |                         1 |                   0
+  7 | Play       |                         0 |                   1
+  8 | Don't Play |                         1 |                   0
+  9 | Play       |                         0 |                   1
+ 10 | Play       |                         0 |                   1
+ 11 | Play       |                         0 |                   1
+ 12 | Play       |                         0 |                   1
+ 13 | Play       |                         0 |                   1
+ 14 | Don't Play |                         1 |                   0
+(14 rows)
+
      4. +
    4. View the tree in text format: 
      +SELECT madlib.tree_display('train_output', FALSE);
+
      + -------------------------------------
+ - Each node represented by 'id' inside ().
+ - Each internal nodes has the split condition at the end, while each
+        leaf node has a * at the end.
+ - For each internal node (i), its child nodes are indented by 1 level
+        with ids (2i+1) for True node and (2i+2) for False node.
+ - Number of (weighted) rows for each response variable inside [].'
+        The response label order is given as ['"\'Don\'t Play\'"', '"\'Play\'"'].
+        For each leaf, the prediction is given after the '-->'
+ -------------------------------------
+ (0)[5 9]  "OUTLOOK" in {overcast}
+    (1)[0 4]  * --> "Play"
+    (2)[5 5]  temperature <= 75
+       (5)[3 5]  temperature <= 65
+          (11)[1 0]  * --> "Don't Play"
+          (12)[2 5]  temperature <= 70
+             (25)[0 3]  * --> "Play"
+             (26)[2 2]  temperature <= 72
+                (53)[2 0]  * --> "Don't Play"
+                (54)[0 2]  * --> "Play"
+       (6)[2 0]  * --> "Don't Play"
+ -------------------------------------
+
      Here are some details on how to interpret the tree display above:
        +
      • Node numbering starts at 0 for the root node and would be contiguous 1,2...n if the tree was completely full (no pruning). Since the tree has been pruned, the node numbering is not contiguous.
        • +
      • The order of values [x y] indicates the number of weighted rows that correspond to ["Don't play" "Play"] before the node test. For example, at (root) node 0, there are 5 rows for "Don't play" and 9 rows for "Play" in the raw data.
        • +
      • If we apply the test of "OUTLOOK" being overcast, then the True (yes) result is leaf node 1 which is "Play". There are 0 "Don't play" rows and 4 "Play" rows that correspond to this case (overcast). In other words, if it is overcast, you always play golf. If it is not overcast, you may or may not play golf, depending on the rest of the tree.
        • +
      • The remaining 5 "Don't play" rows and 5 "Play rows" are then tested at node 2 on temperature<=75. The False (no) result is leaf node 6 which is "Don't Play". The True (yes) result proceeds to leaf node 5 to test on temperature<=65. And so on down the tree.
        • +
      • Creating a dot format visualization of the tree, as described below, can help with following the decision flows.
        • +
      +
      5. +
    5. Create a dot format display of the tree: 
      +SELECT madlib.tree_display('train_output', TRUE);
+
      + digraph "Classification tree for dt_golf" {
+          subgraph "cluster0"{
+          label=""
+ "g0_0" [label="\"OUTLOOK" <= overcast", shape=ellipse];
+ "g0_0" -> "g0_1"[label="yes"];
+ "g0_1" [label=""Play"",shape=box];
+ "g0_0" -> "g0_2"[label="no"];
+ "g0_2" [label="temperature <= 75", shape=ellipse];
+ "g0_2" -> "g0_5"[label="yes"];
+ "g0_2" -> "g0_6"[label="no"];
+ "g0_6" [label=""Don't Play"",shape=box];
+ "g0_5" [label="temperature <= 65", shape=ellipse];
+ "g0_5" -> "g0_11"[label="yes"];
+ "g0_11" [label=""Don't Play"",shape=box];
+ "g0_5" -> "g0_12"[label="no"];
+ "g0_12" [label="temperature <= 70", shape=ellipse];
+ "g0_12" -> "g0_25"[label="yes"];
+ "g0_25" [label=""Play"",shape=box];
+ "g0_12" -> "g0_26"[label="no"];
+ "g0_26" [label="temperature <= 72", shape=ellipse];
+ "g0_26" -> "g0_53"[label="yes"];
+ "g0_53" [label=""Don't Play"",shape=box];
+ "g0_26" -> "g0_54"[label="no"];
+ "g0_54" [label=""Play"",shape=box];
+   } //--- end of subgraph------------
+ } //---end of digraph---------
+
      One important difference to note about the dot format above is how categorical variable tests are displayed:
        +
      • In the text format of the tree, the node 0 test is "OUTLOOK" in {overcast}, but in the dot format of the tree, the same node 0 test reads "\"OUTLOOK" <= overcast". This is because in dot format for categorical variables, the '<=' symbol represents the location in the array 'cat_levels_in_text' from the output table for the "OUTLOOK" levels. The array is ['overcast', 'rain', 'sunny', 'False', 'True'] with the first 3 entries corresponding to "OUTLOOK" and the last 2 entries corresponding to 'windy'. So the test "\"OUTLOOK" <= overcast" means all "OUTLOOK" levels to the left of, and including, 'overcast'. In this case there are no levels to the left of 'overcast' in the array so it is simply a test on whether it is overcast or not.
        • +
      • If there was a test "\"OUTLOOK" <= rain", this would include both 'overcast' and 'rain', since 'overcast' is to the left of 'rain' in the array.
        • +
      • If there was a test "windy <= True", this would include both 'False' and 'True', since 'False' is to the left of 'True' in the array.
        • +
      +
      6. +
    6. Now create a dot format display of the tree with additional information: 
      +SELECT madlib.tree_display('train_output', TRUE, TRUE);
+
      + digraph "Classification tree for dt_golf" {
+          subgraph "cluster0"{
+          label=""
+ "g0_0" [label="\"OUTLOOK" <= overcast\n impurity = 0.459184\n samples = 14\n value = [5 9]\n class = "Play"", shape=ellipse];
+ "g0_0" -> "g0_1"[label="yes"];
+ "g0_1" [label=""Play"\n impurity = 0\n samples = 4\n value = [0 4]",shape=box];
+ "g0_0" -> "g0_2"[label="no"];
+ "g0_2" [label="temperature <= 75\n impurity = 0.5\n samples = 10\n value = [5 5]\n class = "Don't Play"", shape=ellipse];
+ "g0_2" -> "g0_5"[label="yes"];
+ "g0_2" -> "g0_6"[label="no"];
+ "g0_6" [label=""Don't Play"\n impurity = 0\n samples = 2\n value = [2 0]",shape=box];
+ "g0_5" [label="temperature <= 65\n impurity = 0.46875\n samples = 8\n value = [3 5]\n class = "Play"", shape=ellipse];
+ "g0_5" -> "g0_11"[label="yes"];
+ "g0_11" [label=""Don't Play"\n impurity = 0\n samples = 1\n value = [1 0]",shape=box];
+ "g0_5" -> "g0_12"[label="no"];
+ "g0_12" [label="temperature <= 70\n impurity = 0.408163\n samples = 7\n value = [2 5]\n class = "Play"", shape=ellipse];
+ "g0_12" -> "g0_25"[label="yes"];
+ "g0_25" [label=""Play"\n impurity = 0\n samples = 3\n value = [0 3]",shape=box];
+ "g0_12" -> "g0_26"[label="no"];
+ "g0_26" [label="temperature <= 72\n impurity = 0.5\n samples = 4\n value = [2 2]\n class = "Don't Play"", shape=ellipse];
+ "g0_26" -> "g0_53"[label="yes"];
+ "g0_53" [label=""Don't Play"\n impurity = 0\n samples = 2\n value = [2 0]",shape=box];
+ "g0_26" -> "g0_54"[label="no"];
+ "g0_54" [label=""Play"\n impurity = 0\n samples = 2\n value = [0 2]",shape=box];
+   } //--- end of subgraph------------
+ } //---end of digraph---------
+
      The additional information in each node is: impurity, sample size, number of weighted rows for each response variable, and classification if the tree was pruned at this level. If your tree is not too big, you may wish to convert the dot format to PDF or another format for better visualization of the tree structure.
      7. +
    7. Arrays of features. Categorical and continuous features can be array columns, in which case the array is expanded to treat each element of the array as a feature: 
      +DROP TABLE IF EXISTS train_output, train_output_summary;
+SELECT madlib.tree_train('dt_golf',         -- source table
+                         'train_output',    -- output model table
+                         'id',              -- id column
+                         'class',           -- response
+                         '"Temp_Humidity", clouds_airquality',   -- features
+                         NULL::text,        -- exclude columns
+                         'gini',            -- split criterion
+                         NULL::text,        -- no grouping
+                         NULL::text,        -- no weights, all observations treated equally
+                         5,                 -- max depth
+                         3,                 -- min split
+                         1,                 -- min bucket
+                         10                 -- number of bins per continuous variable
+                         );
+
      View the output table (excluding the tree which is in binary format): 
      +\x on
+SELECT pruning_cp, cat_levels_in_text, cat_n_levels, impurity_var_importance, tree_depth FROM train_output;
+
      +-[ RECORD 1 ]-----------+-----------------------------------------------------
+pruning_cp              | 0
+cat_levels_in_text      | {medium,none,high,low,unhealthy,good,moderate}
+cat_n_levels            | {4,3}
+impurity_var_importance | {0,0.330612244897959,0.0466666666666666,0.444444444444444}
+tree_depth              | 3
+
      The first 4 levels correspond to cloud ceiling and the next 3 levels correspond to air quality.
      8. +
    8. Weighting observations. Use the 'weights' parameter to adjust a row's vote to balance the dataset. In our example, the weights are somewhat random but show that a different decision tree is create compared to the case where no weights are used: 
      +DROP TABLE IF EXISTS train_output, train_output_summary;
+SELECT madlib.tree_train('dt_golf',         -- source table
+                         'train_output',    -- output model table
+                         'id',              -- id column
+                         'class',           -- response
+                         '"OUTLOOK", temperature, windy',   -- features
+                         NULL::text,        -- exclude columns
+                         'gini',            -- split criterion
+                         NULL::text,        -- no grouping
+                         'observation_weight', -- weight observations
+                         5,                 -- max depth
+                         3,                 -- min split
+                         1,                 -- min bucket
+                         10                 -- number of bins per continuous variable
+                         );
+SELECT madlib.tree_display('train_output', FALSE);
+
      +  -------------------------------------
+  - Each node represented by 'id' inside ().
+  - Each internal nodes has the split condition at the end, while each
+         leaf node has a * at the end.
+  - For each internal node (i), its child nodes are indented by 1 level
+         with ids (2i+1) for True node and (2i+2) for False node.
+  - Number of (weighted) rows for each response variable inside [].'
+         The response label order is given as ['"Don\'t Play"', '"Play"'].
+         For each leaf, the prediction is given after the '-->'
+  -------------------------------------
+ (0)[17 19]  temperature <= 75
+    (1)[ 7 16]  temperature <= 72
+       (3)[ 7 10]  temperature <= 70
+          (7)[  1 8.5]  * --> "Play"
+          (8)[  6 1.5]  "OUTLOOK" in {overcast}
+             (17)[  0 1.5]  * --> "Play"
+             (18)[6 0]  * --> "Don't Play"
+       (4)[0 6]  * --> "Play"
+    (2)[10  3]  "OUTLOOK" in {overcast}
+       (5)[0 3]  * --> "Play"
+       (6)[10  0]  * --> "Don't Play"
+
      9. +
    +

    Decision Tree Regression Examples

    +
      +
    1. Load input data related to fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). Data was extracted from the 1974 Motor Trend US magazine. 
      +DROP TABLE IF EXISTS mt_cars;
+CREATE TABLE mt_cars (
+    id integer NOT NULL,
+    mpg double precision,
+    cyl integer,
+    disp double precision,
+    hp integer,
+    drat double precision,
+    wt double precision,
+    qsec double precision,
+    vs integer,
+    am integer,
+    gear integer,
+    carb integer
+);
+INSERT INTO mt_cars VALUES
+(1,18.7,8,360,175,3.15,3.44,17.02,0,0,3,2),
+(2,21,6,160,110,3.9,2.62,16.46,0,1,4,4),
+(3,24.4,4,146.7,62,3.69,3.19,20,1,0,4,2),
+(4,21,6,160,110,3.9,2.875,17.02,0,1,4,4),
+(5,17.8,6,167.6,123,3.92,3.44,18.9,1,0,4,4),
+(6,16.4,8,275.8,180,3.078,4.07,17.4,0,0,3,3),
+(7,22.8,4,108,93,3.85,2.32,18.61,1,1,4,1),
+(8,17.3,8,275.8,180,3.078,3.73,17.6,0,0,3,3),
+(9,21.4,null,258,110,3.08,3.215,19.44,1,0,3,1),
+(10,15.2,8,275.8,180,3.078,3.78,18,0,0,3,3),
+(11,18.1,6,225,105,2.768,3.46,20.22,1,0,3,1),
+(12,32.4,4,78.7,66,4.08,2.20,19.47,1,1,4,1),
+(13,14.3,8,360,245,3.21,3.578,15.84,0,0,3,4),
+(14,22.8,4,140.8,95,3.92,3.15,22.9,1,0,4,2),
+(15,30.4,4,75.7,52,4.93,1.615,18.52,1,1,4,2),
+(16,19.2,6,167.6,123,3.92,3.44,18.3,1,0,4,4),
+(17,33.9,4,71.14,65,4.22,1.835,19.9,1,1,4,1),
+(18,15.2,null,304,150,3.15,3.435,17.3,0,0,3,2),
+(19,10.4,8,472,205,2.93,5.25,17.98,0,0,3,4),
+(20,27.3,4,79,66,4.08,1.935,18.9,1,1,4,1),
+(21,10.4,8,460,215,3,5.424,17.82,0,0,3,4),
+(22,26,4,120.3,91,4.43,2.14,16.7,0,1,5,2),
+(23,14.7,8,440,230,3.23,5.345,17.42,0,0,3,4),
+(24,30.4,4,95.14,113,3.77,1.513,16.9,1,1,5,2),
+(25,21.5,4,120.1,97,3.70,2.465,20.01,1,0,3,1),
+(26,15.8,8,351,264,4.22,3.17,14.5,0,1,5,4),
+(27,15.5,8,318,150,2.768,3.52,16.87,0,0,3,2),
+(28,15,8,301,335,3.54,3.578,14.6,0,1,5,8),
+(29,13.3,8,350,245,3.73,3.84,15.41,0,0,3,4),
+(30,19.2,8,400,175,3.08,3.845,17.05,0,0,3,2),
+(31,19.7,6,145,175,3.62,2.77,15.5,0,1,5,6),
+(32,21.4,4,121,109,4.11,2.78,18.6,1,1,4,2);
+
      2. +
    2. We train a regression decision tree with surrogates in order to handle the NULL feature values: 
      +DROP TABLE IF EXISTS train_output, train_output_summary, train_output_cv;
+SELECT madlib.tree_train('mt_cars',         -- source table
+                         'train_output',    -- output model table
+                         'id',              -- id column
+                         'mpg',             -- dependent variable
+                         '*',               -- features
+                         'id, hp, drat, am, gear, carb',  -- exclude columns
+                         'mse',             -- split criterion
+                         NULL::text,        -- no grouping
+                         NULL::text,        -- no weights, all observations treated equally
+                         10,                -- max depth
+                         8,                 -- min split
+                         3,                 -- number of bins per continuous variable
+                         10,                -- number of splits
+                         NULL,              -- pruning parameters
+                         'max_surrogates=2' -- number of surrogates
+                         );
+
      View the output table (excluding the tree which is in binary format) which shows ordering of levels of categorical variables 'vs' and 'cyl': 
      +SELECT pruning_cp, cat_levels_in_text, cat_n_levels, impurity_var_importance, tree_depth FROM train_output;
+
      +-[ RECORD 1 ]-----------+------------------------------------------------------------------------
+pruning_cp              | 0
+cat_levels_in_text      | {0,1,4,6,8}
+cat_n_levels            | {2,3}
+impurity_var_importance | {0,22.6309172500675,4.79024943310651,2.32115000000003,13.8967382920111}
+tree_depth              | 4
+
      View the summary table: 
      +\x on
+SELECT * FROM train_output_summary;
+
      +-[ RECORD 1 ]---------------+-----------------------------------------------------------------------
+method                      | tree_train
+is_classification           | f
+source_table                | mt_cars
+model_table                 | train_output
+id_col_name                 | id
+list_of_features            | *
+list_of_features_to_exclude | id, hp, drat, am, gear, carb
+dependent_varname           | mpg
+independent_varnames        | vs,cyl,disp,qsec,wt
+cat_features                | vs,cyl
+con_features                | disp,qsec,wt
+grouping_cols               |
+num_all_groups              | 1
+num_failed_groups           | 0
+total_rows_processed        | 32
+total_rows_skipped          | 0
+dependent_var_levels        |
+dependent_var_type          | double precision
+input_cp                    | 0
+independent_var_types       | integer, integer, double precision, double precision, double precision
+n_folds                     | 0
+null_proxy                  |
+
      View the normalized impurity importance table using the helper function: 
      +\x off
+DROP TABLE IF EXISTS imp_output;
+SELECT madlib.get_var_importance('train_output','imp_output');
+SELECT * FROM imp_output ORDER BY impurity_var_importance DESC;
+
      + feature | impurity_var_importance
+---------+-------------------------
+ cyl     |        51.8593190075796
+ wt      |        31.8447271176382
+ disp    |        10.9769776775887
+ qsec    |        5.31897390566817
+ vs      |                       0
+
      3. +
    3. Predict regression output for the same data and compare with original: 
      +\x off
+DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.tree_predict('train_output',
+                           'mt_cars',
+                           'prediction_results',
+                           'response');
+SELECT s.id, mpg, estimated_mpg, mpg-estimated_mpg as delta
+FROM prediction_results p,
+mt_cars s WHERE s.id = p.id ORDER BY id;
+
      Result: 
      + id | mpg  |  estimated_mpg   |        delta
+----+------+------------------+---------------------
+  1 | 18.7 |            16.84 |                1.86
+  2 |   21 | 19.7428571428571 |    1.25714285714286
+  3 | 24.4 |            22.58 |                1.82
+  4 |   21 | 19.7428571428571 |    1.25714285714286
+  5 | 17.8 | 19.7428571428571 |   -1.94285714285714
+  6 | 16.4 |            16.84 |  -0.439999999999998
+  7 | 22.8 |            22.58 |   0.219999999999999
+  8 | 17.3 |           13.325 |               3.975
+  9 | 21.4 | 19.7428571428571 |    1.65714285714286
+ 10 | 15.2 |           13.325 |               1.875
+ 11 | 18.1 | 19.7428571428571 |   -1.64285714285714
+ 12 | 32.4 | 30.0666666666667 |    2.33333333333334
+ 13 | 14.3 |            14.78 |               -0.48
+ 14 | 22.8 |            22.58 |   0.219999999999999
+ 15 | 30.4 | 30.0666666666667 |   0.333333333333336
+ 16 | 19.2 | 19.7428571428571 |  -0.542857142857141
+ 17 | 33.9 | 30.0666666666667 |    3.83333333333334
+ 18 | 15.2 |            16.84 |               -1.64
+ 19 | 10.4 |           13.325 |              -2.925
+ 20 | 27.3 | 30.0666666666667 |   -2.76666666666666
+ 21 | 10.4 |           13.325 |              -2.925
+ 22 |   26 | 30.0666666666667 |   -4.06666666666666
+ 23 | 14.7 |            16.84 |               -2.14
+ 24 | 30.4 | 30.0666666666667 |   0.333333333333336
+ 25 | 21.5 |            22.58 |               -1.08
+ 26 | 15.8 |            14.78 |                1.02
+ 27 | 15.5 |            14.78 |   0.719999999999999
+ 28 |   15 |            14.78 |   0.219999999999999
+ 29 | 13.3 |            14.78 |               -1.48
+ 30 | 19.2 |            16.84 |                2.36
+ 31 | 19.7 | 19.7428571428571 | -0.0428571428571409
+ 32 | 21.4 |            22.58 |               -1.18
+(32 rows)
+
      4. +
    4. Display the decision tree in basic text format: 
      +SELECT madlib.tree_display('train_output', FALSE);
+
      +  -------------------------------------
+ - Each node represented by 'id' inside ().
+ - Each internal nodes has the split condition at the end, while each
+     leaf node has a * at the end.
+ - For each internal node (i), its child nodes are indented by 1 level
+     with ids (2i+1) for True node and (2i+2) for False node.
+ - Number of rows and average response value inside []. For a leaf node, this is the prediction.
+ -------------------------------------
+ (0)[32, 20.0906]  cyl in {4}
+    (1)[11, 26.6636]  wt <= 2.2
+       (3)[6, 30.0667]  *
+       (4)[5, 22.58]  *
+    (2)[21, 16.6476]  disp <= 258
+       (5)[7, 19.7429]  *
+       (6)[14, 15.1]  qsec <= 17.42
+          (13)[10, 15.81]  qsec <= 16.9
+             (27)[5, 14.78]  *
+             (28)[5, 16.84]  *
+          (14)[4, 13.325]  *
+  -------------------------------------
+(1 row)
+
      5. +
    5. Display the surrogate variables that are used to compute the split for each node when the primary variable is NULL: 
      +SELECT madlib.tree_surr_display('train_output');
+
      + -------------------------------------
+       Surrogates for internal nodes
+ -------------------------------------
+ (0) cyl in {4}
+      1: disp <= 146.7    [common rows = 29]
+      2: vs in {1}    [common rows = 26]
+      [Majority branch = 11 ]
+ (1) wt <= 2.2
+      [Majority branch = 19 ]
+ (2) disp <= 258
+      1: cyl in {4,6}    [common rows = 19]
+      2: vs in {1}    [common rows = 18]
+      [Majority branch = 7 ]
+ (6) qsec <= 17.42
+      1: disp > 275.8    [common rows = 11]
+      2: vs in {0}    [common rows = 10]
+      [Majority branch = 10 ]
+ (13) qsec <= 16.9
+      1: wt <= 3.84    [common rows = 8]
+      2: disp <= 360    [common rows = 7]
+      [Majority branch = 5 ]
+ -------------------------------------
+(1 row)
+
      Note
      The 'cyl' parameter in the data set has two tuples with NULL values (id = 9 and id = 18). In the prediction based on this tree, the surrogate splits for the cyl in {4} split in node 0 are used to predict those two tuples. The splits are used in descending order until a surrogate variable is found that is not NULL. In this case, the two tuples have non-NULL values for disp, hence the disp <= 146.7 split is used to make the prediction. If all the surrogate variables are NULL then the majority branch would be followed.
      +
      6. +
    6. Now let's use cross validation to select the best value of the complexity parameter cp: 
      +DROP TABLE IF EXISTS train_output, train_output_summary, train_output_cv;
+SELECT madlib.tree_train('mt_cars',         -- source table
+                         'train_output',    -- output model table
+                         'id',              -- id column
+                         'mpg',             -- dependent variable
+                         '*',               -- features
+                         'id, hp, drat, am, gear, carb',  -- exclude columns
+                         'mse',             -- split criterion
+                         NULL::text,        -- no grouping
+                         NULL::text,        -- no weights, all observations treated equally
+                         10,                -- max depth
+                         8,                 -- min split
+                         3,                 -- number of bins per continuous variable
+                         10,                -- number of splits
+                         'n_folds=3'       -- pruning parameters for cross validation
+                         );
+
      View the output table (excluding the tree which is in binary format). The input cp value was 0 (default) and the best 'pruning_cp' value turns out to be 0 as well in this small example: 
      +\x on
+SELECT pruning_cp, cat_levels_in_text, cat_n_levels, impurity_var_importance, tree_depth FROM train_output;
+
      +-[ RECORD 1 ]-----------+-----------------------------------------------------------------------
+pruning_cp              | 0
+cat_levels_in_text      | {0,1,4,6,8}
+cat_n_levels            | {2,3}
+impurity_var_importance | {0,22.6309172500677,4.79024943310653,2.32115,13.8967382920109}
+tree_depth              | 4
+
      The cp values tested and average error and standard deviation are: 
      +\x off
+SELECT * FROM train_output_cv ORDER BY cv_error_avg ASC;
+
      +         cp          |   cv_error_avg   | cv_error_stddev
+---------------------+------------------+------------------
+                   0 | 4.60222321567406 | 1.14990035501294
+ 0.00942145242026098 | 4.71906243157825 | 1.21587651168567
+  0.0156685263245236 | 4.86688342751006 | 1.30225133441406
+  0.0893348335770666 |  5.0608834230282 | 1.42488238861617
+   0.135752855572154 | 5.33192746100332 | 1.62718329150341
+   0.643125226048458 | 5.76814538295394 | 2.10750950120742
+(6 rows)
+

      NULL Handling Example

      +
      7. +
    +
      +
    1. Create toy example to illustrate 'null-as-category' handling for categorical features: 
      +DROP TABLE IF EXISTS null_handling_example;
+CREATE TABLE null_handling_example (
+    id integer,
+    country text,
+    city text,
+    weather text,
+    response text
+);
+INSERT INTO null_handling_example VALUES
+(1,null,null,null,'a'),
+(2,'US',null,null,'b'),
+(3,'US','NY',null,'c'),
+(4,'US','NY','rainy','d');
+
      2. +
    2. Train decision tree. Note that 'NULL' is set as a valid level for the categorical features country, weather and city: 
      +DROP TABLE IF EXISTS train_output, train_output_summary;
+SELECT madlib.tree_train('null_handling_example',         -- source table
+                         'train_output',                  -- output model table
+                         'id',                            -- id column
+                         'response',                      -- dependent variable
+                         'country, weather, city',        -- features
+                         NULL,                            -- features to exclude
+                         'gini',                          -- split criterion
+                         NULL::text,                      -- no grouping
+                         NULL::text,                      -- no weights, all observations treated equally
+                         4,                               -- max depth
+                         1,                               -- min split
+                         1,                               -- number of bins per continuous variable
+                         10,                              -- number of splits
+                         NULL,                            -- pruning parameters
+                         'null_as_category=true'          -- null handling
+                         );
+SELECT cat_levels_in_text, cat_n_levels FROM train_output;
+
      +            cat_levels_in_text            | cat_n_levels
+------------------------------------------+--------------
+ {US,__NULL__,rainy,__NULL__,NY,__NULL__} | {2,2,2}
+
      View the summary table: 
      +\x on
+SELECT * FROM train_output_summary;
+
      +-[ RECORD 1 ]---------------+-----------------------
+method                      | tree_train
+is_classification           | t
+source_table                | null_handling_example
+model_table                 | train_output
+id_col_name                 | id
+list_of_features            | country, weather, city
+list_of_features_to_exclude | None
+dependent_varname           | response
+independent_varnames        | country,weather,city
+cat_features                | country,weather,city
+con_features                |
+grouping_cols               | [NULL]
+num_all_groups              | 1
+num_failed_groups           | 0
+total_rows_processed        | 4
+total_rows_skipped          | 0
+dependent_var_levels        | "a","b","c","d"
+dependent_var_type          | text
+input_cp                    | 0
+independent_var_types       | text, text, text
+n_folds                     | 0
+null_proxy                  | __NULL__
+
      3. +
    3. Predict for data not previously seen by assuming NULL value as the default: 
      +\x off
+DROP TABLE IF EXISTS table_test;
+CREATE TABLE table_test (
+    id integer,
+    country text,
+    city text,
+    weather text,
+    expected_response text
+);
+INSERT INTO table_test VALUES
+(1,'IN','MUM','cloudy','a'),
+(2,'US','HOU','humid','b'),
+(3,'US','NY','sunny','c'),
+(4,'US','NY','rainy','d');
+ 
+DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.tree_predict('train_output',
+                           'table_test',
+                           'prediction_results',
+                           'response');
+SELECT s.id, expected_response, estimated_response
+FROM prediction_results p, table_test s
+WHERE s.id = p.id ORDER BY id;
+
      + id | expected_response | estimated_response
+----+-------------------+--------------------
+  1 | a                 | a
+  2 | b                 | b
+  3 | c                 | c
+  4 | d                 | d
+(4 rows)
+
      There is only training data for country 'US' so the response for country 'IN' is 'a', corresponding to a NULL (not 'US') country level. Likewise, any city in the 'US' that is not 'NY' will predict response 'b', corresponding to a NULL (not 'NY') city level.
      4. +
    4. Display the decision tree in basic text format: 
      +SELECT madlib.tree_display('train_output', FALSE);
+
      +  -------------------------------------
+ - Each node represented by 'id' inside ().
+ - Each internal nodes has the split condition at the end, while each
+     leaf node has a * at the end.
+ - For each internal node (i), its child nodes are indented by 1 level
+     with ids (2i+1) for True node and (2i+2) for False node.
+ - Number of rows and average response value inside []. For a leaf node, this is the prediction.
+ -------------------------------------
+  (0)[1 1 1 1]  city in {NY}
+    (1)[0 0 1 1]  weather in {rainy}
+       (3)[0 0 0 1]  * --> "d"
+       (4)[0 0 1 0]  * --> "c"
+    (2)[1 1 0 0]  country in {US}
+       (5)[0 1 0 0]  * --> "b"
+       (6)[1 0 0 0]  * --> "a"
+ -------------------------------------
+(1 row)
+
      5. +
    +

    Literature
    [1] Breiman, Leo; Friedman, J. H.; Olshen, R. A.; Stone, C. J. (1984). Classification and Regression Trees. Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software.
    +

    Related Topics
    +

    File decision_tree.sql_in documenting the training function

    +

    Random Forest

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__dense__linear__solver.html b/docs/docs/v2.1.0/group__grp__dense__linear__solver.html new file mode 100644 index 00000000..ee6f5a17 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__dense__linear__solver.html @@ -0,0 +1,253 @@ + + + + + + + + +MADlib: Dense Linear Systems + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Dense Linear Systems
    Utilities » Linear Solvers
    +
    +
    +
    Contents +

    The linear systems module implements solution methods for systems of consistent linear equations. Systems of linear equations take the form:

    +\[ Ax = b \] +

    +

    where \(x \in \mathbb{R}^{n}\), \(A \in \mathbb{R}^{m \times n} \) and \(b \in \mathbb{R}^{m}\). We assume that there are no rows of \(A\) where all elements are zero. The algorithms implemented in this module can handle large dense linear systems. Currently, the algorithms implemented in this module solve the linear system by a direct decomposition. Hence, these methods are known as direct method.

    +

    Solution Function
    +linear_solver_dense( tbl_source,
+                     tbl_result,
+                     row_id,
+                     LHS,
+                     RHS,
+                     grouping_col,
+                     optimizer,
+                     optimizer_params
+                   )
+
    Arguments
    +
    tbl_source
    +

    TEXT. The name of the table containing the training data. The input data is expected to be of the following form: 

    {TABLE|VIEW} sourceName (
+    ...
+    row_id          FLOAT8,
+    left_hand_side  FLOAT8[],
+    right_hand_side FLOAT8,
+    ...
+)

    Each row represents a single equation. The right_hand_side column refers to the right hand side of the equations while the left_hand_side column refers to the multipliers on the variables on the left hand side of the same equations.

    +

    +
    +
    tbl_result
    +

    TEXT. The name of the table where the output is saved. The output is stored in the table named by the tbl_result argument. It contains the following columns:

    + + + + + + +
    solution FLOAT8[]. The solution variables in the same order as that provided as input in the 'left_hand_side' column name of the source_table
    residual_norm FLOAT8. The scaled residual norm, defined as \( \frac{|Ax - b|}{|b|} \). This value is an indication of the accuracy of the solution.
    iters INTEGER. Number of iterations required by the algorithm (only applicable for iterative algorithms). The output is NULL for 'direct' methods.
    +

    +
    +
    row_id
    +

    TEXT. The name of the column storing the 'row id' of the equations.

    +

    For a system with N equations, the row_id's must be a continuous range of integers from \( 0 \ldots n-1 \).

    +

    +
    +
    LHS
    +

    TEXT. The name of the column storing the 'left hand side' of the equations, stored as an array.

    +

    +
    +
    RHS
    +

    TEXT. The name of the column storing the 'right hand side' of the equations.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. Group by column names. Not currently implemented. Any non-NULL value is ignored.
    +
    optimizer (optional)
    +

    TEXT, default: 'direct'. The type of optimizer.

    +

    +
    +
    optimizer_params (optional)
    +
    TEXT, default: NULL. Optimizer specific parameters.
    +
    +
    +

    Optimizer Parameters
    +

    For each optimizer, there are specific parameters that can be tuned for better performance.

    +
    +
    algorithm (default: householderqr)
    +

    There are several algorithms that can be classified as 'direct' methods of solving linear systems. MADlib dense linear system solvers provide various algorithmic options for users.

    +

    The following table provides a guideline on the choice of algorithm based on conditions on the A matrix, speed of the algorithms and numerical stability. 

     Algorithm            | Conditions on A  | Speed | Accuracy
+ ----------------------------------------------------------
+ householderqr        | None             |  ++   |  +
+ partialpivlu         | Invertable       |  ++   |  +
+ fullpivlu            | None             |  -    |  +++
+ colpivhouseholderqr  | None             |  +    |  ++
+ fullpivhouseholderqr | None             |  -    |  +++
+ llt                  | Pos. Definite    |  +++  |  +
+ ldlt                 | Pos. or Neg Def  |  +++  |  ++
+

    For speed '++' is faster than '+', which is faster than '-'. For accuracy '+++' is better than '++'.

    +

    More details about the individual algorithms can be found in the Eigen documentation. Eigen is an open source library for linear algebra.

    +
    +
    +

    Examples
    +
      +
    1. View online help for the linear systems solver function. 
      +SELECT madlib.linear_solver_dense();
+
      2. +
    2. Create the sample data set. 
      +CREATE TABLE linear_systems_test_data( id INTEGER NOT NULL,
+                                       lhs DOUBLE PRECISION[],
+                                       rhs DOUBLE PRECISION
+                                     );
+INSERT INTO linear_systems_test_data(id, lhs, rhs)
+       VALUES
+        (0, ARRAY[1,0,0], 20),
+        (1, ARRAY[0,1,0], 15),
+        (2, ARRAY[0,0,1], 20);
+
      3. +
    3. Solve the linear systems with default parameters. 
      +SELECT madlib.linear_solver_dense( 'linear_systems_test_data',
+                                   'output_table',
+                                   'id',
+                                   'lhs',
+                                   'rhs'
+                                 );
+
      4. +
    4. Obtain the output from the output table. 
      +\x on
+SELECT * FROM output_table;
+
      Result: 
      +--------------------+-------------------------------------
+solution            | {20,15,20}
+residual_norm       | 0
+iters               | NULL
+
      5. +
    5. Choose an algorithm different than the default. 
      +DROP TABLE IF EXISTS result_table;
+SELECT madlib.linear_solver_dense( 'linear_systems_test_data',
+                                   'result_table',
+                                   'id',
+                                   'lhs',
+                                   'rhs',
+                                   NULL,
+                                   'direct',
+                                   'algorithm=llt'
+                                 );
+
      6. +
    +

    Related Topics
    File dense_linear_systems.sql_in documenting the SQL functions
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__deprecated.html b/docs/docs/v2.1.0/group__grp__deprecated.html new file mode 100644 index 00000000..b6e5683f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__deprecated.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: Deprecated Modules + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Deprecated Modules
    +
    +
    +

    Detailed Description

    +

    Deprecated modules that will be removed in the next major version (2.0). There are newer MADlib modules that have replaced these functions.

    + + + + + + + + +

    +Modules

     Create Indicator Variables
     Provides utility functions helpful for data preparation before modeling.
     
     Multinomial Logistic Regression
     Also called as softmax regression, models the relationship between one or more independent variables and a categorical dependent variable.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__deprecated.js b/docs/docs/v2.1.0/group__grp__deprecated.js new file mode 100644 index 00000000..05ef03b1 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__deprecated.js @@ -0,0 +1,5 @@ +var group__grp__deprecated = +[ + [ "Create Indicator Variables", "group__grp__indicator.html", null ], + [ "Multinomial Logistic Regression", "group__grp__mlogreg.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__desc__stats.html b/docs/docs/v2.1.0/group__grp__desc__stats.html new file mode 100644 index 00000000..6f7787da --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__desc__stats.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: Descriptive Statistics + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Descriptive Statistics
    Statistics
    +
    +
    +

    Detailed Description

    +

    Methods to compute descriptive statistics of a dataset.

    + + + + + + + + + + + +

    +Modules

     Cardinality Estimators
     Methods to estimate the number of unique values contained in data.
     
     Covariance and Correlation
     Generates a covariance or Pearson correlation matrix for pairs of numeric columns in a table.
     
     Summary
     Calculates general descriptive statistics for any data table.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__desc__stats.js b/docs/docs/v2.1.0/group__grp__desc__stats.js new file mode 100644 index 00000000..d49a7aa4 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__desc__stats.js @@ -0,0 +1,6 @@ +var group__grp__desc__stats = +[ + [ "Cardinality Estimators", "group__grp__sketches.html", "group__grp__sketches" ], + [ "Covariance and Correlation", "group__grp__correlation.html", null ], + [ "Summary", "group__grp__summary.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__dl.html b/docs/docs/v2.1.0/group__grp__dl.html new file mode 100644 index 00000000..f46dd1bb --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__dl.html @@ -0,0 +1,145 @@ + + + + + + + + +MADlib: Deep Learning + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Deep Learning
    +
    +
    +

    Detailed Description

    +

    There are three main steps in order to run deep learning workloads with MADlib:

      +
    1. Preparation, which includes data preprocessing and model definition. Data preprocessing is required to format training data for use by frameworks like Keras and TensorFlow that support mini-batching as an optimization option. Model definition involves describing model architectures (and optionally custom functions) and loading them into tables.
      2. +
    2. Model training, either one model at a time or multiple models in parallel. In the latter case, you will need to define the configurations for the multiple models that you want to train - this can be done manually or in an automated way using autoML methods. The trained models can then be used for evaluation and inference.
      3. +
    +

    This flowchart shows the workflow in more detail:

    +
    +
    + + + + + + + + + + + + + + +

    +Modules

     Model Preparation
     Prepare models and data for deep learning.
     
     Train Single Model
     Fit, evaluate and predict for one model.
     
     Train Multiple Models
     Train multiple deep learning models at the same time for model architecture search and hyperparameter selection.
     
     Utilities for Deep Learning
     Utilities specific to deep learning workflows.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__dl.js b/docs/docs/v2.1.0/group__grp__dl.js new file mode 100644 index 00000000..998a0b74 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__dl.js @@ -0,0 +1,7 @@ +var group__grp__dl = +[ + [ "Model Preparation", "group__grp__model__prep.html", "group__grp__model__prep" ], + [ "Train Single Model", "group__grp__keras.html", null ], + [ "Train Multiple Models", "group__grp__model__selection.html", "group__grp__model__selection" ], + [ "Utilities for Deep Learning", "group__grp__dl__utilities.html", "group__grp__dl__utilities" ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__dl__utilities.html b/docs/docs/v2.1.0/group__grp__dl__utilities.html new file mode 100644 index 00000000..ec70e1c7 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__dl__utilities.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: Utilities for Deep Learning + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Utilities for Deep Learning
    Deep Learning
    +
    +
    +

    Detailed Description

    +

    Utilities specific to deep learning workflows.

    + + + + + +

    +Modules

     Show GPU Configuration
     Utility function to report number and type of GPUs in the database cluster.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__dl__utilities.js b/docs/docs/v2.1.0/group__grp__dl__utilities.js new file mode 100644 index 00000000..ba4c9b5f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__dl__utilities.js @@ -0,0 +1,4 @@ +var group__grp__dl__utilities = +[ + [ "Show GPU Configuration", "group__grp__gpu__configuration.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__early__stage.html b/docs/docs/v2.1.0/group__grp__early__stage.html new file mode 100644 index 00000000..e68e206c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__early__stage.html @@ -0,0 +1,142 @@ + + + + + + + + +MADlib: Early Stage Development + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Early Stage Development
    +
    +
    +

    Detailed Description

    +

    Implementations which are in an early stage of development. Interface and implementation are subject to change.

    + + + + + + + + + + + + + + + + + +

    +Modules

     Conjugate Gradient
     Finds the solution to the function \( \boldsymbol Ax = \boldsymbol b \), where \(A\) is a symmetric, positive-definite matrix and \(x\) and \( \boldsymbol b \) are vectors.
     
     DBSCAN
     Partitions a set of observations into clusters of arbitrary shape based on the density of nearby neighbors.
     
     Naive Bayes Classification
     Constructs a classification model from a dataset where each attribute independently contributes to the probability that a data point belongs to a category.
     
     Random Sampling
     Provides utility functions for sampling operations.
     
     XGBoost
     This module allows you to use SQL to build gradient boosted tree models designed in XGBoost [1].
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__early__stage.js b/docs/docs/v2.1.0/group__grp__early__stage.js new file mode 100644 index 00000000..edb60a14 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__early__stage.js @@ -0,0 +1,8 @@ +var group__grp__early__stage = +[ + [ "Conjugate Gradient", "group__grp__cg.html", null ], + [ "DBSCAN", "group__grp__dbscan.html", null ], + [ "Naive Bayes Classification", "group__grp__bayes.html", null ], + [ "Random Sampling", "group__grp__sample.html", null ], + [ "XGBoost", "group__grp__xgboost.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__elasticnet.html b/docs/docs/v2.1.0/group__grp__elasticnet.html new file mode 100644 index 00000000..9e1cb6d6 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__elasticnet.html @@ -0,0 +1,779 @@ + + + + + + + + +MADlib: Elastic Net Regularization + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
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    +
    Elastic Net Regularization
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    This module implements elastic net regularization [1] for linear and logistic regression. Regularization is a technique often used to prevent overfitting.

    +

    Training Function
    The training function has the following syntax: 
    +elastic_net_train( tbl_source,
+                   tbl_result,
+                   col_dep_var,
+                   col_ind_var,
+                   regress_family,
+                   alpha,
+                   lambda_value,
+                   standardize,
+                   grouping_col,
+                   optimizer,
+                   optimizer_params,
+                   excluded,
+                   max_iter,
+                   tolerance
+                 )
+
    +

    Arguments

    +
    tbl_source
    +

    TEXT. The name of the table containing the training data.

    +

    +
    +
    tbl_result
    +

    TEXT. Name of the output table containing output model. The output table produced by the elastic_net_train() function has the following columns:

    + + + + + + + + + + + + + + + + + + +
    regress_family The regression type: 'gaussian' or 'binomial'.
    features Array of features (independent variables) passed to the algorithm.
    features_selected Array of features selected by the algorithm.
    coef_nonzero Coefficients of the selected features.
    coef_all Coefficients of all features, both selected and unselected.
    intercept Intercept for the model.
    log_likelihood Log of the likelihood value produced by the algorithm.
    standardize BOOLEAN. If data has been normalized, will be set to TRUE.
    iteration_run The number of iterations executed.
    +

    +
    +
    col_dep_var
    +

    TEXT. An expression for the dependent variable.

    +
    Note
    Both col_dep_var and col_ind_var can be valid PostgreSQL expressions. For example, col_dep_var = 'log(y+1)', and col_ind_var = 'array[exp(x[1]), x[2], 1/(1+x[3])]'. In the binomial case, you can use a Boolean expression, for example, col_dep_var = 'y < 0'.
    +
    +
    col_ind_var
    +

    TEXT. An expression for the independent variables. Use '*' to specify all columns of tbl_source except those listed in the excluded string described below. If col_dep_var is a column name, it is automatically excluded from the independent variables. However, if col_dep_var is a valid PostgreSQL expression, any column names used within the expression are only excluded if they are explicitly listed in the excluded argument. Therefore, it is a good idea to add all column names involved in the dependent variable expression to the excluded string.

    +

    +
    +
    regress_family
    +

    TEXT. For regression type, specify either 'gaussian' ('linear') or 'binomial' ('logistic').

    +

    +
    +
    alpha
    +

    FLOAT8. Elastic net control parameter with a value in the range [0, 1]. A value of 1 means L1 regularization, and a value of 0 means L2 regularization.

    +

    +
    +
    lambda_value
    +

    FLOAT8. Regularization parameter (must be positive).

    +

    +
    +
    standardize (optional)
    +

    BOOLEAN, default: TRUE. Whether to normalize the data or not. Setting to TRUE usually yields better results and faster convergence.

    +

    +
    +
    grouping_col (optional)
    +

    TEXT, default: NULL. A single column or a list of comma-separated columns that divides the input data into discrete groups, resulting in one regression per group. When this value is NULL, no grouping is used and a single model is generated for all data.

    +
    Note
    Expressions are not currently supported for 'grouping_col'.
    +
    +
    optimizer (optional)
    +

    TEXT, default: 'fista'. Name of optimizer, either 'fista' or 'igd'. FISTA [2] is an algorithm with a fast global rate of convergence for solving linear inverse problems. Incremental gradient descent (IGD) is a stochastic approach to minimizing an objective function [4].

    +

    +
    +
    optimizer_params (optional)
    +

    TEXT, default: NULL. Optimizer parameters, delimited with commas. These parameters differ depending on the value of optimizer parameter. See the descriptions below for details.

    +

    +
    +
    excluded (optional)
    +

    TEXT, default: NULL. If the col_ind_var input is '*' then excluded can be provided as a comma-delimited list of column names that are to be excluded from the features. For example, 'col1, col2'. If the col_ind_var is an array, excluded must be a list of the integer array positions to exclude, for example '1,2'. If this argument is NULL or an empty string, no columns are excluded.

    +

    +
    +
    max_iter (optional)
    +

    INTEGER, default: 1000. The maximum number of iterations allowed.

    +

    +
    +
    tolerance (optional)
    +
    FLOAT8, default: 1e-6. This is the criterion to stop iterating. Both the 'fista' and 'igd' optimizers compute the difference between the log likelihood of two consecutive iterations, and when the difference is smaller than tolerance or the iteration number is larger than max_iter, the computation stops.
    +
    +

    Other Parameters
    +

    For optimizer_params, there are several parameters that can be supplied in a string containing a comma-delimited list of name-value pairs . All of these named parameters are optional and use the format "<param_name> = <value>".

    +

    The parameters described below are organized by category: warmup, cross validation and optimization.

    +

    Warmup parameters 

    +  $$
+    warmup = <value>,
+    warmup_lambdas = <value>,
+    warmup_lambda_no = <value>,
+    warmup_tolerance = <value>
+  $$
+
    +
    warmup
    +

    Default: FALSE. If warmup is TRUE, a series of strictly descending lambda values are used, which end with the lambda value that the user wants to calculate. A larger lambda gives a sparser solution, and the sparse solution is then used as the initial guess for the next lambda's solution, which can speed up the computation for the next lambda. For larger data sets, this can sometimes accelerate the whole computation and may in fact be faster than computation with only a single lambda value.

    +

    +
    +
    warmup_lambdas
    +

    Default: NULL. Set of lambda values to use when warmup is TRUE. The default is NULL, which means that lambda values will be automatically generated.

    +

    +
    +
    warmup_lambda_no
    +

    Default: 15. Number of lambda values used in warm-up. If warmup_lambdas is not NULL, this value is overridden by the number of provided lambda values.

    +

    +
    +
    warmup_tolerance
    +
    The value of tolerance used during warmup. The default value is the same as the tolerance argument described above.
    +
    +

    Cross validation parameters

    Note
    Please note that for performance reasons, warmup is disabled whenever cross validation is used. Also, cross validation is not supported if grouping is used.
    +
    +  $$
+    n_folds = <value>,
+    validation_result = <value>,
+    lambda_value = <value>,
+    n_lambdas = <value>,
+    alpha = <value>
+  $$
+

    Hyperparameter optimization can be carried out using the built-in cross validation mechanism, which is activated by assigning a value greater than 1 to the parameter n_folds.

    +

    The cross validation scores are the mean and standard deviation of the accuracy when predicted on the validation fold, averaged over all folds and all rows. For classification, the accuracy metric used is the ratio of correct classifications. For regression, the accuracy metric used is the negative of mean squared error (negative to make it a concave problem, thus selecting max means the highest accuracy). Cross validation scores are written out to a separate table with the user specified name given in the 'validation_result' parameter.

    +

    The values of a parameter to cross validate should be provided in a list. For example, to regularize with the L1 norm and use a lambda value from the set {0.3, 0.4, 0.5}, include 'lambda_value={0.3, 0.4, 0.5}'. Note that the use of '{}' and '[]' are both valid here.

    +
    +
    n_folds
    +

    Default: 0. Number of folds (k). Must be at least 2 to activate cross validation. If a value of k > 2 is specified, each fold is then used as a validation set once, while the other k - 1 folds form the training set.

    +

    +
    +
    validation_result
    +

    Default: NULL. Name of the table to store the cross validation results, including the values of parameters and their averaged error values. The table is only created if the name is not NULL.

    +

    +
    +
    lambda_value
    +

    Default: NULL. Set of regularization values to be used for cross validation. The default is NULL, which means that lambda values will be automatically generated.

    +

    +
    +
    n_lambdas
    +

    Default: 15. Number of lambdas to cross validate over. If a list of lambda values is not provided in the lambda_value set above, this parameter can be used to autogenerate the set of lambdas. If the lambda_value set is not NULL, this value is overridden by the number of provided lambda values.

    +
    Note
    If you want to cross validate over alpha only and not lambda, then set lambda_value to NULL and n_lambdas to 0. In this case, cross validation will be done on the set of alpha values specified in the next parameter. The lambda value used will be the one specified in the main function call at the top of this page.
    +
    +
    alpha
    +
    Elastic net control parameter. This is a list of values to apply cross validation on. (Note that alpha values are not autogenerated.) If not specified, the alpha value used will be the one specified in the main function call at the top of this page.
    +
    +

    Optimizer parameters

    +

    FISTA Parameters 

    +  $$
+    max_stepsize = <value>,
+    eta = <value>,
+    use_active_set = <value>,
+    activeset_tolerance = <value>,
+    random_stepsize = <value>
+  $$
+
    +
    max_stepsize
    +

    Default: 4.0. Initial backtracking step size. At each iteration, the algorithm first tries stepsize = max_stepsize, and if it does not work out, it then tries a smaller step size, stepsize = stepsize/eta, where eta must be larger than 1. At first glance, this seems to perform repeated iterations for even one step, but using a larger step size actually greatly increases the computation speed and minimizes the total number of iterations. A careful choice of max_stepsize can decrease the computation time by more than 10 times.

    +

    +
    +
    eta
    +

    Default: 2.0 If stepsize does not work, stepsize/eta is tried. Must be greater than 1.

    +

    +
    +
    use_active_set
    +

    Default: FALSE. If use_active_set is TRUE, an active-set method is used to speed up the computation. Considerable speedup is obtained by organizing the iterations around the active set of features—those with nonzero coefficients. After a complete cycle through all the variables, we iterate only on the active set until convergence. If another complete cycle does not change the active set, we are done. Otherwise, the process is repeated.

    +

    +
    +
    activeset_tolerance
    +

    The value of tolerance used during active set calculation. The default value is the same as the tolerance argument described above.

    +

    +
    +
    random_stepsize
    +
    Default: FALSE. Whether to add some randomness to the step size. Sometimes, this can speed up the calculation.
    +
    +

    IGD parameters 

    +  $$
+      stepsize = <value>,
+      step_decay = <value>,
+      threshold = <value>,
+      parallel = <value>
+  $$
+
    +
    stepsize
    +

    The default is 0.01.

    +

    +
    +
    step_decay
    +

    The actual stepsize used for current step is (previous stepsize) / exp(step_decay). The default value is 0, which means that a constant stepsize is used in IGD.

    +

    +
    +
    threshold
    +

    Default: 1e-10. When a coefficient is really small, set this coefficient to be 0.

    +

    Due to the stochastic nature of SGD, we can only obtain very small values for the fitting coefficients. Therefore, threshold is needed at the end of the computation to screen out tiny values and hard-set them to zeros. This is accomplished as follows: (1) multiply each coefficient with the standard deviation of the corresponding feature; (2) compute the average of absolute values of re-scaled coefficients; (3) divide each rescaled coefficient with the average, and if the resulting absolute value is smaller than threshold, set the original coefficient to zero.

    +

    +
    +
    parallel
    +

    Whether to run the computation on multiple segments. The default is TRUE.

    +

    SGD is a sequential algorithm in nature. When running in a distributed manner, each segment of the data runs its own SGD model and then the models are averaged to get a model for each iteration. This averaging might slow down the convergence speed, but it affords the ability to process large datasets on a cluster of machines. This algorithm, therefore, provides the parallel option to allow you to choose whether to do parallel computation.

    +
    +
    +

    Prediction Function
    +

    Per-Tuple Prediction

    +

    The prediction function returns a double value for the Gaussian family and a Boolean value for the Binomial family.

    +

    The predict function has the following syntax (elastic_net_gaussian_predict() and elastic_net_binomial_predict()): 

    +elastic_net_<family>_predict(
+                     coefficients,
+                     intercept,
+                     ind_var
+                   )
+

    Arguments

    +
    coefficients
    +
    DOUBLE PRECISION[]. Fitting coefficients, usually coef_all or coef_nonzero.
    +
    intercept
    +
    DOUBLE PRECISION. Intercept for the model.
    +
    ind_var
    +
    DOUBLE PRECISION[]. Independent variables that correspond to coefficients. Use features column in tbl_result for coef_all, and features_selected for coef_nonzero. See the examples for this case below.
    Note
    Unexpected results or errors may be returned in the case that this argument ind_var is not specified properly.
    +
    +
    +

    For the binomial family, there is a function (elastic_net_binomial_prob()) that outputs the probability of the instance being TRUE: 

    +elastic_net_binomial_prob(
+                     coefficients,
+                     intercept,
+                     ind_var
+                   )
+

    Per-Table Prediction

    +

    Alternatively, you can use another prediction function that stores the prediction result in a table (elastic_net_predict()). This is useful if you want to use elastic net together with the general cross validation function. 

    +elastic_net_predict( tbl_model,
+                     tbl_new_sourcedata,
+                     col_id,
+                     tbl_predict
+                   )
+

    Arguments

    +
    tbl_model
    +
    TEXT. Name of the table containing the output from the training function.
    +
    tbl_new_sourcedata
    +
    TEXT. Name of the table containing the new source data.
    +
    col_id
    +
    TEXT. Unique ID associated with each row.
    +
    tbl_predict
    +
    TEXT. Name of table to store the prediction result.
    +
    +

    You do not need to specify whether the model is "linear" or "logistic" because this information is already included in the tbl_model table.

    +

    Examples
    +
      +
    1. Display online help for the elastic_net_train() function: 
      +SELECT madlib.elastic_net_train();
+
      2. +
    2. Create an input data set of house prices and features: 
      +DROP TABLE IF EXISTS houses;
+CREATE TABLE houses ( id INT,
+                      tax INT,
+                      bedroom INT,
+                      bath FLOAT,
+                      price INT,
+                      size INT,
+                      lot INT,
+                      zipcode INT);
+INSERT INTO houses (id, tax, bedroom, bath, price, size, lot, zipcode) VALUES
+(1  ,  590 ,       2 ,    1 ,  50000 ,  770 , 22100  , 94301),
+(2  , 1050 ,       3 ,    2 ,  85000 , 1410 , 12000  , 94301),
+(3  ,   20 ,       3 ,    1 ,  22500 , 1060 ,  3500  , 94301),
+(4  ,  870 ,       2 ,    2 ,  90000 , 1300 , 17500  , 94301),
+(5  , 1320 ,       3 ,    2 , 133000 , 1500 , 30000  , 94301),
+(6  , 1350 ,       2 ,    1 ,  90500 ,  820 , 25700  , 94301),
+(7  , 2790 ,       3 ,  2.5 , 260000 , 2130 , 25000  , 94301),
+(8  ,  680 ,       2 ,    1 , 142500 , 1170 , 22000  , 94301),
+(9  , 1840 ,       3 ,    2 , 160000 , 1500 , 19000  , 94301),
+(10 , 3680 ,       4 ,    2 , 240000 , 2790 , 20000  , 94301),
+(11 , 1660 ,       3 ,    1 ,  87000 , 1030 , 17500  , 94301),
+(12 , 1620 ,       3 ,    2 , 118600 , 1250 , 20000  , 94301),
+(13 , 3100 ,       3 ,    2 , 140000 , 1760 , 38000  , 94301),
+(14 , 2070 ,       2 ,    3 , 148000 , 1550 , 14000  , 94301),
+(15 ,  650 ,       3 ,  1.5 ,  65000 , 1450 , 12000  , 94301),
+(16 ,  770 ,       2 ,    2 ,  91000 , 1300 , 17500  , 76010),
+(17 , 1220 ,       3 ,    2 , 132300 , 1500 , 30000  , 76010),
+(18 , 1150 ,       2 ,    1 ,  91100 ,  820 , 25700  , 76010),
+(19 , 2690 ,       3 ,  2.5 , 260011 , 2130 , 25000  , 76010),
+(20 ,  780 ,       2 ,    1 , 141800 , 1170 , 22000  , 76010),
+(21 , 1910 ,       3 ,    2 , 160900 , 1500 , 19000  , 76010),
+(22 , 3600 ,       4 ,    2 , 239000 , 2790 , 20000  , 76010),
+(23 , 1600 ,       3 ,    1 ,  81010 , 1030 , 17500  , 76010),
+(24 , 1590 ,       3 ,    2 , 117910 , 1250 , 20000  , 76010),
+(25 , 3200 ,       3 ,    2 , 141100 , 1760 , 38000  , 76010),
+(26 , 2270 ,       2 ,    3 , 148011 , 1550 , 14000  , 76010),
+(27 ,  750 ,       3 ,  1.5 ,  66000 , 1450 , 12000  , 76010);
+
      3. +
    3. Train the model: 
      +DROP TABLE IF EXISTS houses_en, houses_en_summary;
+SELECT madlib.elastic_net_train( 'houses',                  -- Source table
+                                 'houses_en',               -- Result table
+                                 'price',                   -- Dependent variable
+                                 'array[tax, bath, size]',  -- Independent variable
+                                 'gaussian',                -- Regression family
+                                 0.5,                       -- Alpha value
+                                 0.1,                       -- Lambda value
+                                 TRUE,                      -- Standardize
+                                 NULL,                      -- Grouping column(s)
+                                 'fista',                   -- Optimizer
+                                 '',                        -- Optimizer parameters
+                                 NULL,                      -- Excluded columns
+                                 100,                       -- Maximum iterations
+                                 1e-6                       -- Tolerance value
+                               );
+
      4. +
    4. View the resulting model: 
      +-- Turn on expanded display to make it easier to read results.
+\x on
+SELECT * FROM houses_en;
+
      Result: 
      +-[ RECORD 1 ]-----+-------------------------------------------
+family            | gaussian
+features          | {tax,bath,size}
+features_selected | {tax,bath,size}
+coef_nonzero      | {22.7898419099,10708.6395642,54.7864827154}
+coef_all          | {22.7898419099,10708.6395642,54.7864827154}
+intercept         | -7793.63839228
+log_likelihood    | -512248647.34
+standardize       | t
+iteration_run     | 100
+
      5. +
    5. Use the prediction function to evaluate residuals: 
      +\x off
+SELECT id, price, predict, price - predict AS residual
+FROM (
+    SELECT
+        houses.*,
+        madlib.elastic_net_gaussian_predict(
+            m.coef_all,             -- Coefficients
+            m.intercept,            -- Intercept
+            ARRAY[tax,bath,size]    -- Features (corresponding to coefficients)
+            ) AS predict
+    FROM houses, houses_en m) s
+ORDER BY id;
+
      Result: 
      + id | price  |     predict      |     residual
+----+--------+------------------+-------------------
+  1 |  50000 |  58546.599589619 |   -8546.599589619
+  2 |  85000 | 114801.915370229 |  -29801.915370229
+  3 |  22500 |  61444.469688442 |  -38944.469688442
+  4 |  90000 | 104673.230727753 |  -14673.230727753
+  5 | 133000 | 125885.956130288 |  7114.04386971201
+  6 |  90500 |  78606.203576913 |   11893.796423087
+  7 | 260000 | 199256.827630643 |   60743.172369357
+  8 | 142500 |   82512.27844767 |    59987.72155233
+  9 | 160000 | 137736.673923436 |   22263.326076564
+ 10 | 240000 | 250344.545740518 |  -10344.545740518
+ 11 |  87000 |  97176.215939216 |  -10176.215939216
+ 12 | 118600 | 119026.288024408 | -426.288024408001
+ 13 | 140000 | 180696.360235914 |  -40696.360235914
+ 14 | 148000 | 156426.301262683 |   -8426.301262683
+ 15 |  65000 | 102523.118132785 |  -37523.118132785
+ 16 |  91000 | 102394.246536763 |  -11394.246536763
+ 17 | 132300 | 123606.971939298 |    8693.028060702
+ 18 |  91100 |  74048.235194933 |   17051.764805067
+ 19 | 260011 | 196977.843439653 |   63033.156560347
+ 20 | 141800 |   84791.26263866 |    57008.73736134
+ 21 | 160900 | 139331.962857129 |   21568.037142871
+ 22 | 239000 | 248521.358387726 | -9521.35838772598
+ 23 |  81010 |  95808.825424622 |  -14798.825424622
+ 24 | 117910 | 118342.592767111 | -432.592767110997
+ 25 | 141100 | 182975.344426904 |  -41875.344426904
+ 26 | 148011 | 160984.269644663 |  -12973.269644663
+ 27 |  66000 | 104802.102323775 |  -38802.102323775
+
      6. +
    +

    Example with Grouping

    +
      +
    1. Reuse the houses table above and train the model by grouping on zip code: 
      +DROP TABLE IF EXISTS houses_en1, houses_en1_summary;
+SELECT madlib.elastic_net_train( 'houses',                  -- Source table
+                                 'houses_en1',              -- Result table
+                                 'price',                   -- Dependent variable
+                                 'array[tax, bath, size]',  -- Independent variable
+                                 'gaussian',                -- Regression family
+                                 0.5,                       -- Alpha value
+                                 0.1,                       -- Lambda value
+                                 TRUE,                      -- Standardize
+                                 'zipcode',                 -- Grouping column(s)
+                                 'fista',                   -- Optimizer
+                                 '',                        -- Optimizer parameters
+                                 NULL,                      -- Excluded columns
+                                 100,                       -- Maximum iterations
+                                 1e-6                       -- Tolerance value
+                               );
+
      2. +
    2. View the resulting model with a separate model for each group: 
      +-- Turn on expanded display to make it easier to read results.
+\x on
+SELECT * FROM houses_en1;
+
      Result: 
      +-[ RECORD 1 ]-----+--------------------------------------------
+zipcode           | 94301
+family            | gaussian
+features          | {tax,bath,size}
+features_selected | {tax,bath,size}
+coef_nonzero      | {27.6936321338,11508.8932488,49.0964826846}
+coef_all          | {27.6936321338,11508.8932488,49.0964826846}
+intercept         | -11146.6219839
+log_likelihood    | -520356660.297
+standardize       | t
+iteration_run     | 100
+-[ RECORD 2 ]-----+--------------------------------------------
+zipcode           | 76010
+family            | gaussian
+features          | {tax,bath,size}
+features_selected | {tax,bath,size}
+coef_nonzero      | {14.9934758192,9134.7157512,62.796927836}
+coef_all          | {14.9934758192,9134.7157512,62.796927836}
+intercept         | 27.0655065032
+log_likelihood    | -525632815.441
+standardize       | t
+iteration_run     | 100
+
      3. +
    3. Use the prediction function to evaluate residuals: 
      +\x off
+SELECT madlib.elastic_net_predict(
+                'houses_en1',             -- Model table
+                'houses',                 -- New source data table
+                'id',                     -- Unique ID associated with each row
+                'houses_en1_prediction'   -- Table to store prediction result
+              );
+SELECT  houses.id,
+        houses.price,
+        houses_en1_prediction.prediction,
+        houses.price - houses_en1_prediction.prediction AS residual
+FROM houses_en1_prediction, houses
+WHERE houses.id = houses_en1_prediction.id ORDER BY id;
+
      Result: 
      + id | price  |    prediction    |     residual
+----+--------+------------------+-------------------
+  1 |  50000 |  54505.805890984 | -4505.80589098399
+  2 |  85000 | 110175.518839476 |  -25175.518839476
+  3 |  22500 |  52958.415553252 |  -30458.415553252
+  4 |  90000 |  99790.051960086 | -9790.05196008601
+  5 | 133000 | 122071.482957216 |   10928.517042784
+  6 |  90500 |  78007.790446902 |   12492.209553098
+  7 | 260000 |   199466.3529096 |     60533.6470904
+  8 | 142500 |  76636.825856866 |   65863.174143134
+  9 | 160000 | 136472.171666792 |   23527.828333208
+ 10 | 240000 | 250762.917456118 |  -10762.917456118
+ 11 |  87000 |  96903.077772146 |   -9903.077772146
+ 12 | 118600 | 118105.451926206 |  494.548073793994
+ 13 | 140000 | 184131.233653376 |  -44131.233653376
+ 14 | 148000 | 156805.424440596 | -8805.42444059599
+ 15 |  65000 |   95307.47866894 |   -30307.47866894
+ 16 |  91000 | 111477.479576487 | -20477.4795764872
+ 17 | 132300 | 130783.929262327 |   1516.0707376728
+ 18 |  91100 | 77897.7592753032 |  13202.2407246968
+ 19 | 260011 | 196953.761128831 |  63057.2388711688
+ 20 | 141800 | 94329.0979647992 |  47470.9020352008
+ 21 | 160900 | 141129.427577575 |  19770.5724224248
+ 22 | 239000 | 247476.438620463 | -8476.43862046322
+ 23 |  81010 | 97832.1782395032 | -16822.1782395032
+ 24 | 117910 | 120632.283356431 |  -2722.2833564312
+ 25 | 141100 | 176798.212621703 | -35698.2126217032
+ 26 | 148011 | 158801.641015487 | -10790.6410154872
+ 27 |  66000 | 116029.791359903 | -50029.7913599032
+

      Example where coef_nonzero is different from coef_all

      +
      4. +
    +
      +
    1. Reuse the houses table above and train the model with alpha=1 (L1) and a large lambda value (30000). 
      +DROP TABLE IF EXISTS houses_en2, houses_en2_summary;
+SELECT madlib.elastic_net_train( 'houses',                  -- Source table
+                                 'houses_en2',              -- Result table
+                                 'price',                   -- Dependent variable
+                                 'array[tax, bath, size]',  -- Independent variable
+                                 'gaussian',                -- Regression family
+                                 1,                         -- Alpha value
+                                 30000,                     -- Lambda value
+                                 TRUE,                      -- Standardize
+                                 NULL,                      -- Grouping column(s)
+                                 'fista',                   -- Optimizer
+                                 '',                        -- Optimizer parameters
+                                 NULL,                      -- Excluded columns
+                                 1000,                     -- Maximum iterations
+                                 1e-6                       -- Tolerance value
+                               );
+
      2. +
    2. View the resulting model and see coef_nonzero is different from coef_all: 
      +-- Turn on expanded display to make it easier to read results.
+\x on
+SELECT * FROM houses_en2;
+
      Result: 
      +-[ RECORD 1 ]-----+--------------------------------
+family            | gaussian
+features          | {tax,bath,size}
+features_selected | {tax,size}
+coef_nonzero      | {6.94502439324,29.7183899065}
+coef_all          | {6.94502439324,0,29.7183899065}
+intercept         | 74442.858956
+log_likelihood    | -1635348583.9
+standardize       | t
+iteration_run     | 297
+
      3. +
    3. We can still use the prediction function with coef_all to evaluate residuals: 
      +\x off
+SELECT id, price, predict, price - predict AS residual
+FROM (
+    SELECT
+        houses.*,
+        madlib.elastic_net_gaussian_predict(
+            m.coef_all,                   -- All coefficients
+            m.intercept,                  -- Intercept
+            ARRAY[tax,bath,size]          -- All features
+            ) AS predict
+    FROM houses, houses_en2 m) s
+ORDER BY id;
+
      4. +
    4. We can speed up the prediction function with coef_nonzero to evaluate residuals. This requires the user to examine the feature_selected column in the result table to construct the correct set of independent variables to provide to the prediction function: 
      +\x off
+SELECT id, price, predict, price - predict AS residual
+FROM (
+    SELECT
+        houses.*,
+        madlib.elastic_net_gaussian_predict(
+            m.coef_nonzero,               -- Non-zero coefficients
+            m.intercept,                  -- Intercept
+            ARRAY[tax,size]               -- Features corresponding to non-zero coefficients
+            ) AS predict
+    FROM houses, houses_en2 m) s
+ORDER BY id;
+
      The two queries above will result in same residuals: 
      + id | price  |     predict      |     residual
+----+--------+------------------+-------------------
+  1 |  50000 | 101423.583576017 | -51423.5835760166
+  2 |  85000 | 123638.064337067 |  -38638.064337067
+  3 |  22500 | 106083.252744755 | -83583.2527447548
+  4 |  90000 | 119118.937056569 | -29118.9370565688
+  5 | 133000 | 128187.876014827 |  4812.12398517321
+  6 |  90500 | 108187.721610204 |  -17687.721610204
+  7 | 260000 | 157119.647513985 |  102880.352486015
+  8 | 142500 | 113935.991734008 |  28564.0082659918
+  9 | 160000 | 131799.288699312 |  28200.7113006884
+ 10 | 240000 | 182914.856562258 |  57085.1434377418
+ 11 |  87000 | 116581.541052473 | -29581.5410524734
+ 12 | 118600 | 122841.785856174 |  -4241.7858561738
+ 13 | 140000 | 148276.800810484 | -8276.80081048398
+ 14 | 148000 | 134882.563805082 |  13117.4361949182
+ 15 |  65000 | 122048.790176031 |  -57048.790176031
+ 16 |  91000 | 118424.434617245 | -27424.4346172448
+ 17 | 132300 | 127493.373575503 |   4806.6264244972
+ 18 |  91100 | 106798.716731556 |  -15698.716731556
+ 19 | 260011 | 156425.145074661 |  103585.854925339
+ 20 | 141800 | 114630.494173332 |  27169.5058266678
+ 21 | 160900 | 132285.440406838 |  28614.5595931616
+ 22 | 239000 | 182359.254610799 |   56640.745389201
+ 23 |  81010 | 116164.839588879 |  -35154.839588879
+ 24 | 117910 | 122633.435124377 |  -4723.4351243766
+ 25 | 141100 | 148971.303249808 |   -7871.303249808
+ 26 | 148011 |  136271.56868373 |  11739.4313162702
+ 27 |  66000 | 122743.292615355 |  -56743.292615355
+(27 rows)
+
      5. +
    +

    Example with Cross Validation

    +
      +
    1. Reuse the houses table above. Here we use 3-fold cross validation with 3 automatically generated lambda values and 3 specified alpha values. (This can take some time to run since elastic net is effectively being called 27 times for these combinations, then a 28th time for the whole dataset.) 
      +DROP TABLE IF EXISTS houses_en3, houses_en3_summary, houses_en3_cv;
+SELECT madlib.elastic_net_train( 'houses',                  -- Source table
+                                 'houses_en3',              -- Result table
+                                 'price',                   -- Dependent variable
+                                 'array[tax, bath, size]',  -- Independent variable
+                                 'gaussian',                -- Regression family
+                                 0.5,                       -- Alpha value
+                                 0.1,                       -- Lambda value
+                                 TRUE,                      -- Standardize
+                                 NULL,                      -- Grouping column(s)
+                                 'fista',                   -- Optimizer
+                                 $$ n_folds = 3,            -- Cross validation parameters
+                                    validation_result=houses_en3_cv,
+                                    n_lambdas = 3,
+                                    alpha = {0, 0.1, 1}
+                                 $$,
+                                 NULL,                      -- Excluded columns
+                                 200,                       -- Maximum iterations
+                                 1e-6                       -- Tolerance value
+                               );
+\x on
+SELECT * FROM houses_en3;
+
      +-[ RECORD 1 ]-----+--------------------------------------------
+family            | gaussian
+features          | {tax,bath,size}
+features_selected | {tax,bath,size}
+coef_nonzero      | {22.4584875792,11657.0840746,52.1622709646}
+coef_all          | {22.4584875792,11657.0840746,52.1622709646}
+intercept         | -5067.2628524
+log_likelihood    | -543193170.15
+standardize       | t
+iteration_run     | 200
+
      2. +
    2. Details of the cross validation: 
      +\x off
+SELECT * FROM houses_en3_cv ORDER BY mean_neg_loss DESC;
+
      + alpha | lambda_value |     mean_score     |   std_dev_score
+-------+--------------+--------------------+--------------------
+   0.0 |          0.1 | -36964.1349749     | 7006.24916542
+   0.1 |          0.1 | -37033.6458432     | 7094.45992609
+   1.0 |        100.0 | -38060.4537864     | 7891.42815774
+   1.0 |          0.1 | -38097.4491274     | 7957.27212821
+   0.1 |        100.0 | -58955.454086      | 12733.6947097
+   0.0 |        100.0 | -59062.3214246     | 12731.3011318
+   1.0 |     100000.0 | -60055.6624133     | 12708.5131797
+   0.1 |     100000.0 | {large neg number} | {large pos number}
+   0.0 |     100000.0 | {large neg number} | {large pos number}
+(9 rows)
+
      3. +
    +

    Note
    It is strongly recommended that you run elastic_net_train() on a subset of the data with a limited max_iter before applying it to the full data set with a large max_iter. In the pre-run, you can adjust the parameters to get the best performance and then apply the best set of parameters to the whole data set.
    +

    Technical Background
    +

    Elastic net regularization seeks to find a weight vector that, for any given training example set, minimizes:

    +\[\min_{w \in R^N} L(w) + \lambda \left(\frac{(1-\alpha)}{2} \|w\|_2^2 + \alpha \|w\|_1 \right)\] +

    +

    where \(L\) is the metric function that the user wants to minimize. Here \( \alpha \in [0,1] \) and \( lambda \geq 0 \). If \(alpha = 0\), we have the ridge regularization (known also as Tikhonov regularization), and if \(\alpha = 1\), we have the LASSO regularization.

    +

    For the Gaussian response family (or linear model), we have

    +\[L(\vec{w}) = \frac{1}{2}\left[\frac{1}{M} \sum_{m=1}^M (w^{t} x_m + w_{0} - y_m)^2 \right] \] +

    +

    For the Binomial response family (or logistic model), we have

    +\[ L(\vec{w}) = \sum_{m=1}^M\left[y_m \log\left(1 + e^{-(w_0 + \vec{w}\cdot\vec{x}_m)}\right) + (1-y_m) \log\left(1 + e^{w_0 + \vec{w}\cdot\vec{x}_m}\right)\right]\ , \] +

    +

    where \(y_m \in {0,1}\).

    +

    To get better convergence, one can rescale the value of each element of x

    +\[ x' \leftarrow \frac{x - \bar{x}}{\sigma_x} \] +

    +

    and for Gaussian case we also let

    +\[y' \leftarrow y - \bar{y} \] +

    +

    and then minimize with the regularization terms. At the end of the calculation, the orginal scales will be restored and an intercept term will be obtained at the same time as a by-product.

    +

    Note that fitting after scaling is not equivalent to directly fitting.

    +

    Literature
    +

    [1] Elastic net regularization, http://en.wikipedia.org/wiki/Elastic_net_regularization

    +

    [2] Beck, A. and M. Teboulle (2009), A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. on Imaging Sciences 2(1), 183-202.

    +

    [3] Shai Shalev-Shwartz and Ambuj Tewari, Stochastic Methods for L1 Regularized Loss Minimization. Proceedings of the 26th International Conference on Machine Learning, Montreal, Canada, 2009.

    +

    [4] Stochastic gradient descent, https://en.wikipedia.org/wiki/Stochastic_gradient_descent

    +

    Related Topics
    +

    File elastic_net.sql_in documenting the SQL functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__encode__categorical.html b/docs/docs/v2.1.0/group__grp__encode__categorical.html new file mode 100644 index 00000000..a0122d0a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__encode__categorical.html @@ -0,0 +1,684 @@ + + + + + + + + +MADlib: Encoding Categorical Variables + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Encoding Categorical Variables
    Data Types and Transformations
    +
    +
    +
    Contents +

    Coding Systems for Categorical Variables
    Categorical variables [1] require special attention in regression analysis because, unlike dichotomous or continuous variables, they cannot be entered into the regression equation just as they are. For example, if you have a variable called race that is coded with 1=Hispanic, 2=Asian, 3=Black, 4=White, then entering race in your regression will look at the linear effect of the race variable, which is probably not what you intended. Instead, categorical variables like this need to be coded into a series of indicator variables which can then be entered into the regression model. There are a variety of coding systems that can be used for coding categorical variables, including one-hot, dummy, effects, orthogonal, and Helmert.
    +

    We currently support one-hot and dummy coding techniques.

    +

    Dummy coding is used when a researcher wants to compare other groups of the predictor variable with one specific group of the predictor variable. Often, the specific group to compare with is called the reference group.

    +

    One-hot encoding is similar to dummy coding except it builds indicator (0/1) columns (cast as numeric) for each value of each category. Only one of these columns could take on the value 1 for each row (data point). There is no reference category for this function.

    +
    +encode_categorical_variables (
+        source_table,
+        output_table,
+        categorical_cols,
+        categorical_cols_to_exclude,    -- Optional
+        row_id,                         -- Optional
+        top,                            -- Optional
+        value_to_drop,                  -- Optional
+        encode_null,                    -- Optional
+        output_type,                    -- Optional
+        output_dictionary,              -- Optional
+        distributed_by                  -- Optional
+        )
+

    Arguments

    +
    source_table
    +

    VARCHAR. Name of the table containing the source categorical data to encode.

    +

    +
    +
    output_table
    +

    VARCHAR. Name of the result table.

    +
    Note
    If there are index columns in the 'source_table' specified by the parameter 'row_id' (see below), then the output table will contain only the index columns 'row_id' and the encoded columns. If the parameter 'row_id' is not specified, then all columns from the 'source_table', with the exception of the original columns that have been encoded, will be included in the 'output_table'.
    +
    +
    categorical_cols
    +

    VARCHAR. Comma-separated string of column names of categorical variables to encode. Can also be '*' meaning all columns are to be encoded, except the ones specified in 'categorical_cols_to_exclude' and 'row_id'. Please note that all Boolean, integer and text columns are considered categorical columns and will be encoded when ‘*’ is specified for this argument.

    +

    +
    +
    categorical_cols_to_exclude (optional)
    +

    VARCHAR. Comma-separated string of column names to exclude from the categorical variables to encode. Applicable only if 'categorical_cols' = '*'.

    +

    +
    +
    row_id (optional)
    +

    VARCHAR. Comma-separated column name(s) corresponding to the primary key(s) of the source table. This parameter determines the format of the 'output_table' as described above. If 'categorical_cols' = '*', these columns will be excluded from encoding (but will be included in the output table).

    +
    Note
    If you want to see both the raw categorical variable and its encoded form in the output_table, then include the categorical variable in the 'row_id' parameter. However, this will not work if you specify '*' for the parameter 'categorical_cols', because in this case 'row_id' columns will not be encoded at all.
    +
    +
    top (optional)
    +

    VARCHAR. default: NULL. If integer, encodes the top n values by frequency. If float in the range (0.0, 1.0), encodes the specified fraction of values by frequency (e.g., 0.1 means top 10%). Can be specified as a global for all categorical columns, or as a dictionary with separate 'top' values for each categorical variable. Set to NULL to encode all levels (values) for all categorical columns.

    +

    +
    +
    value_to_drop (optional)
    +

    VARCHAR. Default: NULL.

    +
      +
    • For dummy coding, indicate the desired value (reference) to drop for each categorical variable. Can be specified as a global for all categorical columns, or a comma-separated string containing items of the form 'name=value', where 'name' is the column name and 'value' is the reference value to be dropped.
      • +
    • Set to NULL for one-hot encoding (default)
      • +
    +
    Note
    If you specify both 'value_to_drop' and 'top' parameters, the 'value_to_drop' will be applied first (takes priority), then 'top' will be applied to the remaining values.
    +
    +
    encode_null (optional)
    +

    BOOLEAN. default: FALSE. Whether NULL should be treated as one of the values of the categorical variable. If TRUE, then an indicator variable is created corresponding to the NULL value. If FALSE, then all encoded values for that variable will be set to 0.

    +

    +
    +
    output_type (optional)
    +

    VARCHAR. default: 'column'. This parameter controls the output format of the indicator variables. If 'column', a column is created for each indicator variable. PostgreSQL limits the number of columns in a table. If the total number of indicator columns exceeds the limit, then make this parameter either 'array' to combine the indicator columns into an array or 'svec' to cast the array output to 'madlib.svec' type.

    +

    Since the array output for any single tuple would be sparse (only one non-zero entry for each categorical column), the 'svec' output would be most efficient for storage. The 'array' output is useful if the array is used for post-processing, including concatenating with other non-categorical features.

    +

    The order of the array is the same as specified in 'categorical_cols'. A dictionary will be created when 'output_type' is 'array' or 'svec' to define an index into the array. The dictionary table will be given the name of the 'output_table' appended by '_dictionary'.

    +

    +
    +
    output_dictionary (optional)
    +

    BOOLEAN. default: FALSE. This parameter is used to handle auto-generated column names that exceed the PostgreSQL limit of 63 bytes.

    +
      +
    • If TRUE, column names will include numerical IDs and will create a dictionary table called 'output_table_dictionary' ('output_table' appended with '_dictionary').
      • +
    • If FALSE, will auto-generate column names in the usual way unless the limit of 63 bytes will be exceeded. In this case, a dictionary output file will be created and a message given to the user.
      • +
    +

    +
    +
    distributed_by (optional)
    +

    VARCHAR. default: NULL. Columns to use for the distribution policy of the output table. When NULL, either 'row_id' is used as distribution policy (when provided), or else the distribution policy of 'source_table' will be used. This argument does not apply to PostgreSQL platforms.

    +
      +
    • NULL: By default, the distribution policy of the source_table will be used.
      • +
    • Comma-separated column names: Column(s) to be used for the distribution key.
      • +
    • RANDOMLY: Use random distribution policy (only if there does not exist a column named 'randomly').
      • +
    +

    +
    +
    +

    Examples
    +
      +
    1. Use a subset of the abalone dataset [2]: 
      +DROP TABLE IF EXISTS abalone;
+CREATE TABLE abalone (
+    id serial,
+    sex character varying,
+    length double precision,
+    diameter double precision,
+    height double precision,
+    rings int
+);
+INSERT INTO abalone (sex, length, diameter, height, rings) VALUES
+('M',    0.455,  0.365,  0.095,  15),
+('M',    0.35,   0.265,  0.09,   7),
+('F',    0.53,   0.42,   0.135,  9),
+('M',    0.44,   0.365,  0.125,  10),
+('I',    0.33,   0.255,  0.08,   7),
+('I',    0.425,  0.3,    0.095,  8),
+('F',    0.53,   0.415,  0.15,   20),
+('F',    0.545,  0.425,  0.125,  16),
+('M',    0.475,  0.37,   0.125,  9),
+(NULL,   0.55,   0.44,   0.15,   19),
+('F',    0.525,  0.38,   0.14,   14),
+('M',    0.43,   0.35,   0.11,   10),
+('M',    0.49,   0.38,   0.135,  11),
+('F',    0.535,  0.405,  0.145,  10),
+('F',    0.47,   0.355,  0.1,    10),
+('M',    0.5,    0.4,    0.13,   12),
+('I',    0.355,  0.28,   0.085,  7),
+('F',    0.44,   0.34,   0.1,    10),
+('M',    0.365,  0.295,  0.08,   7),
+(NULL,   0.45,   0.32,   0.1,    9);
+
      2. +
    2. Create new table with one-hot encoding. The column 'sex' is replaced by three columns encoding the values 'F', 'M' and 'I'. Null values are not encoded by default: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        'sex'                        -- Categorical columns
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      +  id | length | diameter | height | rings | sex_F | sex_I | sex_M
+----+--------+----------+--------+-------+-------+-------+-------
+  1 |  0.455 |    0.365 |  0.095 |    15 |     0 |     0 |     1
+  2 |   0.35 |    0.265 |   0.09 |     7 |     0 |     0 |     1
+  3 |   0.53 |     0.42 |  0.135 |     9 |     1 |     0 |     0
+  4 |   0.44 |    0.365 |  0.125 |    10 |     0 |     0 |     1
+  5 |   0.33 |    0.255 |   0.08 |     7 |     0 |     1 |     0
+  6 |  0.425 |      0.3 |  0.095 |     8 |     0 |     1 |     0
+  7 |   0.53 |    0.415 |   0.15 |    20 |     1 |     0 |     0
+  8 |  0.545 |    0.425 |  0.125 |    16 |     1 |     0 |     0
+  9 |  0.475 |     0.37 |  0.125 |     9 |     0 |     0 |     1
+ 10 |   0.55 |     0.44 |   0.15 |    19 |     0 |     0 |     0
+ 11 |  0.525 |     0.38 |   0.14 |    14 |     1 |     0 |     0
+ 12 |   0.43 |     0.35 |   0.11 |    10 |     0 |     0 |     1
+ 13 |   0.49 |     0.38 |  0.135 |    11 |     0 |     0 |     1
+ 14 |  0.535 |    0.405 |  0.145 |    10 |     1 |     0 |     0
+ 15 |   0.47 |    0.355 |    0.1 |    10 |     1 |     0 |     0
+ 16 |    0.5 |      0.4 |   0.13 |    12 |     0 |     0 |     1
+ 17 |  0.355 |     0.28 |  0.085 |     7 |     0 |     1 |     0
+ 18 |   0.44 |     0.34 |    0.1 |    10 |     1 |     0 |     0
+ 19 |  0.365 |    0.295 |   0.08 |     7 |     0 |     0 |     1
+ 20 |   0.45 |     0.32 |    0.1 |     9 |     0 |     0 |     0
+(20 rows)
+
      3. +
    3. Now include NULL values in encoding (note the additional column 'sex_null'): 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        'sex',                       -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        NULL,                        -- Index columns
+        NULL,                        -- Top values
+        NULL,                        -- Value to drop for dummy encoding
+        TRUE                         -- Encode nulls
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | length | diameter | height | rings | sex_F | sex_I | sex_M | sex_null
+----+--------+----------+--------+-------+-------+-------+-------+----------
+  1 |  0.455 |    0.365 |  0.095 |    15 |     0 |     0 |     1 |        0
+  2 |   0.35 |    0.265 |   0.09 |     7 |     0 |     0 |     1 |        0
+  3 |   0.53 |     0.42 |  0.135 |     9 |     1 |     0 |     0 |        0
+  4 |   0.44 |    0.365 |  0.125 |    10 |     0 |     0 |     1 |        0
+  5 |   0.33 |    0.255 |   0.08 |     7 |     0 |     1 |     0 |        0
+  6 |  0.425 |      0.3 |  0.095 |     8 |     0 |     1 |     0 |        0
+  7 |   0.53 |    0.415 |   0.15 |    20 |     1 |     0 |     0 |        0
+  8 |  0.545 |    0.425 |  0.125 |    16 |     1 |     0 |     0 |        0
+  9 |  0.475 |     0.37 |  0.125 |     9 |     0 |     0 |     1 |        0
+ 10 |   0.55 |     0.44 |   0.15 |    19 |     0 |     0 |     0 |        1
+ 11 |  0.525 |     0.38 |   0.14 |    14 |     1 |     0 |     0 |        0
+ 12 |   0.43 |     0.35 |   0.11 |    10 |     0 |     0 |     1 |        0
+ 13 |   0.49 |     0.38 |  0.135 |    11 |     0 |     0 |     1 |        0
+ 14 |  0.535 |    0.405 |  0.145 |    10 |     1 |     0 |     0 |        0
+ 15 |   0.47 |    0.355 |    0.1 |    10 |     1 |     0 |     0 |        0
+ 16 |    0.5 |      0.4 |   0.13 |    12 |     0 |     0 |     1 |        0
+ 17 |  0.355 |     0.28 |  0.085 |     7 |     0 |     1 |     0 |        0
+ 18 |   0.44 |     0.34 |    0.1 |    10 |     1 |     0 |     0 |        0
+ 19 |  0.365 |    0.295 |   0.08 |     7 |     0 |     0 |     1 |        0
+ 20 |   0.45 |     0.32 |    0.1 |     9 |     0 |     0 |     0 |        1
+(20 rows)
+
      4. +
    4. Encode all categorical variables in the source table. Also, specify the column 'id' as the index (primary key) which changes the output table to include only the index and the encoded variables: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        '*',                         -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        'id'                         -- Index columns
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | sex_F | sex_I | sex_M | rings_7 | rings_8 | rings_9 | rings_10 | rings_11 | rings_12 | rings_14 | rings_15 | rings_16 | rings_19 | rings_20
+----+-------+-------+-------+---------+---------+---------+----------+----------+----------+----------+----------+----------+----------+----------
+  1 |     0 |     0 |     1 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        1 |        0 |        0 |        0
+  2 |     0 |     0 |     1 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  3 |     1 |     0 |     0 |       0 |       0 |       1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  4 |     0 |     0 |     1 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  5 |     0 |     1 |     0 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  6 |     0 |     1 |     0 |       0 |       1 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  7 |     1 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        1
+  8 |     1 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        1 |        0 |        0
+  9 |     0 |     0 |     1 |       0 |       0 |       1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 10 |     0 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        1 |        0
+ 11 |     1 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        1 |        0 |        0 |        0 |        0
+ 12 |     0 |     0 |     1 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 13 |     0 |     0 |     1 |       0 |       0 |       0 |        0 |        1 |        0 |        0 |        0 |        0 |        0 |        0
+ 14 |     1 |     0 |     0 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 15 |     1 |     0 |     0 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 16 |     0 |     0 |     1 |       0 |       0 |       0 |        0 |        0 |        1 |        0 |        0 |        0 |        0 |        0
+ 17 |     0 |     1 |     0 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 18 |     1 |     0 |     0 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 19 |     0 |     0 |     1 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 20 |     0 |     0 |     0 |       0 |       0 |       1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+(20 rows)
+
      5. +
    5. Now let's encode only the top values and group others into a miscellaneous bucket column. Top values can be global across all columns or specified by column. As an example of the latter, here are the top 2 'sex' values and the top 50% of 'rings' values: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        '*',                         -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        'id',                        -- Index columns
+        'sex=2, rings=0.5'           -- Top values
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | sex_M | sex_F | sex__misc__ | rings_10 | rings_7 | rings_9 | rings__misc__
+----+-------+-------+-------------+----------+---------+---------+---------------
+  1 |     1 |     0 |           0 |        0 |       0 |       0 |             1
+  2 |     1 |     0 |           0 |        0 |       1 |       0 |             0
+  3 |     0 |     1 |           0 |        0 |       0 |       1 |             0
+  4 |     1 |     0 |           0 |        1 |       0 |       0 |             0
+  5 |     0 |     0 |           1 |        0 |       1 |       0 |             0
+  6 |     0 |     0 |           1 |        0 |       0 |       0 |             1
+  7 |     0 |     1 |           0 |        0 |       0 |       0 |             1
+  8 |     0 |     1 |           0 |        0 |       0 |       0 |             1
+  9 |     1 |     0 |           0 |        0 |       0 |       1 |             0
+ 10 |     0 |     0 |           0 |        0 |       0 |       0 |             1
+ 11 |     0 |     1 |           0 |        0 |       0 |       0 |             1
+ 12 |     1 |     0 |           0 |        1 |       0 |       0 |             0
+ 13 |     1 |     0 |           0 |        0 |       0 |       0 |             1
+ 14 |     0 |     1 |           0 |        1 |       0 |       0 |             0
+ 15 |     0 |     1 |           0 |        1 |       0 |       0 |             0
+ 16 |     1 |     0 |           0 |        0 |       0 |       0 |             1
+ 17 |     0 |     0 |           1 |        0 |       1 |       0 |             0
+ 18 |     0 |     1 |           0 |        1 |       0 |       0 |             0
+ 19 |     1 |     0 |           0 |        0 |       1 |       0 |             0
+ 20 |     0 |     0 |           0 |        0 |       0 |       1 |             0
+(20 rows)
+
      6. +
    6. If you want to see both the raw categorical variable and its encoded form in the output_table, then include the categorical variable(s) in the index parameter. (Remember that this will not work if you specify '*' for the parameter 'categorical_cols', because in this case 'row_id' columns will not be encoded at all.) 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        'sex, rings',                -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        'id, sex, rings'             -- Index columns
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | sex | rings | sex_F | sex_I | sex_M | rings_7 | rings_8 | rings_9 | rings_10 | rings_11 | rings_12 | rings_14 | rings_15 | rings_16 | rings_19 | rings_20
+----+-----+-------+-------+-------+-------+---------+---------+---------+----------+----------+----------+----------+----------+----------+----------+----------
+  1 | M   |    15 |     0 |     0 |     1 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        1 |        0 |        0 |        0
+  2 | M   |     7 |     0 |     0 |     1 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  3 | F   |     9 |     1 |     0 |     0 |       0 |       0 |       1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  4 | M   |    10 |     0 |     0 |     1 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  5 | I   |     7 |     0 |     1 |     0 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  6 | I   |     8 |     0 |     1 |     0 |       0 |       1 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+  7 | F   |    20 |     1 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        1
+  8 | F   |    16 |     1 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        1 |        0 |        0
+  9 | M   |     9 |     0 |     0 |     1 |       0 |       0 |       1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 10 |     |    19 |     0 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        1 |        0
+ 11 | F   |    14 |     1 |     0 |     0 |       0 |       0 |       0 |        0 |        0 |        0 |        1 |        0 |        0 |        0 |        0
+ 12 | M   |    10 |     0 |     0 |     1 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 13 | M   |    11 |     0 |     0 |     1 |       0 |       0 |       0 |        0 |        1 |        0 |        0 |        0 |        0 |        0 |        0
+ 14 | F   |    10 |     1 |     0 |     0 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 15 | F   |    10 |     1 |     0 |     0 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 16 | M   |    12 |     0 |     0 |     1 |       0 |       0 |       0 |        0 |        0 |        1 |        0 |        0 |        0 |        0 |        0
+ 17 | I   |     7 |     0 |     1 |     0 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 18 | F   |    10 |     1 |     0 |     0 |       0 |       0 |       0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 19 | M   |     7 |     0 |     0 |     1 |       1 |       0 |       0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+ 20 |     |     9 |     0 |     0 |     0 |       0 |       0 |       1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0
+(20 rows)
+
      7. +
    7. For dummy encoding, let's make the 'I' value from the 'sex' variable as the reference. Here we use the 'value_to_drop' parameter: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        '*',                         -- Categorical columns
+        'rings',                     -- Categorical columns to exclude
+        'id',                        -- Index columns
+        NULL,                        -- Top value
+        'sex=I'                      -- Value to drop for dummy encoding
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      +  id | sex_F | sex_M
+----+-------+-------
+  1 |     0 |     1
+  2 |     0 |     1
+  3 |     1 |     0
+  4 |     0 |     1
+  5 |     0 |     0
+  6 |     0 |     0
+  7 |     1 |     0
+  8 |     1 |     0
+  9 |     0 |     1
+ 10 |     0 |     0
+ 11 |     1 |     0
+ 12 |     0 |     1
+ 13 |     0 |     1
+ 14 |     1 |     0
+ 15 |     1 |     0
+ 16 |     0 |     1
+ 17 |     0 |     0
+ 18 |     1 |     0
+ 19 |     0 |     1
+ 20 |     0 |     0
+(20 rows)
+
      8. +
    8. Create an array output for the two categorical variables in the source table: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        '*',                         -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        'id',                        -- Index columns
+        NULL,                        -- Top values
+        NULL,                        -- Value to drop for dummy encoding
+        NULL,                        -- Encode nulls
+        'array'                      -- Array output type
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id |     __encoded_variables__
+----+-------------------------------
+  1 | {0,0,1,0,0,0,0,0,0,0,1,0,0,0}
+  2 | {0,0,1,1,0,0,0,0,0,0,0,0,0,0}
+  3 | {1,0,0,0,0,1,0,0,0,0,0,0,0,0}
+  4 | {0,0,1,0,0,0,1,0,0,0,0,0,0,0}
+  5 | {0,1,0,1,0,0,0,0,0,0,0,0,0,0}
+  6 | {0,1,0,0,1,0,0,0,0,0,0,0,0,0}
+  7 | {1,0,0,0,0,0,0,0,0,0,0,0,0,1}
+  8 | {1,0,0,0,0,0,0,0,0,0,0,1,0,0}
+  9 | {0,0,1,0,0,1,0,0,0,0,0,0,0,0}
+ 10 | {0,0,0,0,0,0,0,0,0,0,0,0,1,0}
+ 11 | {1,0,0,0,0,0,0,0,0,1,0,0,0,0}
+ 12 | {0,0,1,0,0,0,1,0,0,0,0,0,0,0}
+ 13 | {0,0,1,0,0,0,0,1,0,0,0,0,0,0}
+ 14 | {1,0,0,0,0,0,1,0,0,0,0,0,0,0}
+ 15 | {1,0,0,0,0,0,1,0,0,0,0,0,0,0}
+ 16 | {0,0,1,0,0,0,0,0,1,0,0,0,0,0}
+ 17 | {0,1,0,1,0,0,0,0,0,0,0,0,0,0}
+ 18 | {1,0,0,0,0,0,1,0,0,0,0,0,0,0}
+ 19 | {0,0,1,1,0,0,0,0,0,0,0,0,0,0}
+ 20 | {0,0,0,0,0,1,0,0,0,0,0,0,0,0}
+(20 rows)
+
      View the dictionary table that gives the index into the array: 
      +SELECT * FROM abalone_out_dictionary;
+
      +  encoded_column_name  | index | variable | value
+-----------------------+-------+----------+-------
+ __encoded_variables__ |     1 | sex      | F
+ __encoded_variables__ |     2 | sex      | I
+ __encoded_variables__ |     3 | sex      | M
+ __encoded_variables__ |     4 | rings    | 7
+ __encoded_variables__ |     5 | rings    | 8
+ __encoded_variables__ |     6 | rings    | 9
+ __encoded_variables__ |     7 | rings    | 10
+ __encoded_variables__ |     8 | rings    | 11
+ __encoded_variables__ |     9 | rings    | 12
+ __encoded_variables__ |    10 | rings    | 14
+ __encoded_variables__ |    11 | rings    | 15
+ __encoded_variables__ |    12 | rings    | 16
+ __encoded_variables__ |    13 | rings    | 19
+ __encoded_variables__ |    14 | rings    | 20
+(14 rows)
+
      9. +
    9. Create a dictionary output: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        '*',                         -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        'id',                        -- Index columns
+        NULL,                        -- Top values
+        NULL,                        -- Value to drop for dummy encoding
+        NULL,                        -- Encode nulls
+        NULL,                        -- Output type
+        TRUE                         -- Dictionary output
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | sex_1 | sex_2 | sex_3 | rings_1 | rings_2 | rings_3 | rings_4 | rings_5 | rings_6 | rings_7 | rings_8 | rings_9 | rings_10 | rings_11
+----+-------+-------+-------+---------+---------+---------+---------+---------+---------+---------+---------+---------+----------+----------
+  1 |     0 |     0 |     1 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       1 |       0 |        0 |        0
+  2 |     0 |     0 |     1 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+  3 |     1 |     0 |     0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+  4 |     0 |     0 |     1 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+  5 |     0 |     1 |     0 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+  6 |     0 |     1 |     0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+  7 |     1 |     0 |     0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        1
+  8 |     1 |     0 |     0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       1 |        0 |        0
+  9 |     0 |     0 |     1 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 10 |     0 |     0 |     0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        1 |        0
+ 11 |     1 |     0 |     0 |       0 |       0 |       0 |       0 |       0 |       0 |       1 |       0 |       0 |        0 |        0
+ 12 |     0 |     0 |     1 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 13 |     0 |     0 |     1 |       0 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |        0 |        0
+ 14 |     1 |     0 |     0 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 15 |     1 |     0 |     0 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 16 |     0 |     0 |     1 |       0 |       0 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |        0 |        0
+ 17 |     0 |     1 |     0 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 18 |     1 |     0 |     0 |       0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 19 |     0 |     0 |     1 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+ 20 |     0 |     0 |     0 |       0 |       0 |       1 |       0 |       0 |       0 |       0 |       0 |       0 |        0 |        0
+(20 rows)
+
      View the dictionary table that defines the numerical columns in the output table: 
      +SELECT * FROM abalone_out_dictionary ORDER BY encoded_column_name;
+
      + encoded_column_name | index | variable | value
+---------------------+-------+----------+-------
+ "rings_1"           |     1 | rings    | 7
+ "rings_10"          |    10 | rings    | 19
+ "rings_11"          |    11 | rings    | 20
+ "rings_2"           |     2 | rings    | 8
+ "rings_3"           |     3 | rings    | 9
+ "rings_4"           |     4 | rings    | 10
+ "rings_5"           |     5 | rings    | 11
+ "rings_6"           |     6 | rings    | 12
+ "rings_7"           |     7 | rings    | 14
+ "rings_8"           |     8 | rings    | 15
+ "rings_9"           |     9 | rings    | 16
+ "sex_1"             |     1 | sex      | F
+ "sex_2"             |     2 | sex      | I
+ "sex_3"             |     3 | sex      | M
+(14 rows)
+
      10. +
    10. We can chose from various distribution policies of the output table, for examply RANDOMLY: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        '*',                         -- Categorical columns
+        NULL,                        -- Categorical columns to exclude
+        'id',                        -- Index columns
+        NULL,                        -- Top values
+        NULL,                        -- Value to drop for dummy encoding
+        NULL,                        -- Encode nulls
+        NULL,                        -- Output type
+        NULL,                        -- Dictionary output
+        'RANDOMLY'                   -- Distribution policy
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | sex_F | sex_I | sex_M | rings_10 | rings_11 | rings_12 | rings_14 | rings_15 | rings_16 | rings_19 | rings_20 | rings_7 | rings_8 | rings_9
+----+-------+-------+-------+----------+----------+----------+----------+----------+----------+----------+----------+---------+---------+---------
+  1 |     0 |     0 |     1 |        0 |        0 |        0 |        0 |        1 |        0 |        0 |        0 |       0 |       0 |       0
+  2 |     0 |     0 |     1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       1 |       0 |       0
+  3 |     1 |     0 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       1
+  4 |     0 |     0 |     1 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+  5 |     0 |     1 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       1 |       0 |       0
+  6 |     0 |     1 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       1 |       0
+  7 |     1 |     0 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        1 |       0 |       0 |       0
+  8 |     1 |     0 |     0 |        0 |        0 |        0 |        0 |        0 |        1 |        0 |        0 |       0 |       0 |       0
+  9 |     0 |     0 |     1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       1
+ 10 |     0 |     0 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        1 |        0 |       0 |       0 |       0
+ 11 |     1 |     0 |     0 |        0 |        0 |        0 |        1 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 12 |     0 |     0 |     1 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 13 |     0 |     0 |     1 |        0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 14 |     1 |     0 |     0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 15 |     1 |     0 |     0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 16 |     0 |     0 |     1 |        0 |        0 |        1 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 17 |     0 |     1 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       1 |       0 |       0
+ 18 |     1 |     0 |     0 |        1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       0
+ 19 |     0 |     0 |     1 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       1 |       0 |       0
+ 20 |     0 |     0 |     0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |        0 |       0 |       0 |       1
+(20 rows)
+
      11. +
    11. If you have a reason to encode FLOAT variables, you can cast them as TEXT in the following way within the function call: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        'height::TEXT'               -- Categorical columns
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      +id | sex | length | diameter | height | rings | height::TEXT_0.08 | height::TEXT_0.085 | height::TEXT_0.09 | height::TEXT_0.095 | height::TEXT_0.1 | height::TEXT_0.11 | height::TEXT_0.125 | height::TEXT_0.13 | height::TEXT_0.135 | height::TEXT_0.14 | height::TEXT_0.145 | height::TEXT_0.15
+----+-----+--------+----------+--------+-------+-------------------+--------------------+-------------------+--------------------+------------------+-------------------+--------------------+-------------------+--------------------+-------------------+--------------------+-------------------
+  1 | M   |  0.455 |    0.365 |  0.095 |    15 |                 0 |                  0 |                 0 |                  1 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+  2 | M   |   0.35 |    0.265 |   0.09 |     7 |                 0 |                  0 |                 1 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+  3 | F   |   0.53 |     0.42 |  0.135 |     9 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  1 |                 0 |                  0 |                 0
+  4 | M   |   0.44 |    0.365 |  0.125 |    10 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  1 |                 0 |                  0 |                 0 |                  0 |                 0
+  5 | I   |   0.33 |    0.255 |   0.08 |     7 |                 1 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+  6 | I   |  0.425 |      0.3 |  0.095 |     8 |                 0 |                  0 |                 0 |                  1 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+  7 | F   |   0.53 |    0.415 |   0.15 |    20 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 1
+  8 | F   |  0.545 |    0.425 |  0.125 |    16 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  1 |                 0 |                  0 |                 0 |                  0 |                 0
+  9 | M   |  0.475 |     0.37 |  0.125 |     9 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  1 |                 0 |                  0 |                 0 |                  0 |                 0
+ 10 |     |   0.55 |     0.44 |   0.15 |    19 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 1
+ 11 | F   |  0.525 |     0.38 |   0.14 |    14 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 1 |                  0 |                 0
+ 12 | M   |   0.43 |     0.35 |   0.11 |    10 |                 0 |                  0 |                 0 |                  0 |                0 |                 1 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+ 13 | M   |   0.49 |     0.38 |  0.135 |    11 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  1 |                 0 |                  0 |                 0
+ 14 | F   |  0.535 |    0.405 |  0.145 |    10 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  1 |                 0
+ 15 | F   |   0.47 |    0.355 |    0.1 |    10 |                 0 |                  0 |                 0 |                  0 |                1 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+ 16 | M   |    0.5 |      0.4 |   0.13 |    12 |                 0 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 1 |                  0 |                 0 |                  0 |                 0
+ 17 | I   |  0.355 |     0.28 |  0.085 |     7 |                 0 |                  1 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+ 18 | F   |   0.44 |     0.34 |    0.1 |    10 |                 0 |                  0 |                 0 |                  0 |                1 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+ 19 | M   |  0.365 |    0.295 |   0.08 |     7 |                 1 |                  0 |                 0 |                  0 |                0 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+ 20 |     |   0.45 |     0.32 |    0.1 |     9 |                 0 |                  0 |                 0 |                  0 |                1 |                 0 |                  0 |                 0 |                  0 |                 0 |                  0 |                 0
+(20 rows)
+
      12. +
    12. You can also use a logical expression in the categorical columns, which will be passed as boolean, and in the output table there will be two columns with name logical_expression_true and logical_expression_false: 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_dictionary;
+SELECT madlib.encode_categorical_variables (
+        'abalone',                   -- Source table
+        'abalone_out',               -- Output table
+        'height>.10'                 -- Categorical columns
+        );
+SELECT * FROM abalone_out ORDER BY id;
+
      + id | sex | length | diameter | height | rings | height>.10_false | height>.10_true
+----+-----+--------+----------+--------+-------+------------------+-----------------
+  1 | M   |  0.455 |    0.365 |  0.095 |    15 |                1 |               0
+  2 | M   |   0.35 |    0.265 |   0.09 |     7 |                1 |               0
+  3 | F   |   0.53 |     0.42 |  0.135 |     9 |                0 |               1
+  4 | M   |   0.44 |    0.365 |  0.125 |    10 |                0 |               1
+  5 | I   |   0.33 |    0.255 |   0.08 |     7 |                1 |               0
+  6 | I   |  0.425 |      0.3 |  0.095 |     8 |                1 |               0
+  7 | F   |   0.53 |    0.415 |   0.15 |    20 |                0 |               1
+  8 | F   |  0.545 |    0.425 |  0.125 |    16 |                0 |               1
+  9 | M   |  0.475 |     0.37 |  0.125 |     9 |                0 |               1
+ 10 |     |   0.55 |     0.44 |   0.15 |    19 |                0 |               1
+ 11 | F   |  0.525 |     0.38 |   0.14 |    14 |                0 |               1
+ 12 | M   |   0.43 |     0.35 |   0.11 |    10 |                0 |               1
+ 13 | M   |   0.49 |     0.38 |  0.135 |    11 |                0 |               1
+ 14 | F   |  0.535 |    0.405 |  0.145 |    10 |                0 |               1
+ 15 | F   |   0.47 |    0.355 |    0.1 |    10 |                1 |               0
+ 16 | M   |    0.5 |      0.4 |   0.13 |    12 |                0 |               1
+ 17 | I   |  0.355 |     0.28 |  0.085 |     7 |                1 |               0
+ 18 | F   |   0.44 |     0.34 |    0.1 |    10 |                1 |               0
+ 19 | M   |  0.365 |    0.295 |   0.08 |     7 |                1 |               0
+ 20 |     |   0.45 |     0.32 |    0.1 |     9 |                1 |               0
+(20 rows)
+
      13. +
    +

    Literature
    +

    [1] https://en.wikipedia.org/wiki/Categorical_variable

    +

    [2] https://archive.ics.uci.edu/ml/datasets/Abalone

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__fmsketch.html b/docs/docs/v2.1.0/group__grp__fmsketch.html new file mode 100644 index 00000000..6c01563d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__fmsketch.html @@ -0,0 +1,158 @@ + + + + + + + + +MADlib: FM (Flajolet-Martin) + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    FM (Flajolet-Martin)
    Statistics » Descriptive Statistics » Cardinality Estimators
    +
    +
    +
    Contents +

    fmsketch_dcount can be run on a column of any type. It returns an approximation to the number of distinct values (a la COUNT(DISTINCT x)), but faster and approximate. Like any aggregate, it can be combined with a GROUP BY clause to do distinct counts per group.

    +

    Syntax
    +

    Get the number of distinct values in a designated column. 

    +fmsketch_dcount( col_name )
+
    Note
    This is a User Defined Aggregate which returns the results when used in a query. Use "CREATE TABLE AS ", with the UDA as subquery if the results are to be stored. This is unlike the usual MADlib stored procedure interface which places the results in a table instead of returning it.
    +

    Examples
      +
    1. Generate some data. 
      +CREATE TABLE data(class INT, a1 INT);
+INSERT INTO data SELECT 1,1 FROM generate_series(1,10000);
+INSERT INTO data SELECT 1,2 FROM generate_series(1,15000);
+INSERT INTO data SELECT 1,3 FROM generate_series(1,10000);
+INSERT INTO data SELECT 2,5 FROM generate_series(1,1000);
+INSERT INTO data SELECT 2,6 FROM generate_series(1,1000);
+
      2. +
    2. Find the distinct number of values for each class. 
      +SELECT class, fmsketch_dcount(a1)
+FROM data
+GROUP BY data.class;
+
      Result: 
      +class | fmsketch_dcount
+ ------+-----------------
+    2 |               2
+    1 |               3
+(2 rows)
+
      3. +
    +
    +

    Literature
    [1] P. Flajolet and N.G. Martin. Probabilistic counting algorithms for data base applications, Journal of Computer and System Sciences 31(2), pp 182-209, 1985. http://algo.inria.fr/flajolet/Publications/FlMa85.pdf
    +

    Related Topics
    File sketch.sql_in documenting the SQL function.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__glm.html b/docs/docs/v2.1.0/group__grp__glm.html new file mode 100644 index 00000000..21817c5f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__glm.html @@ -0,0 +1,574 @@ + + + + + + + + +MADlib: Generalized Linear Models + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Generalized Linear Models
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    Generalized linear models extends ordinary linear regression by allowing the response variable to follow a more general set of distributions (rather than simply Gaussian distributions), and for a general family of functions of the response variable (the link function) to vary linearly with the predicted values (rather than assuming that the response itself must vary linearly).

    +

    For example, data of counts would typically be modeled with a Poisson distribution and a log link, while binary outcomes would typically be modeled with a Bernoulli distribution (or binomial distribution, depending on exactly how the problem is phrased) and a log-odds (or logit) link function.

    +

    Currently, the implemented distribution families are

    + + + + + + + + + + + + +
    Distribution Family Link Functions
    Binomial logit, probit
    Gamma inverse, identity, log
    Gaussian identity, inverse, log
    Inverse Gaussian inverse of square, inverse, identity, log
    Poisson log, identity, square-root
    +
    +

    Training Function
    GLM training function has the following format: 
    +glm(source_table,
+    model_table,
+    dependent_varname,
+    independent_varname,
+    family_params,
+    grouping_col,
+    optim_params,
+    verbose
+    )
+
    Arguments
    +
    source_table
    +

    TEXT. The name of the table containing the training data.

    +

    +
    +
    model_table
    +

    TEXT. Name of the generated table containing the model.

    +

    The model table produced by glm contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + +
    <...>

    Text. Grouping columns, if provided in input. This could be multiple columns depending on the grouping_col input.

    +

    +
    coef

    FLOAT8. Vector of the coefficients in linear predictor.

    +

    +
    log_likelihood

    FLOAT8. The log-likelihood \( l(\boldsymbol \beta) \). We use the maximum likelihood estimate of dispersion parameter to calculate the log-likelihood while R and Python use deviance estimate and Pearson estimate respectively.

    +

    +
    std_err

    FLOAT8[]. Vector of the standard error of the coefficients.

    +

    +
    z_stats or t_stats

    FLOAT8[]. Vector of the z-statistics (in Poisson distribtuion and Binomial distribution) or the t-statistics (in all other distributions) of the coefficients.

    +

    +
    p_values

    FLOAT8[]. Vector of the p-values of the coefficients.

    +

    +
    dispersion

    FLOAT8. The dispersion value (Pearson estimate). When family=poisson or family=binomial, the dispersion is always 1.

    +

    +
    num_rows_processed

    BIGINT. Numbers of rows processed.

    +

    +
    num_rows_skipped

    BIGINT. Numbers of rows skipped due to missing values or failures.

    +

    +
    num_iterations INTEGER. The number of iterations actually completed. This would be different from the nIterations argument if a tolerance parameter is provided and the algorithm converges before all iterations are completed.
    +

    A summary table named <model_table>_summary is also created at the same time, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + +
    method

    'glm'

    +

    +
    source_table

    The data source table name.

    +

    +
    model_table

    The model table name.

    +

    +
    dependent_varname

    The dependent variable.

    +

    +
    independent_varname

    The independent variables

    +

    +
    family_params

    A string that contains family parameters, and has the form of 'family=..., link=...'

    +

    +
    grouping_col

    Name of grouping columns.

    +

    +
    optimizer_params

    A string that contains optimizer parameters, and has the form of 'optimizer=..., max_iter=..., tolerance=...'

    +

    +
    num_all_groups

    Number of groups in glm training.

    +

    +
    num_failed_groups

    Number of failed groups in glm training.

    +

    +
    total_rows_processed

    BIGINT. Total numbers of rows processed in all groups.

    +

    +
    total_rows_skipped

    BIGINT. Total numbers of rows skipped in all groups due to missing values or failures.

    +

    +
    +

    +
    +
    dependent_varname
    +

    TEXT. Name of the dependent variable column.

    +

    +
    +
    independent_varname
    +

    TEXT. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list.

    +

    +
    +
    family_params (optional)
    +

    TEXT, Parameters for distribution family. Currently, we support

    +

    (1) family=poisson and link=[log or identity or sqrt].

    +

    (2) family=gaussian and link=[identity or log or inverse]. And when family=gaussian and link=identity, the GLM model is exactly the same as the linear regression.

    +

    (3) family=gamma and link=[inverse or identity or log].

    +

    (4) family=inverse_gaussian and link=[sqr_inverse or log or identity or inverse].

    +

    (5) family=binomial and link=[probit or logit].

    +

    +
    +
    grouping_col (optional)
    +

    TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated.

    +

    +
    +
    optim_params (optional)
    +

    TEXT, default: 'max_iter=100,optimizer=irls,tolerance=1e-6'. Parameters for optimizer. Currently, we support tolerance=[tolerance for relative error between log-likelihoods], max_iter=[maximum iterations to run], optimizer=irls.

    +

    +
    +
    verbose (optional)
    +
    BOOLEAN, default: FALSE. Provides verbose output of the results of training.
    +
    +
    +
    Note
    For p-values, we just return the computation result directly. Other statistical packages, like 'R', produce the same result, but on printing the result to screen, another format function is used and any p-value that is smaller than the machine epsilon (the smallest positive floating-point number 'x' such that '1 + x != 1') will be printed on screen as "< xxx" (xxx is the value of the machine epsilon). Although the results may look different, they are in fact the same.
    +

    Prediction Function
    The prediction function is provided to estimate the conditional mean given a new predictor. It has the following syntax: 
    +glm_predict(coef,
+            col_ind_var
+            link)
+
    +

    Arguments

    +
    coef
    +

    DOUBLE PRECISION[]. Model coefficients obtained from glm().

    +

    +
    +
    col_ind_var
    +

    New predictor, as a DOUBLE array. This should be the same length as the array obtained by evaluation of the 'independent_varname' argument in glm().

    +

    +
    +
    link
    +
    link function, as a string. This should match the link function the user inputted in glm().
    +
    +

    Examples
      +
    1. Create the training data table. 
      +CREATE TABLE warpbreaks(
+    id      serial,
+    breaks  integer,
+    wool    char(1),
+    tension char(1)
+);
+INSERT INTO warpbreaks(breaks, wool, tension) VALUES
+(26, 'A', 'L'),
+(30, 'A', 'L'),
+(54, 'A', 'L'),
+(25, 'A', 'L'),
+(70, 'A', 'L'),
+(52, 'A', 'L'),
+(51, 'A', 'L'),
+(26, 'A', 'L'),
+(67, 'A', 'L'),
+(18, 'A', 'M'),
+(21, 'A', 'M'),
+(29, 'A', 'M'),
+(17, 'A', 'M'),
+(12, 'A', 'M'),
+(18, 'A', 'M'),
+(35, 'A', 'M'),
+(30, 'A', 'M'),
+(36, 'A', 'M'),
+(36, 'A', 'H'),
+(21, 'A', 'H'),
+(24, 'A', 'H'),
+(18, 'A', 'H'),
+(10, 'A', 'H'),
+(43, 'A', 'H'),
+(28, 'A', 'H'),
+(15, 'A', 'H'),
+(26, 'A', 'H'),
+(27, 'B', 'L'),
+(14, 'B', 'L'),
+(29, 'B', 'L'),
+(19, 'B', 'L'),
+(29, 'B', 'L'),
+(31, 'B', 'L'),
+(41, 'B', 'L'),
+(20, 'B', 'L'),
+(44, 'B', 'L'),
+(42, 'B', 'M'),
+(26, 'B', 'M'),
+(19, 'B', 'M'),
+(16, 'B', 'M'),
+(39, 'B', 'M'),
+(28, 'B', 'M'),
+(21, 'B', 'M'),
+(39, 'B', 'M'),
+(29, 'B', 'M'),
+(20, 'B', 'H'),
+(21, 'B', 'H'),
+(24, 'B', 'H'),
+(17, 'B', 'H'),
+(13, 'B', 'H'),
+(15, 'B', 'H'),
+(15, 'B', 'H'),
+(16, 'B', 'H'),
+(28, 'B', 'H');
+SELECT create_indicator_variables('warpbreaks', 'warpbreaks_dummy', 'wool,tension');
+
      2. +
    2. Train a GLM model. 
      +DROP TABLE IF EXISTS glm_model, glm_model_summary;
+SELECT glm('warpbreaks_dummy',
+           'glm_model',
+           'breaks',
+           'ARRAY[1.0,"wool_B","tension_M", "tension_H"]',
+           'family=poisson, link=log');
+
      3. +
    3. View the regression results. 
      +-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM glm_model;
+
      Result: 
      +coef               | {3.69196314494079,-0.205988442638621,-0.321320431600611,-0.51848849651156}
+log_likelihood     | -242.527983208979
+std_err            | {0.04541079434248,0.0515712427835191,0.0602659166951256,0.0639595193956924}
+z_stats            | {81.3014438174473,-3.99425011926316,-5.3317106786264,-8.10651020224019}
+p_values           | {0,6.48993254938271e-05,9.72918600322907e-08,5.20943463005751e-16}
+num_rows_processed | 54
+num_rows_skipped   | 0
+iteration          | 5
+
      Alternatively, unnest the arrays in the results for easier reading of output: 
      +\x off
+SELECT unnest(coef) as coefficient,
+       unnest(std_err) as standard_error,
+       unnest(z_stats) as z_stat,
+       unnest(p_values) as pvalue
+FROM glm_model;
+
      4. +
    4. Predicting dependent variable using GLM model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) 
      +\x off
+-- Display predicted mean value on the original dataset
+SELECT
+    w.id,
+    madlib.glm_predict(
+        coef,
+        ARRAY[1, "wool_B", "tension_M", "tension_H"]::float8[],
+        'log') AS mu
+FROM warpbreaks_dummy w, glm_model m
+ORDER BY w.id;
+
      +-- Display predicted counts (which are predicted mean values rounded to the nearest integral value) on the original dataset
+SELECT
+    w.id,
+    madlib.glm_predict_poisson(
+        coef,
+        ARRAY[1, "wool_B", "tension_M", "tension_H"]::float8[],
+        'log') AS poisson_count
+FROM warpbreaks_dummy w, glm_model m
+ORDER BY w.id;
+
      5. +
    +
    +

    Example for Gaussian family:

    +
      +
    1. Create a testing data table 
      +CREATE TABLE abalone (
+    id integer,
+    sex text,
+    length double precision,
+    diameter double precision,
+    height double precision,
+    whole double precision,
+    shucked double precision,
+    viscera double precision,
+    shell double precision,
+    rings integer
+);
+INSERT INTO abalone VALUES
+(3151, 'F', 0.655000000000000027, 0.505000000000000004, 0.165000000000000008, 1.36699999999999999, 0.583500000000000019, 0.351499999999999979, 0.396000000000000019, 10),
+(2026, 'F', 0.550000000000000044, 0.469999999999999973, 0.149999999999999994, 0.920499999999999985, 0.381000000000000005, 0.243499999999999994, 0.267500000000000016, 10),
+(3751, 'I', 0.434999999999999998, 0.375, 0.110000000000000001, 0.41549999999999998, 0.170000000000000012, 0.0759999999999999981, 0.14499999999999999, 8),
+(720, 'I', 0.149999999999999994, 0.100000000000000006, 0.0250000000000000014, 0.0149999999999999994, 0.00449999999999999966, 0.00400000000000000008, 0.0050000000000000001, 2),
+(1635, 'F', 0.574999999999999956, 0.469999999999999973, 0.154999999999999999, 1.1160000000000001, 0.509000000000000008, 0.237999999999999989, 0.340000000000000024, 10),
+(2648, 'I', 0.5, 0.390000000000000013, 0.125, 0.582999999999999963, 0.293999999999999984, 0.132000000000000006, 0.160500000000000004, 8),
+(1796, 'F', 0.57999999999999996, 0.429999999999999993, 0.170000000000000012, 1.47999999999999998, 0.65349999999999997, 0.32400000000000001, 0.41549999999999998, 10),
+(209, 'F', 0.525000000000000022, 0.41499999999999998, 0.170000000000000012, 0.832500000000000018, 0.275500000000000023, 0.168500000000000011, 0.309999999999999998, 13),
+(1451, 'I', 0.455000000000000016, 0.33500000000000002, 0.135000000000000009, 0.501000000000000001, 0.274000000000000021, 0.0995000000000000051, 0.106499999999999997, 7),
+(1108, 'I', 0.510000000000000009, 0.380000000000000004, 0.115000000000000005, 0.515499999999999958, 0.214999999999999997, 0.113500000000000004, 0.166000000000000009, 8),
+(3675, 'F', 0.594999999999999973, 0.450000000000000011, 0.165000000000000008, 1.08099999999999996, 0.489999999999999991, 0.252500000000000002, 0.279000000000000026, 12),
+(2108, 'F', 0.675000000000000044, 0.550000000000000044, 0.179999999999999993, 1.68849999999999989, 0.562000000000000055, 0.370499999999999996, 0.599999999999999978, 15),
+(3312, 'F', 0.479999999999999982, 0.380000000000000004, 0.135000000000000009, 0.507000000000000006, 0.191500000000000004, 0.13650000000000001, 0.154999999999999999, 12),
+(882, 'M', 0.655000000000000027, 0.520000000000000018, 0.165000000000000008, 1.40949999999999998, 0.585999999999999965, 0.290999999999999981, 0.405000000000000027, 9),
+(3402, 'M', 0.479999999999999982, 0.395000000000000018, 0.149999999999999994, 0.681499999999999995, 0.214499999999999996, 0.140500000000000014, 0.2495, 18),
+(829, 'I', 0.409999999999999976, 0.325000000000000011, 0.100000000000000006, 0.394000000000000017, 0.20799999999999999, 0.0655000000000000027, 0.105999999999999997, 6),
+(1305, 'M', 0.535000000000000031, 0.434999999999999998, 0.149999999999999994, 0.716999999999999971, 0.347499999999999976, 0.14449999999999999, 0.194000000000000006, 9),
+(3613, 'M', 0.599999999999999978, 0.46000000000000002, 0.179999999999999993, 1.1399999999999999, 0.422999999999999987, 0.257500000000000007, 0.364999999999999991, 10),
+(1068, 'I', 0.340000000000000024, 0.265000000000000013, 0.0800000000000000017, 0.201500000000000012, 0.0899999999999999967, 0.0475000000000000006, 0.0550000000000000003, 5),
+(2446, 'M', 0.5, 0.380000000000000004, 0.135000000000000009, 0.583500000000000019, 0.22950000000000001, 0.126500000000000001, 0.179999999999999993, 12),
+(1393, 'M', 0.635000000000000009, 0.474999999999999978, 0.170000000000000012, 1.19350000000000001, 0.520499999999999963, 0.269500000000000017, 0.366499999999999992, 10),
+(359, 'M', 0.744999999999999996, 0.584999999999999964, 0.214999999999999997, 2.49900000000000011, 0.92649999999999999, 0.471999999999999975, 0.699999999999999956, 17),
+(549, 'F', 0.564999999999999947, 0.450000000000000011, 0.160000000000000003, 0.79500000000000004, 0.360499999999999987, 0.155499999999999999, 0.23000000000000001, 12),
+(1154, 'F', 0.599999999999999978, 0.474999999999999978, 0.160000000000000003, 1.02649999999999997, 0.484999999999999987, 0.2495, 0.256500000000000006, 9),
+(1790, 'F', 0.54500000000000004, 0.385000000000000009, 0.149999999999999994, 1.11850000000000005, 0.542499999999999982, 0.244499999999999995, 0.284499999999999975, 9),
+(3703, 'F', 0.665000000000000036, 0.540000000000000036, 0.195000000000000007, 1.76400000000000001, 0.850500000000000034, 0.361499999999999988, 0.469999999999999973, 11),
+(1962, 'F', 0.655000000000000027, 0.515000000000000013, 0.179999999999999993, 1.41199999999999992, 0.619500000000000051, 0.248499999999999999, 0.496999999999999997, 11),
+(1665, 'I', 0.604999999999999982, 0.469999999999999973, 0.14499999999999999, 0.802499999999999991, 0.379000000000000004, 0.226500000000000007, 0.220000000000000001, 9),
+(635, 'M', 0.359999999999999987, 0.294999999999999984, 0.100000000000000006, 0.210499999999999993, 0.0660000000000000031, 0.0524999999999999981, 0.0749999999999999972, 9),
+(3901, 'M', 0.445000000000000007, 0.344999999999999973, 0.140000000000000013, 0.475999999999999979, 0.205499999999999988, 0.101500000000000007, 0.108499999999999999, 15),
+(2734, 'I', 0.41499999999999998, 0.33500000000000002, 0.100000000000000006, 0.357999999999999985, 0.169000000000000011, 0.067000000000000004, 0.104999999999999996, 7),
+(3856, 'M', 0.409999999999999976, 0.33500000000000002, 0.115000000000000005, 0.440500000000000003, 0.190000000000000002, 0.0850000000000000061, 0.135000000000000009, 8),
+(827, 'I', 0.395000000000000018, 0.28999999999999998, 0.0950000000000000011, 0.303999999999999992, 0.127000000000000002, 0.0840000000000000052, 0.076999999999999999, 6),
+(3381, 'I', 0.190000000000000002, 0.130000000000000004, 0.0449999999999999983, 0.0264999999999999993, 0.00899999999999999932, 0.0050000000000000001, 0.00899999999999999932, 5),
+(3972, 'I', 0.400000000000000022, 0.294999999999999984, 0.0950000000000000011, 0.252000000000000002, 0.110500000000000001, 0.0575000000000000025, 0.0660000000000000031, 6),
+(1155, 'M', 0.599999999999999978, 0.455000000000000016, 0.170000000000000012, 1.1915, 0.695999999999999952, 0.239499999999999991, 0.239999999999999991, 8),
+(3467, 'M', 0.640000000000000013, 0.5, 0.170000000000000012, 1.4544999999999999, 0.642000000000000015, 0.357499999999999984, 0.353999999999999981, 9),
+(2433, 'F', 0.609999999999999987, 0.484999999999999987, 0.165000000000000008, 1.08699999999999997, 0.425499999999999989, 0.232000000000000012, 0.380000000000000004, 11),
+(552, 'I', 0.614999999999999991, 0.489999999999999991, 0.154999999999999999, 0.988500000000000045, 0.41449999999999998, 0.195000000000000007, 0.344999999999999973, 13),
+(1425, 'F', 0.729999999999999982, 0.57999999999999996, 0.190000000000000002, 1.73750000000000004, 0.678499999999999992, 0.434499999999999997, 0.520000000000000018, 11),
+(2402, 'F', 0.584999999999999964, 0.41499999999999998, 0.154999999999999999, 0.69850000000000001, 0.299999999999999989, 0.145999999999999991, 0.195000000000000007, 12),
+(1748, 'F', 0.699999999999999956, 0.535000000000000031, 0.174999999999999989, 1.77299999999999991, 0.680499999999999994, 0.479999999999999982, 0.512000000000000011, 15),
+(3983, 'I', 0.57999999999999996, 0.434999999999999998, 0.149999999999999994, 0.891499999999999959, 0.362999999999999989, 0.192500000000000004, 0.251500000000000001, 6),
+(335, 'F', 0.739999999999999991, 0.599999999999999978, 0.195000000000000007, 1.97399999999999998, 0.597999999999999976, 0.408499999999999974, 0.709999999999999964, 16),
+(1587, 'I', 0.515000000000000013, 0.349999999999999978, 0.104999999999999996, 0.474499999999999977, 0.212999999999999995, 0.122999999999999998, 0.127500000000000002, 10),
+(2448, 'I', 0.275000000000000022, 0.204999999999999988, 0.0800000000000000017, 0.096000000000000002, 0.0359999999999999973, 0.0184999999999999991, 0.0299999999999999989, 6),
+(1362, 'F', 0.604999999999999982, 0.474999999999999978, 0.174999999999999989, 1.07600000000000007, 0.463000000000000023, 0.219500000000000001, 0.33500000000000002, 9),
+(2799, 'M', 0.640000000000000013, 0.484999999999999987, 0.149999999999999994, 1.09800000000000009, 0.519499999999999962, 0.222000000000000003, 0.317500000000000004, 10),
+(1413, 'F', 0.67000000000000004, 0.505000000000000004, 0.174999999999999989, 1.01449999999999996, 0.4375, 0.271000000000000019, 0.3745, 10),
+(1739, 'F', 0.67000000000000004, 0.540000000000000036, 0.195000000000000007, 1.61899999999999999, 0.739999999999999991, 0.330500000000000016, 0.465000000000000024, 11),
+(1152, 'M', 0.584999999999999964, 0.465000000000000024, 0.160000000000000003, 0.955500000000000016, 0.45950000000000002, 0.235999999999999988, 0.265000000000000013, 7),
+(2427, 'I', 0.564999999999999947, 0.434999999999999998, 0.154999999999999999, 0.782000000000000028, 0.271500000000000019, 0.16800000000000001, 0.284999999999999976, 14),
+(1777, 'M', 0.484999999999999987, 0.369999999999999996, 0.154999999999999999, 0.967999999999999972, 0.418999999999999984, 0.245499999999999996, 0.236499999999999988, 9),
+(3294, 'M', 0.574999999999999956, 0.455000000000000016, 0.184999999999999998, 1.15599999999999992, 0.552499999999999991, 0.242999999999999994, 0.294999999999999984, 13),
+(1403, 'M', 0.650000000000000022, 0.510000000000000009, 0.190000000000000002, 1.54200000000000004, 0.715500000000000025, 0.373499999999999999, 0.375, 9),
+(2256, 'M', 0.510000000000000009, 0.395000000000000018, 0.14499999999999999, 0.61850000000000005, 0.215999999999999998, 0.138500000000000012, 0.239999999999999991, 12),
+(3984, 'F', 0.584999999999999964, 0.450000000000000011, 0.125, 0.873999999999999999, 0.354499999999999982, 0.20749999999999999, 0.225000000000000006, 6),
+(1116, 'M', 0.525000000000000022, 0.405000000000000027, 0.119999999999999996, 0.755499999999999949, 0.3755, 0.155499999999999999, 0.201000000000000012, 9),
+(1366, 'M', 0.609999999999999987, 0.474999999999999978, 0.170000000000000012, 1.02649999999999997, 0.434999999999999998, 0.233500000000000013, 0.303499999999999992, 10),
+(3759, 'I', 0.525000000000000022, 0.400000000000000022, 0.140000000000000013, 0.605500000000000038, 0.260500000000000009, 0.107999999999999999, 0.209999999999999992, 9);
+
      2. +
    2. Train a model with family=gaussian and link=identity 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
+SELECT madlib.glm(
+    'abalone',
+    'abalone_out',
+    'rings',
+    'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+    'family=gaussian, link=identity');
+
      3. +
    +

    Example for Gamma family: (reuse the dataset in Gaussian case)

    +
      +
    1. Reuse the test data set in Gaussian
      2. +
    2. Train a model with family=gamma and link=inverse 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
+SELECT madlib.glm(
+    'abalone',
+    'abalone_out',
+    'rings',
+    'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+    'family=gamma, link=inverse');
+
      3. +
    +

    Example for Inverse Gaussian family: (reuse the dataset in Gaussian case)

    +
      +
    1. Reuse the test data set in Gaussian
      2. +
    2. Train a model with family=inverse_gaussian and link=sqr_inverse 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
+SELECT madlib.glm(
+    'abalone',
+    'abalone_out',
+    'rings',
+    'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+    'family=inverse_gaussian, link=sqr_inverse');
+
      3. +
    +

    Example for Binomial family: (reuse the dataset in Gaussian case)

    +
      +
    1. Reuse the test data set in Gaussian
      2. +
    2. Train a model with family=binomial and link=probit 
      +DROP TABLE IF EXISTS abalone_out, abalone_out_summary;
+SELECT madlib.glm(
+    'abalone',
+    'abalone_out',
+    'rings < 10',
+    'ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]',
+    'family=binomial, link=probit');
+
      3. +
    3. Predict output probabilities 
      +SELECT madlib.glm_predict(
+    coef,
+    ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]::float8[],
+    'probit')
+FROM abalone_out, abalone;
+
      4. +
    4. Predict output categories 
      +SELECT madlib.glm_predict(
+SELECT madlib.glm_predict_binomial(
+    coef,
+    ARRAY[1, length, diameter, height, whole, shucked, viscera, shell]::float8[],
+    'probit')
+FROM abalone_out, abalone;
+
      5. +
    +

    Notes
    All table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').
    +

    Currently implementation uses Newton's method and, according to performance tests, when number of features are over 1000, this GLM function could be running slowly.

    +

    Functions in Linear Regression is prefered to GLM with family=gaussian,link=identity, as the former require only a single pass over the training data. In addition, if user expects to use robust variance, clustered variance, or marginal effects on top of the trained model, functions in Linear Regression and Logistic Regression should be used.

    +

    Related Topics
    +

    File glm.sql_in documenting the training function

    +

    Linear Regression

    +

    Logistic Regression

    +

    Multinomial Logistic Regression

    +

    Robust Variance

    +

    Clustered Variance

    +

    Cross Validation

    +

    Marginal Effects

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__gpu__configuration.html b/docs/docs/v2.1.0/group__grp__gpu__configuration.html new file mode 100644 index 00000000..a33fe1ef --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__gpu__configuration.html @@ -0,0 +1,262 @@ + + + + + + + + +MADlib: Show GPU Configuration + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Show GPU Configuration
    Deep Learning » Utilities for Deep Learning
    +
    +
    +
    Contents +

    This utility function reports the number and type of GPUs attached to hosts on the database cluster.

    +

    This can be useful when determining which segments to use for training deep neural nets. For example, for economic reasons you may wish to set up a heterogeneous clusters with GPUs only on some of the hosts, not all of them. This utility can help you identify where the GPUS are and direct the compute to those locations only for model training.

    +

    GPU Confuguration
    +
    +gpu_configuration( output_table,
+                   source
+                   )
+

    Arguments

    +
    output_table
    +

    TEXT. Name of the output table to write out the GPU information.

    +

    +
    +
    source (optional)
    +

    TEXT, default: 'tensorflow'. Source for determining GPU configuration. Using 'tensorflow' returns a description based on what TensorFlow reports. Using 'nvidia' returns a description based on what the Nvidia Systems Management Interface (nvidia-smi) reports [1]. Note that MADlib and Keras will use the TensorFlow information; the lower level nvidia-smi info is provided for convenience.

    +
    Note
    If the command 'nvidia-smi -L' returns an error, we do not pass through the error message, but instead will show no GPUs for that host in the output table. You may want to run nvidia-smi from the command line to see error and informational messages.
    +
    +
    +

    Output
    + The output table contains the following:

    + + + + +
    hostname TEXT. Name of the host machine in the cluster. Does not include master or mirrors. For PostgreSQL this will always return 'localhost'.
    gpu_descr TEXT. String reported by TensorFlow or nvidia-smi. The formats are different and shown in the examples below.
    +

    Examples
    +
      +
    1. Get GPU configuration as per TensorFlow: 
      +DROP TABLE IF EXISTS host_gpu_mapping_tf;
+SELECT * FROM madlib.gpu_configuration('host_gpu_mapping_tf');
+SELECT * FROM host_gpu_mapping_tf ORDER BY hostname, gpu_descr;
+
      + hostname |                                        gpu_descr
+----------+------------------------------------------------------------------------------------------
+ phoenix0 | device: 0, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:04.0, compute capability: 6.0
+ phoenix0 | device: 1, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:05.0, compute capability: 6.0
+ phoenix0 | device: 2, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:06.0, compute capability: 6.0
+ phoenix0 | device: 3, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:07.0, compute capability: 6.0
+ phoenix1 | device: 0, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:04.0, compute capability: 6.0
+ phoenix1 | device: 1, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:05.0, compute capability: 6.0
+ phoenix3 | device: 0, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:04.0, compute capability: 6.0
+ phoenix3 | device: 1, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:05.0, compute capability: 6.0
+ phoenix3 | device: 2, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:06.0, compute capability: 6.0
+ phoenix3 | device: 3, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:07.0, compute capability: 6.0
+ phoenix4 | device: 0, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:04.0, compute capability: 6.0
+ phoenix4 | device: 1, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:05.0, compute capability: 6.0
+ phoenix4 | device: 2, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:06.0, compute capability: 6.0
+ phoenix4 | device: 3, name: Tesla P100-PCIE-16GB, pci bus id: 0000:00:07.0, compute capability: 6.0
+(14 rows)
+
      In this heterogeneous cluster there are 4 GPUs attached to hosts 0, 3 and 4. There are 2 GPUs attached to host 1 and no GPUs attached to host 2.
      2. +
    2. Get GPU configuration as per nvidia-smi: 
      +DROP TABLE IF EXISTS host_gpu_mapping_nvidia;
+SELECT * FROM madlib.gpu_configuration('host_gpu_mapping_nvidia', -- output table
+                                       'nvidia'                   -- source for GPU info
+                                       );
+SELECT * FROM host_gpu_mapping_nvidia ORDER BY hostname, gpu_descr;
+
      + hostname |                                  gpu_descr
+----------+------------------------------------------------------------------------------
+ phoenix0 | GPU 0: Tesla P100-PCIE-16GB (UUID: GPU-f2ccc77e-2501-f6ee-4754-069dda256fb2)
+ phoenix0 | GPU 1: Tesla P100-PCIE-16GB (UUID: GPU-b1fc40ca-c7c6-bc86-f20f-6e9a62cda3f8)
+ phoenix0 | GPU 2: Tesla P100-PCIE-16GB (UUID: GPU-d93bb21b-96f9-7c1d-3bab-cdd92b7bbc9d)
+ phoenix0 | GPU 3: Tesla P100-PCIE-16GB (UUID: GPU-2d79c4a8-479e-2f33-39f8-3ba80b63f830)
+ phoenix1 | GPU 0: Tesla P100-PCIE-16GB (UUID: GPU-0af6bb1e-5b5b-4988-ad3a-a917e9584702)
+ phoenix1 | GPU 1: Tesla P100-PCIE-16GB (UUID: GPU-d824c976-a8aa-ef26-a13c-9a9a7fe86bfd)
+ phoenix3 | GPU 0: Tesla P100-PCIE-16GB (UUID: GPU-3681d0b6-1ec6-0453-fd81-29d88e549cd9)
+ phoenix3 | GPU 1: Tesla P100-PCIE-16GB (UUID: GPU-d4b1f2e7-b238-ac9a-bbfe-918adeb69472)
+ phoenix3 | GPU 2: Tesla P100-PCIE-16GB (UUID: GPU-42a32ef1-a60c-e599-c8cf-0e669111ab6f)
+ phoenix3 | GPU 3: Tesla P100-PCIE-16GB (UUID: GPU-1cce09c4-6856-8031-be0b-8e8bbf9a10f3)
+ phoenix4 | GPU 0: Tesla P100-PCIE-16GB (UUID: GPU-a71bdc18-fdd5-ba25-617e-19b23cc8e827)
+ phoenix4 | GPU 1: Tesla P100-PCIE-16GB (UUID: GPU-f9d13688-7fe6-a029-24d1-985a5659f18f)
+ phoenix4 | GPU 2: Tesla P100-PCIE-16GB (UUID: GPU-06a7f54b-c07a-e87a-20d6-09bd99b19531)
+ phoenix4 | GPU 3: Tesla P100-PCIE-16GB (UUID: GPU-af3b32f3-8bd9-cb75-a8fb-25253b9da926)
+(14 rows)
+
      3. +
    3. To get a fuller picture at the segment level, combine with the Greenplum catalog table 'gp_segment_configuration' which contains information about segment instance configuration [2]. Here is an example of this table filtering out master and mirrors: 
      +SELECT * FROM gp_segment_configuration WHERE role='p' AND content>=0 ORDER BY hostname, dbid;
+
      + dbid | content | role | preferred_role | mode | status | port  | hostname | address  | replication_port
+------+---------+------+----------------+------+--------+-------+----------+----------+------------------
+    2 |       0 | p    | p              | c    | u      | 40000 | phoenix0 | phoenix0 |            70000
+    3 |       1 | p    | p              | c    | u      | 40001 | phoenix0 | phoenix0 |            70001
+    4 |       2 | p    | p              | c    | u      | 40002 | phoenix0 | phoenix0 |            70002
+    5 |       3 | p    | p              | c    | u      | 40003 | phoenix0 | phoenix0 |            70003
+    6 |       4 | p    | p              | c    | u      | 40000 | phoenix1 | phoenix1 |            70000
+    7 |       5 | p    | p              | c    | u      | 40001 | phoenix1 | phoenix1 |            70001
+    8 |       6 | p    | p              | c    | u      | 40002 | phoenix1 | phoenix1 |            70002
+    9 |       7 | p    | p              | c    | u      | 40003 | phoenix1 | phoenix1 |            70003
+   10 |       8 | p    | p              | c    | u      | 40000 | phoenix2 | phoenix2 |            70000
+   11 |       9 | p    | p              | c    | u      | 40001 | phoenix2 | phoenix2 |            70001
+   12 |      10 | p    | p              | c    | u      | 40002 | phoenix2 | phoenix2 |            70002
+   13 |      11 | p    | p              | c    | u      | 40003 | phoenix2 | phoenix2 |            70003
+   14 |      12 | p    | p              | c    | u      | 40000 | phoenix3 | phoenix3 |            70000
+   15 |      13 | p    | p              | c    | u      | 40001 | phoenix3 | phoenix3 |            70001
+   16 |      14 | p    | p              | c    | u      | 40002 | phoenix3 | phoenix3 |            70002
+   17 |      15 | p    | p              | c    | u      | 40003 | phoenix3 | phoenix3 |            70003
+   18 |      16 | p    | p              | c    | u      | 40000 | phoenix4 | phoenix4 |            70000
+   19 |      17 | p    | p              | c    | u      | 40001 | phoenix4 | phoenix4 |            70001
+   20 |      18 | p    | p              | c    | u      | 40002 | phoenix4 | phoenix4 |            70002
+   21 |      19 | p    | p              | c    | u      | 40003 | phoenix4 | phoenix4 |            70003
+(20 rows)
+
      Now join this table with the GPU resources table to create a table containing a list of all segments on hosts with GPUs attached: 
      +DROP TABLE IF EXISTS segments_to_use;
+CREATE TABLE segments_to_use AS
+  SELECT DISTINCT dbid, hostname FROM gp_segment_configuration JOIN host_gpu_mapping_tf USING (hostname)
+  WHERE role='p' AND content>=0;
+SELECT * FROM segments_to_use ORDER BY hostname, dbid;
+
      + dbid | hostname
+------+----------
+    2 | phoenix0
+    3 | phoenix0
+    4 | phoenix0
+    5 | phoenix0
+    6 | phoenix1
+    7 | phoenix1
+    8 | phoenix1
+    9 | phoenix1
+   14 | phoenix3
+   15 | phoenix3
+   16 | phoenix3
+   17 | phoenix3
+   18 | phoenix4
+   19 | phoenix4
+   20 | phoenix4
+   21 | phoenix4
+(16 rows)
+
      4. +
    +

    References
    +

    [1] Nvidia Systems Management Interface (nvidia-smi) https://developer.nvidia.com/nvidia-system-management-interface

    +

    [2] Greenplum 'gp_segment_configuration' table https://gpdb.docs.pivotal.io/latest/ref_guide/system_catalogs/gp_segment_configuration.html

    +

    Related Topics
    +

    See madlib_keras_gpu_info.sql_in

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__graph.html b/docs/docs/v2.1.0/group__grp__graph.html new file mode 100644 index 00000000..64ef8b6c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph.html @@ -0,0 +1,148 @@ + + + + + + + + +MADlib: Graph + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Graph
    +
    +
    +

    Detailed Description

    +

    Graph algorithms and measures associated with graphs.

    + + + + + + + + + + + + + + + + + + + + + + + +

    +Modules

     All Pairs Shortest Path
     Finds the shortest paths between every vertex pair in a given graph.
     
     Breadth-First Search
     Finds the nodes reachable from a given source vertex using a breadth-first approach.
     
     HITS
     Find the HITS scores (authority and hub) of all vertices in a directed graph.
     
     Measures
     A collection of metrics computed on a graph.
     
     PageRank
     Find the PageRank of all vertices in a directed graph.
     
     Single Source Shortest Path
     Finds the shortest path from a single source vertex to every other vertex in a given graph.
     
     Weakly Connected Components
     Find all weakly connected components of a graph.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__graph.js b/docs/docs/v2.1.0/group__grp__graph.js new file mode 100644 index 00000000..40f61f1d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph.js @@ -0,0 +1,10 @@ +var group__grp__graph = +[ + [ "All Pairs Shortest Path", "group__grp__apsp.html", null ], + [ "Breadth-First Search", "group__grp__bfs.html", null ], + [ "HITS", "group__grp__hits.html", null ], + [ "Measures", "group__grp__graph__measures.html", "group__grp__graph__measures" ], + [ "PageRank", "group__grp__pagerank.html", null ], + [ "Single Source Shortest Path", "group__grp__sssp.html", null ], + [ "Weakly Connected Components", "group__grp__wcc.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__graph__avg__path__length.html b/docs/docs/v2.1.0/group__grp__graph__avg__path__length.html new file mode 100644 index 00000000..649882cd --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph__avg__path__length.html @@ -0,0 +1,229 @@ + + + + + + + + +MADlib: Average Path Length + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Average Path Length
    Graph » Measures
    +
    +
    +
    Contents +

    This function computes the average of the shortest paths between each pair of vertices. Average path length is based on "reachable target vertices", so it ignores infinite-length paths between vertices that are not connected. This means the function will average the path lengths in each connected component. If the user requires the average path length of a particular component, the weakly_connected_components function may be used to isolate the relevant vertices.

    +
    Note
    This function assumes a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 * E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.
    +

    Average Path Length
    +graph_avg_path_length( apsp_table,
+                       output_table
+                     )
+
    +

    Arguments

    +
    apsp_table
    +

    TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP).

    +

    +
    +
    out_table
    +
    TEXT. Name of the table to store the average path length. It contains a row for every group, and the average path value.
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER,
+        name TEXT
+        );
+CREATE TABLE edge(
+        src_id INTEGER,
+        dest_id INTEGER,
+        edge_weight FLOAT8
+        );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+
      2. +
    2. Calculate the all-pair shortest paths: 
      +DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
+SELECT madlib.graph_apsp('vertex',      -- Vertex table
+                         'id',          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         'src=src_id, dest=dest_id, weight=edge_weight',
+                                        -- Edge arguments (NULL means use default naming)
+                         'out_apsp');        -- Output table of shortest paths
+
      3. +
    3. Compute the average path length measure: 
      +DROP TABLE IF EXISTS out_avg_path_length;
+SELECT madlib.graph_avg_path_length('out_apsp', 'out_avg_path_length');
+SELECT * FROM out_avg_path_length;
+
      + avg_path_length
+------------------
+ 2.973684210526316
+(1 row)
+
      4. +
    4. Create a graph with 2 groups and find APSP for each group: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+  SELECT *, 0 AS grp FROM edge
+  UNION
+  SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+
      5. +
    5. Find APSP for all groups: 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         'src=src_id, dest=dest_id, weight=edge_weight',
+                         'out_gr',      -- Output table of shortest paths
+                         'grp'          -- Grouping columns
+);
+
      6. +
    6. Find the average path length in every group 
      +DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_avg_path_length('out_gr', 'out_gr_path');
+SELECT * FROM out_gr_path ORDER BY grp;
+
      + grp |  avg_path_length
+----—+-------------------—
+   0 |  2.973684210526316
+   1 |               0.56
+(2 rows)
+
      7. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__graph__closeness.html b/docs/docs/v2.1.0/group__grp__graph__closeness.html new file mode 100644 index 00000000..06dc0d9b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph__closeness.html @@ -0,0 +1,265 @@ + + + + + + + + +MADlib: Closeness + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Closeness
    Graph » Measures
    +
    +
    +
    Contents +

    The Closeness function returns various closeness centrality measures and the k-degree for given subset of vertices. The closeness measures are the inverse of the sum, the inverse of the average, and the sum of inverses of the shortest distances to all reachable target vertices (excluding the source vertex).

    +
    Note
    The closeness measures require a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.
    +

    Closeness
    +graph_closeness( apsp_table,
+                 output_table,
+                 vertex_filter_expr
+               )
+
    +

    Arguments

    +
    apsp_table
    +

    TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP).

    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the closeness measures. It contains a row for every vertex of every group and have the following columns (in addition to the grouping columns):

      +
    • inverse_sum_dist: Inverse of the sum of shortest distances to all reachable vertices.
      • +
    • inverse_average_dist: Inverse of the average of shortest distances to all reachable vertices.
      • +
    • sum_inverse_dist: Sum of the inverse of shortest distances to all reachable vertices.
      • +
    • k_degree: Total number of reachable vertices.
      • +
    +

    +
    +
    vertex_filter_expr (optional)
    +

    TEXT, default = NULL. Valid PostgreSQL expression that describes the vertices to generate closeness measures for. If this parameter is not specified, closeness measures are generated for all vertices in the apsp table. You can think of this input parameter as being like a WHERE clause.

    +

    Some example inputs:

      +
    • If you want a short list of vertices, say 1, 2 and 3: 
      vertex_id IN (1, 2, 3)
      • +
    • If you want a range of vertices between 1000 and 2000: 
      vertix_id BETWEEN 1000 AND 2000
      • +
    • If you want a set of vertices from a separate table satisfying to a condition 
      EXISTS (SELECT vertex_id FROM vertices_of_interest
+             WHERE vertex_id > 5000 AND condition = 'xyz')
+
      • +
    +

    +
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER,
+        name TEXT
+        );
+CREATE TABLE edge(
+        src_id INTEGER,
+        dest_id INTEGER,
+        edge_weight FLOAT8
+        );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+
      2. +
    2. Calculate the all-pair shortest paths: 
      +DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
+SELECT madlib.graph_apsp('vertex',      -- Vertex table
+                         'id',          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         'src=src_id, dest=dest_id, weight=edge_weight',
+                                        -- Edge arguments (NULL means use default naming)
+                         'out_apsp');        -- Output table of shortest paths
+
      3. +
    3. Compute the closeness measure for all nodes: 
      +DROP TABLE IF EXISTS out_closeness;
+SELECT madlib.graph_closeness('out_apsp', 'out_closeness');
+SELECT * FROM out_closeness;
+
      + src_id |  inverse_sum_dist  | inverse_avg_dist  | sum_inverse_dist | k_degree
+--------+--------------------+-------------------+------------------+----------
+      1 | 0.0285714285714286 |               0.2 | 1.93809523809524 |        7
+      3 | 0.0357142857142857 |              0.25 | 2.87424242424242 |        7
+      4 |                 -1 |                -7 |               -1 |        7
+      0 | 0.0434782608695652 | 0.304347826086957 | 3.68333333333333 |        7
+      6 |                  1 |                 1 |                1 |        1
+      2 | 0.0416666666666667 | 0.291666666666667 |             3.75 |        7
+      5 |  0.333333333333333 | 0.666666666666667 |              1.5 |        2
+      7 |             [NULL] |            [NULL] |                0 |        0
+(8 rows)
+
      4. +
    4. Create a graph with 2 groups and find APSP for each group: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+  SELECT *, 0 AS grp FROM edge
+  UNION
+  SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+
      5. +
    5. Find APSP for all groups: 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         'src=src_id, dest=dest_id, weight=edge_weight',
+                         'out_gr',      -- Output table of shortest paths
+                         'grp'          -- Grouping columns
+);
+
      6. +
    6. Compute closeness measure for vertex 0 to vertex 5 in every group 
      +DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_closeness('out_gr', 'out_gr_closeness', 'src_id >= 0 and src_id <=5');
+SELECT * FROM out_gr_closeness ORDER BY grp;
+
      + grp | src_id |  inverse_sum_dist   |  inverse_avg_dist  | sum_inverse_dist  | k_degree
+----—+-------—+--------------------—+-------------------—+------------------—+---------—
+   0 |      0 |  0.0434782608695652 |  0.304347826086957 |  3.68333333333333 |        7
+   0 |      5 |   0.333333333333333 |  0.666666666666667 |               1.5 |        2
+   0 |      4 |                  -1 |                 -7 |                -1 |        7
+   0 |      3 |  0.0357142857142857 |               0.25 |  2.87424242424242 |        7
+   0 |      1 |  0.0285714285714286 |                0.2 |  1.93809523809524 |        7
+   0 |      2 |  0.0416666666666667 |  0.291666666666667 |              3.75 |        7
+   1 |      3 |   0.142857142857143 |  0.714285714285714 |  1.97979797979798 |        5
+   1 |      5 |              [NULL] |             [NULL] |                 0 |        0
+   1 |      0 |                0.25 |               1.25 |               2.5 |        5
+   1 |      1 |  0.0588235294117647 |  0.294117647058824 | 0.988095238095238 |        5
+   1 |      2 |                 0.1 |                0.5 |  1.79166666666667 |        5
+   1 |      4 | -0.0416666666666667 | -0.208333333333333 |             -2.55 |        5
+(12 rows)
+
      7. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__graph__diameter.html b/docs/docs/v2.1.0/group__grp__graph__diameter.html new file mode 100644 index 00000000..9e31c9cf --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph__diameter.html @@ -0,0 +1,231 @@ + + + + + + + + +MADlib: Graph Diameter + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
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    + +
    +
    + + +
    + +
    + +
    +
    +
    Graph Diameter
    Graph » Measures
    +
    +
    +
    Contents +

    Diameter is defined as the longest of all shortest paths in a graph.

    +
    Note
    This function assumes a valid output from a prior APSP run - both the APSP table and the associated output summary table. APSP is a computationally expensive algorithm because it finds the shortest path between all nodes in the graph. The worst case run-time for this implementation is O(V^2 * E) where V is the number of vertices and E is the number of edges. In practice, run-time will be generally be much less than this, depending on the graph.
    +

    Diameter
    +graph_diameter( apsp_table,
+                output_table
+               )
+
    +

    Arguments

    +
    apsp_table
    +

    TEXT. Name of the output table generated by a prior run of all pairs shortest path (APSP).

    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the diameter. It contains a row for every group, the diameter value and the two vertices that are the farthest apart.

    +

    +
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER,
+        name TEXT
+        );
+CREATE TABLE edge(
+        src_id INTEGER,
+        dest_id INTEGER,
+        edge_weight FLOAT8
+        );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+
      2. +
    2. Calculate the all-pair shortest paths: 
      +DROP TABLE IF EXISTS out_apsp, out_apsp_summary;
+SELECT madlib.graph_apsp('vertex',      -- Vertex table
+                         'id',          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         'src=src_id, dest=dest_id, weight=edge_weight',
+                                        -- Edge arguments (NULL means use default naming)
+                         'out_apsp');        -- Output table of shortest paths
+
      3. +
    3. Compute the diameter measure for the graph: 
      +DROP TABLE IF EXISTS out_diameter;
+SELECT madlib.graph_diameter('out_apsp', 'out_diameter');
+SELECT * FROM out_diameter;
+
      +diameter | diameter_end_vertices
+---------+-----------------------
+      14 | {{1,4}}
+(1 row)
+
      4. +
    4. Create a graph with 2 groups and find APSP for each group: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+  SELECT *, 0 AS grp FROM edge
+  UNION
+  SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+
      5. +
    5. Find APSP for all groups: 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_apsp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         'src=src_id, dest=dest_id, weight=edge_weight',
+                         'out_gr',      -- Output table of shortest paths
+                         'grp'          -- Grouping columns
+);
+
      6. +
    6. Find the diameter of graph in every group 
      +DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_diameter('out_gr', 'out_gr_diameter');
+SELECT * FROM out_gr_diameter ORDER BY grp;
+
      +grp | diameter | diameter_end_vertices
+---—+---------—+----------------------—
+  0 |       14 | {{1,4}}
+  1 |       14 | {{1,4}}
+(2 rows)
+
      7. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__graph__measures.html b/docs/docs/v2.1.0/group__grp__graph__measures.html new file mode 100644 index 00000000..d7edfee0 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph__measures.html @@ -0,0 +1,139 @@ + + + + + + + + +MADlib: Measures + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Measures
    Graph
    +
    +
    +

    Detailed Description

    +

    A collection of metrics computed on a graph.

    + + + + + + + + + + + + + + +

    +Modules

     Average Path Length
     Computes the average shortest-path length of a graph.
     
     Closeness
     Computes the closeness centrality value of each node in the graph.
     
     Graph Diameter
     Computes the diameter of a graph.
     
     In-Out Degree
     Computes the degrees for each vertex.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__graph__measures.js b/docs/docs/v2.1.0/group__grp__graph__measures.js new file mode 100644 index 00000000..6272fba0 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph__measures.js @@ -0,0 +1,7 @@ +var group__grp__graph__measures = +[ + [ "Average Path Length", "group__grp__graph__avg__path__length.html", null ], + [ "Closeness", "group__grp__graph__closeness.html", null ], + [ "Graph Diameter", "group__grp__graph__diameter.html", null ], + [ "In-Out Degree", "group__grp__graph__vertex__degrees.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__graph__vertex__degrees.html b/docs/docs/v2.1.0/group__grp__graph__vertex__degrees.html new file mode 100644 index 00000000..dbf99db7 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__graph__vertex__degrees.html @@ -0,0 +1,257 @@ + + + + + + + + +MADlib: In-Out Degree + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
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    +
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    +
    +
    In-Out Degree
    Graph » Measures
    +
    +
    +
    Contents +

    This function computes the degree of each node. The node degree is the number of edges adjacent to that node. The node in-degree is the number of edges pointing in to the node and node out-degree is the number of edges pointing out of the node.

    +

    In-out degrees
    +graph_vertex_degrees(
+    vertex_table,
+    vertex_id,
+    edge_table,
+    edge_args,
+    out_table,
+    grouping_cols
+)
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    +
    +
    vertex_id
    +

    TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous.

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex, destination vertex and edge weight. Column naming convention is described below in the 'edge_args' parameter.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'.
      • +
    • dest (INTEGER or BIGINT): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    • weight (FLOAT8): Name of the column containing the edge weights in the edge table. Default column name is 'weight'.
      • +
    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the result. It contains a row for every vertex of every group and has the following columns (in addition to the grouping columns):

      +
    • vertex: The id for the source vertex. Will use the input vertex column 'id' for column naming.
      • +
    • indegree: Number of incoming edges to the vertex.
      • +
    • outdegree: Number of outgoing edges from the vertex.
      • +
    +

    +
    +
    grouping_cols
    +
    TEXT, default = NULL. List of columns used to group the input into discrete subgraphs. These columns must exist in the edge table. When this value is null, no grouping is used and a single result is generated.
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER,
+        name TEXT
+        );
+CREATE TABLE edge(
+        src_id INTEGER,
+        dest_id INTEGER,
+        edge_weight FLOAT8
+        );
+INSERT INTO vertex VALUES
+(0, 'A'),
+(1, 'B'),
+(2, 'C'),
+(3, 'D'),
+(4, 'E'),
+(5, 'F'),
+(6, 'G'),
+(7, 'H');
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+
      2. +
    2. Calculate the in-out degrees for each node: 
      +DROP TABLE IF EXISTS degrees;
+SELECT madlib.graph_vertex_degrees(
+    'vertex',      -- Vertex table
+    'id',          -- Vertix id column (NULL means use default naming)
+    'edge',        -- Edge table
+    'src=src_id, dest=dest_id, weight=edge_weight',
+    'degrees');        -- Output table of shortest paths
+SELECT * FROM degrees ORDER BY id;
+
      + id | indegree | outdegree
+----+----------+-----------
+  0 |        2 |         3
+  1 |        1 |         2
+  2 |        2 |         3
+  3 |        2 |         1
+  4 |        1 |         1
+  5 |        1 |         1
+  6 |        2 |         1
+  7 |        1 |         0
+
      3. +
    3. Create a graph with 2 groups and find degrees for each group: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+  SELECT *, 0 AS grp FROM edge
+  UNION
+  SELECT *, 1 AS grp FROM edge WHERE src_id < 6 AND dest_id < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+
      4. +
    4. Find in-out degrees for all groups: 
      +DROP TABLE IF EXISTS out_gr;
+SELECT madlib.graph_vertex_degrees(
+    'vertex',      -- Vertex table
+    NULL,          -- Vertex id column (NULL means use default naming)
+    'edge_gr',     -- Edge table
+    'src=src_id, dest=dest_id, weight=edge_weight',
+    'out_gr',      -- Output table of shortest paths
+    'grp'          -- Grouping columns
+);
+SELECT * FROM out_gr WHERE id < 2 ORDER BY grp, id;
+
      + grp | id | indegree |   outdegree
+----—+---—+---------—+----------—
+   0 |  0 |        2 |         3
+   0 |  1 |        1 |         2
+   1 |  0 |        2 |         3
+   1 |  1 |        1 |         2
+(4 rows)
+
      5. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__hits.html b/docs/docs/v2.1.0/group__grp__hits.html new file mode 100644 index 00000000..bec3688f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__hits.html @@ -0,0 +1,393 @@ + + + + + + + + +MADlib: HITS + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
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    + +
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    + +
    + +
    +
    +
    HITS
    Graph
    +
    +
    +
    Contents +

    Given a graph, the HITS (Hyperlink-Induced Topic Search) algorithm outputs the authority score and hub score of every vertex, where authority estimates the value of the content of the page and hub estimates the value of its links to other pages. This algorithm was originally developed to rate web pages [1].

    +

    HITS
    +hits( vertex_table,
+      vertex_id,
+      edge_table,
+      edge_args,
+      out_table,
+      max_iter,
+      threshold,
+      grouping_cols
+    )
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    +
    +
    vertex_id
    +

    TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous.

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex and destination vertex.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'.
      • +
    • dest (INTEGER or BIGINT): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the result of HITS. It will contain a row for every vertex from 'vertex_table' with the following columns:

      +
    • vertex_id : The id of a vertex. Will use the input parameter 'vertex_id' for column naming.
      • +
    • authority : The vertex authority score.
      • +
    • hub : The vertex hub score.
      • +
    • grouping_cols : Grouping column values (if any) associated with the vertex_id.
      • +
    +

    A summary table is also created that contains information regarding the number of iterations required for convergence. It is named by adding the suffix '_summary' to the 'out_table' parameter.

    +

    +
    +
    max_iter (optional)
    +

    INTEGER, default: 100. The maximum number of iterations allowed. Each iteration consists of both authority and hub phases.

    +

    +
    +
    threshold (optional)
    +

    FLOAT8, default: (1/number of vertices * 1000). Threshold must be set to a value between 0 and 1, inclusive of end points. If the difference between two consecutive iterations of authority AND two consecutive iterations of hub is smaller than 'threshold', then the computation stops. That is, both authority and hub value differences must be below the specified threshold for the algorithm to stop. If you set the threshold to 0, then you will force the algorithm to run for the full number of iterations specified in 'max_iter'.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. A single column or a list of comma-separated columns that divides the input data into discrete groups, resulting in one distribution per group. When this value is NULL, no grouping is used and a single model is generated for all data.
    Note
    Expressions are not currently supported for 'grouping_cols'.
    +
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER
+        );
+CREATE TABLE edge(
+        src INTEGER,
+        dest INTEGER,
+        user_id INTEGER
+        );
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6);
+INSERT INTO edge VALUES
+(0, 1, 1),
+(0, 2, 1),
+(0, 4, 1),
+(1, 2, 1),
+(1, 3, 1),
+(2, 3, 1),
+(2, 5, 1),
+(2, 6, 1),
+(3, 0, 1),
+(4, 0, 1),
+(5, 6, 1),
+(6, 3, 1);
+
      2. +
    2. Running HITS with default values for optional parameters: 
      +DROP TABLE IF EXISTS hits_out, hits_out_summary;
+SELECT madlib.hits(
+             'vertex',             -- Vertex table
+             'id',                 -- Vertex id column
+             'edge',               -- Edge table
+             'src=src, dest=dest', -- Comma delimited string of edge arguments
+             'hits_out');          -- Output table of HITS
+SELECT * FROM hits_out ORDER BY id;
+
      + id |      authority       |         hub
+----+----------------------+----------------------
+  0 |    8.43871829093e-07 |    0.338306115082665
+  1 |    0.158459587238244 |    0.527865350448059
+  2 |    0.405627969689677 |    0.675800764727558
+  3 |    0.721775835521825 |    3.95111934817e-07
+  4 |    0.158459587238244 |    3.95111934817e-07
+  5 |    0.316385413093048 |    0.189719957843216
+  6 |    0.405199928761102 |    0.337944978189241
+(7 rows)
+
      +SELECT * FROM hits_out_summary;
+
      + __iterations__
+-----------------+
+              17
+(1 row)
+
      3. +
    3. Running HITS with max_iter of 3 results in different authority and hub scores: 
      +DROP TABLE IF EXISTS hits_out, hits_out_summary;
+SELECT madlib.hits(
+             'vertex',             -- Vertex table
+             'id',                 -- Vertex id column
+             'edge',               -- Edge table
+             'src=src, dest=dest', -- Comma delimited string of edge arguments
+             'hits_out',           -- Output table
+              3);                  -- Max iteration
+SELECT * FROM hits_out ORDER BY id;
+
      + id |     authority     |        hub
+----+-------------------+--------------------
+  0 |   0.08653327387778 | 0.375721659592363
+  1 |   0.18388320699029 | 0.533118571043218
+  2 |   0.43266636938891 | 0.654974244424525
+  3 |   0.70308285025699 | 0.040618557793769
+  4 |   0.18388320699029 | 0.040618557793769
+  5 |   0.30286645857224 | 0.182783510071961
+  6 |   0.38939973245002 | 0.330025782074373
+(7 rows)
+
      +SELECT * FROM hits_out_summary;
+
      + __iterations__
+-----------------+
+              3
+(1 row)
+
      4. +
    4. Running HITS with a low threshold of 0.00001 results in more iterations for convergence: 
      +DROP TABLE IF EXISTS hits_out, hits_out_summary;
+SELECT madlib.hits(
+             'vertex',             -- Vertex table
+             'id',                 -- Vertex id column
+             'edge',               -- Edge table
+             'src=src, dest=dest', -- Comma delimited string of edge arguments
+             'hits_out',           -- Output table
+             NULL,                 -- Default max_iter
+             0.00001);             -- Threshold
+SELECT * FROM hits_out ORDER BY id;
+
      + id |      authority       |         hub
+----+----------------------+---------------------
+  0 |    1.15243075426e-09 |     0.33800946769422
+  1 |    0.158264459912827 |    0.527792117750177
+  2 |    0.405384672299625 |    0.675965453766535
+  3 |     0.72186275724613 |    5.39583282614e-10
+  4 |    0.158264459912827 |    5.39583282614e-10
+  5 |    0.316493740997913 |    0.189793242747412
+  6 |    0.405356461070609 |    0.337985666133163
+(7 rows)
+
      +SELECT * FROM hits_out_summary;
+
      + __iterations__
+-----------------+
+              25
+(1 row)
+
      5. +
    5. Running HITS with both max_iter and threshold: 
      +DROP TABLE IF EXISTS hits_out, hits_out_summary;
+SELECT madlib.hits(
+             'vertex',             -- Vertex table
+             'id',                 -- Vertex id column
+             'edge',               -- Edge table
+             'src=src, dest=dest', -- Comma delimited string of edge arguments
+             'hits_out',           -- Output table
+             20,                   -- Default max_iter
+             0.00001);             -- Threshold
+SELECT * FROM hits_out ORDER BY id;
+
      + id |      authority       |         hub
+----+----------------------+---------------------
+  0 |    7.11260011825e-08 |    0.33810307986005
+  1 |    0.158326035587958 |   0.527815233930963
+  2 |    0.405461453180491 |   0.675913495026452
+  3 |    0.721835343230399 |   3.33021322089e-08
+  4 |    0.158326035587958 |   3.33021322089e-08
+  5 |    0.316459563893809 |   0.189770119973925
+  6 |    0.405307074424261 |   0.337972831786458
+(7 rows)
+
      +SELECT * FROM hits_out_summary;
+
      + __iterations__
+-----------------+
+             20
+(1 row)
+
      The algorithm stopped at 20 iterations even though the convergence for threshold of 0.00001 is at 25 iterations. This is because max_iter was set to 20.
      6. +
    6. Running HITS with grouping column and default values for max_iter and threshold. Add more rows to the edge table to create different graphs based on the user_id column. 
      +INSERT INTO edge VALUES
+(0, 1, 2),
+(0, 2, 2),
+(0, 4, 2),
+(1, 2, 2),
+(1, 3, 2),
+(2, 3, 2),
+(3, 0, 2),
+(4, 0, 2),
+(5, 6, 2),
+(6, 3, 2);
+DROP TABLE IF EXISTS hits_out, hits_out_summary;
+SELECT madlib.hits(
+             'vertex',             -- Vertex table
+             'id',                 -- Vertex id column
+             'edge',               -- Edge table
+             'src=src, dest=dest', -- Comma delimited string of edge arguments
+             'hits_out',           -- Output table
+             NULL,                 -- Default max_iter
+             NULL,                 -- Threshold
+             'user_id');           -- Grouping column
+SELECT * FROM hits_out ORDER BY user_id, id;
+
      + user_id | id |      authority       |         hub
+---------+----+----------------------+----------------------
+       1 |  0 |    8.43871829093e-07 |    0.338306115082665
+       1 |  1 |    0.158459587238244 |    0.527865350448059
+       1 |  2 |    0.405627969689677 |    0.675800764727558
+       1 |  3 |    0.721775835521825 |    3.95111934817e-07
+       1 |  4 |    0.158459587238244 |    3.95111934817e-07
+       1 |  5 |    0.316385413093048 |    0.189719957843216
+       1 |  6 |    0.405199928761102 |    0.337944978189241
+       2 |  0 |    1.60841750444e-05 |    0.632262085114062
+       2 |  1 |    0.316079985713431 |    0.632529390899584
+       2 |  2 |    0.632364174872359 |    0.316347297480213
+       2 |  3 |    0.632694582987791 |    8.04208767442e-06
+       2 |  4 |    0.316079985713431 |    8.04208767442e-06
+       2 |  5 |                    0 |    1.22712519446e-10
+       2 |  6 |    2.45425034248e-10 |    0.316347297480213
+(14 rows)
+
      +SELECT * FROM hits_out_summary order by user_id;
+
      + user_id | __iterations__
+---------+----------------
+       1 |             17
+       2 |             16
+(2 rows)
+
      7. +
    +

    Notes
    +
      +
    1. On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance.
      2. +
    2. This implementation of the HITS algorithm supports multigraph and each duplicated edge is considered for counting when calculating authority and hub scores.
      3. +
    +

    Literature
    +

    [1] Kleinerg, Jon M., "Authoritative Sources in a Hyperlinked +Environment", Journal of the ACM, Sept. 1999. https://www.cs.cornell.edu/home/kleinber/auth.pdf

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__indicator.html b/docs/docs/v2.1.0/group__grp__indicator.html new file mode 100644 index 00000000..c8efd419 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__indicator.html @@ -0,0 +1,241 @@ + + + + + + + + +MADlib: Create Indicator Variables + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Create Indicator Variables
    Deprecated Modules
    +
    +
    +
    Warning
    This version of encoding categorical variables has been deprecated. The new module with more capability can be found here Encoding Categorical Variables
    +
    Contents +

    Coding systems for categorical variables
    Categorical variables require special attention in regression analysis because, unlike dichotomous or continuous variables, they cannot be entered into the regression equation just as they are. For example, if you have a variable called race that is coded 1 = Hispanic, 2 = Asian, 3 = Black, 4 = White, then entering race in your regression will look at the linear effect of race, which is probably not what you intended. Instead, categorical variables like this need to be recoded into a series of indicator variables which can then be entered into the regression model. There are a variety of coding systems (also called as contrasts) that can be used when coding categorical variables. including dummy, effects, orthogonal, and helmert coding.
    +

    We currently only support the dummy coding technique. Dummy coding is used when a researcher wants to compare other groups of the predictor variable with one specific group of the predictor variable. Often, the specific group to compare with is called the reference group.

    +
    +create_indicator_variables(
+    source_table,
+    output_table,
+    categorical_cols,
+    keep_null,
+    distributed_by
+    )
+

    Arguments

    +
    source_table
    +
    VARCHAR. Name of the source table, containing data for categorical variables.
    +
    output_table
    +
    VARCHAR. Name of result table. The output table has the same columns as the original table, adding new indicator variable columns for each categorical column. The column name for the indicator variable is 'categorical column name'_'categorical value'.
    +
    categorical_cols
    +
    VARCHAR. Comma-separated string of column names of categorical variables that need to be dummy-coded.
    +
    keep_null (optional)
    +
    BOOLEAN. default: FALSE. Whether 'NULL' should be treated as one of the categories of the categorical variable. If True, then an indicator variable is created corresponding to the NULL value. If False, then all indicator variables for that record will be set to NULL.
    +
    distributed_by (optional)
    +
    VARCHAR. default: NULL. Columns to use for the distribution policy of the output table. When NULL, the distribution policy of 'source_table' will be used. This argument is not available for POSTGRESQL platforms.
    +
    +

    Examples
    +
      +
    1. Use a subset of the abalone dataset. 
      +DROP TABLE IF EXISTS abalone;
+CREATE TABLE abalone (
+    sex character varying,
+    length double precision,
+    diameter double precision,
+    height double precision
+);
+COPY abalone (sex, length, diameter, height) FROM stdin WITH DELIMITER '|' NULL as '@';
+M| 0.455 |   0.365 | 0.095
+F| 0.53  |   0.42  | 0.135
+M| 0.35  |   0.265 | 0.09
+F| 0.53  |   0.415 | 0.15
+M| 0.44  |   0.365 | 0.125
+F| 0.545 |   0.425 | 0.125
+I| 0.33  |   0.255 | 0.08
+F| 0.55  |   0.44  | 0.15
+I| 0.425 |   0.30  | 0.095
+F| 0.525 |   0.38  | 0.140
+M| 0.475 |   0.37  | 0.125
+F| 0.535 |   0.405 | 0.145
+M| 0.43  |   0.358 | 0.11
+F| 0.47  |   0.355 | 0.100
+M| 0.49  |   0.38  | 0.135
+F| 0.44  |   0.340 | 0.100
+M| 0.5   |   0.400 | 0.13
+F| 0.565 |   0.44  | 0.155
+I| 0.355 |   0.280 | 0.085
+F| 0.550 |   0.415 | 0.135
+| 0.475 |   0.37  | 0.125
+\.
+
      2. +
    2. Create new table with dummy-coded indicator variables 
      +drop table if exists abalone_out;
+select madlib.create_indicator_variables ('abalone', 'abalone_out', 'sex');
+select * from abalone_out;
+
      + sex  | length | diameter | height | sex_F  | sex_I  | sex_M
+  -----+--------+----------+--------+--------+--------+-------
+ F    |   0.53 |     0.42 |  0.135 |      1 |      0 |     0
+ F    |   0.53 |    0.415 |   0.15 |      1 |      0 |     0
+ F    |  0.545 |    0.425 |  0.125 |      1 |      0 |     0
+ F    |   0.55 |     0.44 |   0.15 |      1 |      0 |     0
+ F    |  0.525 |     0.38 |   0.14 |      1 |      0 |     0
+ F    |  0.535 |    0.405 |  0.145 |      1 |      0 |     0
+ F    |   0.47 |    0.355 |    0.1 |      1 |      0 |     0
+ F    |   0.44 |     0.34 |    0.1 |      1 |      0 |     0
+ F    |  0.565 |     0.44 |  0.155 |      1 |      0 |     0
+ F    |   0.55 |    0.415 |  0.135 |      1 |      0 |     0
+ M    |  0.455 |    0.365 |  0.095 |      0 |      0 |     1
+ M    |   0.35 |    0.265 |   0.09 |      0 |      0 |     0
+ M    |   0.44 |    0.365 |  0.125 |      0 |      0 |     0
+ I    |   0.33 |    0.255 |   0.08 |      0 |      1 |     0
+ I    |  0.425 |      0.3 |  0.095 |      0 |      1 |     0
+ M    |  0.475 |     0.37 |  0.125 |      0 |      0 |     0
+ M    |   0.43 |    0.358 |   0.11 |      0 |      0 |     0
+ M    |   0.49 |     0.38 |  0.135 |      0 |      0 |     0
+ M    |    0.5 |      0.4 |   0.13 |      0 |      0 |     0
+ I    |  0.355 |     0.28 |  0.085 |      0 |      1 |     0
+ NULL |   0.55 |    0.415 |  0.135 |   NULL |   NULL |  NULL
+
      3. +
    3. Create indicator variable for 'NULL' value (note the additional column '"sex_NULL"') 
      +drop table if exists abalone_out;
+select madlib.create_indicator_variables'abalone', 'abalone_out', 'sex', True);
+select * from abalone_out;
+
      + sex  | length | diameter | height | sex_F  | sex_I  | sex_M | sex_NULL
+  ---—+-----—+-------—+-----—+-----—+-----—+----—+----—
+ F    |   0.53 |     0.42 |  0.135 |      1 |      0 |     0 |     0
+ F    |   0.53 |    0.415 |   0.15 |      1 |      0 |     0 |     0
+ F    |  0.545 |    0.425 |  0.125 |      1 |      0 |     0 |     0
+ F    |   0.55 |     0.44 |   0.15 |      1 |      0 |     0 |     0
+ F    |  0.525 |     0.38 |   0.14 |      1 |      0 |     0 |     0
+ F    |  0.535 |    0.405 |  0.145 |      1 |      0 |     0 |     0
+ F    |   0.47 |    0.355 |    0.1 |      1 |      0 |     0 |     0
+ F    |   0.44 |     0.34 |    0.1 |      1 |      0 |     0 |     0
+ F    |  0.565 |     0.44 |  0.155 |      1 |      0 |     0 |     0
+ F    |   0.55 |    0.415 |  0.135 |      1 |      0 |     0 |     0
+ M    |  0.455 |    0.365 |  0.095 |      0 |      0 |     1 |     0
+ M    |   0.35 |    0.265 |   0.09 |      0 |      0 |     0 |     0
+ M    |   0.44 |    0.365 |  0.125 |      0 |      0 |     0 |     0
+ I    |   0.33 |    0.255 |   0.08 |      0 |      1 |     0 |     0
+ I    |  0.425 |      0.3 |  0.095 |      0 |      1 |     0 |     0
+ M    |  0.475 |     0.37 |  0.125 |      0 |      0 |     0 |     0
+ M    |   0.43 |    0.358 |   0.11 |      0 |      0 |     0 |     0
+ M    |   0.49 |     0.38 |  0.135 |      0 |      0 |     0 |     0
+ M    |    0.5 |      0.4 |   0.13 |      0 |      0 |     0 |     0
+ I    |  0.355 |     0.28 |  0.085 |      0 |      1 |     0 |     0
+ NULL |   0.55 |    0.415 |  0.135 |      0 |      0 |     0 |     1
+
      4. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__inf__stats.html b/docs/docs/v2.1.0/group__grp__inf__stats.html new file mode 100644 index 00000000..a951dea4 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__inf__stats.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: Inferential Statistics + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Inferential Statistics
    Statistics
    +
    +
    +

    Detailed Description

    +

    Methods to compute inferential statistics of a dataset.

    + + + + + +

    +Modules

     Hypothesis Tests
     Provides functions to perform statistical hypothesis tests.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__inf__stats.js b/docs/docs/v2.1.0/group__grp__inf__stats.js new file mode 100644 index 00000000..7bfc14ae --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__inf__stats.js @@ -0,0 +1,4 @@ +var group__grp__inf__stats = +[ + [ "Hypothesis Tests", "group__grp__stats__tests.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__input__preprocessor__dl.html b/docs/docs/v2.1.0/group__grp__input__preprocessor__dl.html new file mode 100644 index 00000000..23c6a870 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__input__preprocessor__dl.html @@ -0,0 +1,673 @@ + + + + + + + + +MADlib: Preprocess Data + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Preprocess Data
    Deep Learning » Model Preparation
    +
    +
    +
    Contents +

    This preprocessor prepares training data for deep learning.

    +

    It packs multiple training examples into the same row for frameworks like Keras and TensorFlow that support mini-batching as an optimization option. The advantage of using mini-batching is that it can perform better than stochastic gradient descent because it uses more than one training example at a time, typically resulting in faster and smoother convergence [1].

    +

    In the case of image processing, images can be represented as an array of numbers where each element represents grayscale, RGB or other channel values for each pixel in the image. It is standard practice to normalize the image data before training. The normalizing constant in this module is parameterized, so it can be set depending on the format of image data used.

    +

    This preprocessor also sets the distribution rules for the training data. For example, you may only want to train models on segments that reside on hosts that are GPU enabled.

    +

    There are two versions of the preprocessor: training_preprocessor_dl() preprocesses input data to be used for training a deep learning model, while validation_preprocessor_dl() preprocesses validation data used for model evaluation.

    +

    Preprocessor for Training Data
    +
    +training_preprocessor_dl(source_table,
+                         output_table,
+                         dependent_varname,
+                         independent_varname,
+                         buffer_size,
+                         normalizing_const,
+                         num_classes,
+                         distribution_rules
+                        )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing training dataset. Can also be a view.

    +

    +
    +
    output_table
    +

    TEXT. Name of the output table from the training preprocessor which will be used as input to algorithms that support mini-batching. Note that the arrays packed into the output table are shuffled and normalized, by dividing each element in the independent variable array by the optional 'normalizing_const' parameter. For performance reasons, packed arrays are converted to PostgreSQL bytea format, which is a variable-length binary string.

    +

    In the case a validation data set is used (see later on this page), this output table is also used as an input to the validation preprocessor so that the validation and training data are both preprocessed in an identical manner.

    +

    +
    +
    dependent_varname
    +
    TEXT. Name of the dependent variable column. In the case that there are multiple dependent variable columns, representing a multi-output neural network, put the columns as a comma separated list, e.g., 'dep_var1, dep_var2, dep_var3'.
    Note
    The mini-batch preprocessor automatically 1-hot encodes dependent variables of all types. The exception is numeric array types (integer and float), where we assume these are already 1-hot encoded, so these will just be passed through as is.
    +
    +
    independent_varname
    +

    TEXT. Name of the independent variable column. The column must be a numeric array type. In the case that there are multiple independent variable columns, representing a multi-input neural network, put the columns as a comma separated list, e.g., 'indep_var1, indep_var2, indep_var3'.

    +

    +
    +
    buffer_size (optional)
    +
    INTEGER, default: computed. Buffer size is the number of rows from the source table that are packed into one row of the preprocessor output table. In the case of images, the source table will have one image per row, and the output table will have multiple images per row. The default value is computed considering the sizes of the source table and images and the number of segments in the database cluster.
    Note
    Using the default for 'buffer_size' will produce buffers that are relatively large, which generally results in the fastest fit() runtime with Keras. Setting a smaller buffer size may cause the preprocessor to run faster (although this is not guaranteed, since it depends on database cluster size, data set, and other factors). But since preprocessing is usually a one-time operation and fit() is called many times, by default buffer sizes are optimized to make fit() as fast as possible. Note that specifying a 'buffer_size' does not guarantee that exact value will be used. Actual buffer size is adjusted to avoid data skew, which adversely impacts fit() runtime.
    +
    +
    normalizing_const (optional)
    +

    REAL, default: 1.0. The normalizing constant to divide each value in the 'independent_varname' array by. For example, you would use 255 for this value if the image data is in the form 0-255.

    +

    +
    +
    num_classes (optional)
    +

    INTEGER[], default: NULL. Number of class labels of each dependent variable for 1-hot encoding. If NULL, the 1-hot encoded array length will be equal to the number of distinct class values found in the input table.

    +

    +
    +
    distribution_rules (optional)
    +

    TEXT, default: 'all_segments'. Specifies how to distribute the 'output_table'. This is important for how the fit function will use resources on the cluster. The default 'all_segments' means the 'output_table' will be distributed to all segments in the database cluster.

    +

    If you specify 'gpu_segments' then the 'output_table' will be distributed to all segments that are on hosts that have GPUs attached. This will make maximum use of GPU resources when training a deep learning model.

    +

    You can also specify the name of a resources table containing the segments to be used for training. This table must contain a column called 'dbid' that specifies the segment id from the 'gp_segment_configuration' table [2]. Refer to the utility function GPU Configuration for more information on how to identify segments attached to hosts that are GPU enabled.

    +
    +
    +

    Preprocessor for Validation Data
    +validation_preprocessor_dl(source_table,
+                           output_table,
+                           dependent_varname,
+                           independent_varname,
+                           training_preprocessor_table,
+                           buffer_size,
+                           distribution_rules
+                          )
+
    +

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing validation dataset. Can also be a view.

    +

    +
    +
    output_table
    +

    TEXT. Name of the output table from the validation preprocessor which will be used as input to algorithms that support mini-batching. The arrays packed into the output table are normalized using the same normalizing constant from the training preprocessor as specified in the 'training_preprocessor_table' parameter described below. Validation data is not shuffled. For performance reasons, packed arrays are converted to PostgreSQL bytea format, which is a variable-length binary string.

    +

    +
    +
    dependent_varname
    +
    TEXT. Name of the dependent variable column.
    Note
    The mini-batch preprocessor automatically 1-hot encodes dependent variables of all types. The exception is numeric array types (integer and float), where we assume these are already 1-hot encoded, so these will just be passed through as is.
    +
    +
    independent_varname
    +

    TEXT. Name of the independent variable column. The column must be a numeric array type.

    +

    +
    +
    training_preprocessor_table
    +

    TEXT. The output table obtained by running training_preprocessor_dl(). Validation data is preprocessed in the same way as training data, i.e., same normalizing constant and dependent variable class values. Note that even if the validation dataset is missing some of the class values completely, this parameter will ensure that the ordering and labels still match with training dataset.

    +

    +
    +
    buffer_size (optional)
    +
    INTEGER, default: computed. Buffer size is the number of rows from the source table that are packed into one row of the preprocessor output table. In the case of images, the source table will have one image per row, and the output table will have multiple images per row. The default value is computed considering the sizes of the source table and images and the number of segments in the database cluster.
    Note
    Using the default for 'buffer_size' will produce buffers that are relatively large, which generally results in the fastest fit() runtime with Keras. Setting a smaller buffer size may cause the preprocessor to run faster (although this is not guaranteed, since it depends on database cluster size, data set, and other factors). But since preprocessing is usually a one-time operation and fit() is called many times, by default buffer sizes are optimized to make fit() as fast as possible. Note that specifying a 'buffer_size' does not guarantee that exact value will be used. Actual buffer size is adjusted to avoid data skew, which adversely impacts fit() runtime.
    +
    +
    distribution_rules (optional)
    +

    TEXT, default: 'all_segments'. Specifies how to distribute the 'output_table'. This is important for how the fit function will use resources on the cluster. The default 'all_segments' means the 'output_table' will be distributed to all segments in the database cluster.

    +

    If you specify 'gpu_segments' then the 'output_table' will be distributed to all segments that are on hosts that have GPUs attached. This will make maximum use of GPU resources when training a deep learning model.

    +

    You can also specify the name of a resources table containing the segments to be used for training. This table must contain a column called 'dbid' that specifies the segment id from the 'gp_segment_configuration' table [2]. Refer to the utility function GPU Configuration for more information on how to identify segments attached to hosts that are GPU enabled.

    +

    +
    +
    +

    Output Tables

    + The output tables produced by both training_preprocessor_dl() and validation_preprocessor_dl() contain the following columns: + + + + + + + + + + +
    <independent_varname> BYTEA. Packed array of independent variables in PostgreSQL bytea format. Arrays of independent variables packed into the output table are normalized by dividing each element in the independent variable array by the optional 'normalizing_const' parameter. Training data is shuffled, but validation data is not.
    <dependent_varname> BYTEA. Packed array of dependent variables in PostgreSQL bytea format. The dependent variable is always one-hot encoded as an integer array. For now, we are assuming that input_preprocessor_dl() will be used only for classification problems using deep learning. So the dependent variable is one-hot encoded, unless it's already a numeric array in which case we assume it's already one-hot encoded and just cast it to an integer array.
    <independent_varname>_shape INTEGER[]. Shape of the independent variable array after preprocessing. The first element is the number of images packed per row, and subsequent elements will depend on how the image is described (e.g., channels first or last).
    <dependent_varname>_shape INTEGER[]. Shape of the dependent variable array after preprocessing. The first element is the number of images packed per row, and the second element is the number of class values.
    buffer_id INTEGER. Unique id for each row in the packed table.
    +
    +

    A summary table named <output_table>_summary is also created, which has the following columns (the columns are the same for both validation_preprocessor_dl() and training_preprocessor_dl() ):

    + + + + + + + + + + + + + + + + + + + + + + +
    source_table Name of the source table.
    output_table Name of output table generated by preprocessor.
    dependent_varname Dependent variable from the source table.
    independent_varname Independent variable from the source table.
    dependent_vartype Type of the dependent variable from the source table.
    <dependent_varname>_class_values The dependent level values that one-hot encoding maps to for the dependent variable.
    buffer_size Buffer size used in preprocessing step.
    normalizing_const The value used to normalize the input image data.
    num_classes Number of dependent levels the one-hot encoding is created for. NULLs are padded at the end if the number of distinct class levels found in the input data is less than the 'num_classes' parameter specified in training_preprocessor_dl().
    distribution_rules This is the list of segment id's in the form of 'dbid' describing how the 'output_table' is distributed, as per the 'distribution_rules' input parameter. If the 'distribution_rules' parameter is set to 'all_segments', then this will also be set to 'all_segments'.
    __internal_gpu_config__ For internal use. (Note: this is the list of segment id's where data is distributed in the form of 'content' id, which is different from 'dbid' [2].)
    +

    Examples
      +
    1. Create an artificial 2x2 resolution color image data set with 3 possible classifications. The RGB values are per-pixel arrays: 
      +DROP TABLE IF EXISTS image_data;
+CREATE TABLE image_data AS (
+    SELECT ARRAY[
+        ARRAY[
+            ARRAY[(random() * 256)::integer, -- pixel (1,1)
+                (random() * 256)::integer,
+                (random() * 256)::integer],
+            ARRAY[(random() * 256)::integer, -- pixel (2,1)
+                (random() * 256)::integer,
+                (random() * 256)::integer]
+        ],
+        ARRAY[
+            ARRAY[(random() * 256)::integer, -- pixel (1,2)
+                (random() * 256)::integer,
+                (random() * 256)::integer],
+            ARRAY[(random() * 256)::integer, -- pixel (2,1)
+                (random() * 256)::integer,
+                (random() * 256)::integer]
+        ]
+    ] as rgb, ('{cat,dog,bird}'::text[])[ceil(random()*3)] as species
+    FROM generate_series(1, 52)
+);
+SELECT * FROM image_data;
+
      +                             rgb                              | species
+--------------------------------------------------------------+---------
+ {{{124,198,44},{91,47,130}},{{24,175,69},{196,189,166}}}     | dog
+ {{{111,202,129},{198,249,254}},{{141,37,88},{187,167,113}}}  | dog
+ {{{235,53,39},{145,167,209}},{{197,147,222},{55,218,53}}}    | dog
+ {{{231,48,125},{248,233,151}},{{63,125,230},{33,24,70}}}     | dog
+ {{{92,146,121},{163,241,110}},{{75,88,72},{218,90,12}}}      | bird
+ {{{88,114,59},{202,211,152}},{{92,76,58},{77,186,134}}}      | dog
+ {{{2,96,255},{14,48,19}},{{240,55,115},{137,255,245}}}       | dog
+ {{{165,122,98},{16,115,240}},{{4,106,116},{108,242,210}}}    | dog
+ {{{155,207,101},{214,167,24}},{{118,240,228},{199,230,21}}}  | dog
+ {{{94,212,15},{48,66,170}},{{255,167,128},{166,191,246}}}    | dog
+ {{{169,69,131},{16,98,225}},{{228,113,17},{38,27,17}}}       | bird
+ {{{156,183,139},{146,77,46}},{{80,202,230},{146,84,239}}}    | dog
+ {{{190,210,147},{227,31,66}},{{229,251,84},{51,118,240}}}    | bird
+ {{{253,175,200},{237,151,107}},{{207,56,162},{133,39,35}}}   | cat
+ {{{146,185,108},{14,10,105}},{{188,210,86},{83,61,36}}}      | dog
+ {{{223,169,177},{3,200,250}},{{112,91,16},{193,32,151}}}     | cat
+ {{{249,145,240},{144,153,58}},{{131,156,230},{56,50,75}}}    | dog
+ {{{212,186,229},{52,251,197}},{{230,121,201},{35,215,119}}}  | cat
+ {{{234,94,23},{114,196,94}},{{242,249,90},{223,24,109}}}     | bird
+ {{{111,36,145},{77,135,123}},{{171,158,237},{111,252,222}}}  | dog
+ {{{90,74,240},{231,133,95}},{{11,21,173},{146,144,88}}}      | cat
+ {{{170,52,237},{13,114,71}},{{87,99,46},{220,194,56}}}       | bird
+ {{{8,17,92},{64,2,203}},{{10,131,145},{4,129,30}}}           | cat
+ {{{217,218,207},{74,68,186}},{{127,107,76},{38,60,16}}}      | bird
+ {{{193,34,83},{203,99,58}},{{251,224,50},{228,118,113}}}     | dog
+ {{{146,218,155},{32,159,243}},{{146,218,189},{101,114,25}}}  | bird
+ {{{179,160,74},{204,81,246}},{{50,189,39},{60,42,185}}}      | cat
+ {{{13,82,174},{198,151,84}},{{65,249,100},{179,234,104}}}    | cat
+ {{{162,190,124},{184,66,138}},{{10,240,80},{161,68,145}}}    | dog
+ {{{164,144,199},{53,42,111}},{{122,174,128},{220,143,100}}}  | cat
+ {{{160,138,104},{177,86,3}},{{104,226,149},{181,16,229}}}    | dog
+ {{{246,119,211},{229,249,119}},{{117,192,172},{159,47,38}}}  | cat
+ {{{175,1,220},{18,78,124}},{{156,181,45},{242,185,148}}}     | bird
+ {{{50,113,246},{101,213,180}},{{56,103,151},{87,169,124}}}   | cat
+ {{{73,109,147},{22,81,197}},{{135,71,42},{91,251,98}}}       | bird
+ {{{206,61,255},{25,151,211}},{{211,124,7},{206,64,237}}}     | cat
+ {{{201,71,34},{182,142,43}},{{198,172,171},{230,1,23}}}      | bird
+ {{{142,158,2},{223,45,205}},{{118,177,223},{232,178,141}}}   | cat
+ {{{86,190,128},{195,172,14}},{{97,173,237},{142,123,99}}}    | cat
+ {{{26,72,148},{79,226,156}},{{96,62,220},{99,9,230}}}        | bird
+ {{{154,234,103},{184,18,65}},{{146,225,139},{214,156,10}}}   | cat
+ {{{244,169,103},{218,143,2}},{{196,246,186},{214,55,76}}}    | bird
+ {{{20,226,7},{96,153,200}},{{130,236,147},{229,38,142}}}     | bird
+ {{{172,102,107},{50,11,109}},{{145,9,123},{193,28,107}}}     | bird
+ {{{143,243,247},{132,104,137}},{{94,3,169},{253,246,59}}}    | bird
+ {{{78,74,228},{51,200,218}},{{170,155,190},{164,18,51}}}     | dog
+ {{{163,226,161},{56,182,239}},{{129,154,35},{73,116,205}}}   | bird
+ {{{74,243,3},{172,182,149}},{{101,34,163},{111,138,95}}}     | cat
+ {{{224,178,126},{4,61,93}},{{174,238,96},{118,232,208}}}     | bird
+ {{{55,236,249},{7,189,242}},{{151,173,130},{49,232,5}}}      | bird
+ {{{9,16,30},{128,32,85}},{{108,25,91},{41,11,243}}}          | bird
+ {{{141,35,191},{146,240,141}},{{207,239,166},{102,194,121}}} | bird
+(52 rows)
+
      2. +
    2. Run the preprocessor for training image data: 
      +DROP TABLE IF EXISTS image_data_packed, image_data_packed_summary;
+SELECT madlib.training_preprocessor_dl('image_data',         -- Source table
+                                        'image_data_packed',  -- Output table
+                                        'species',            -- Dependent variable
+                                        'rgb',                -- Independent variable
+                                        NULL,                 -- Buffer size
+                                        255                   -- Normalizing constant
+                                        );
+
      For small datasets like in this example, buffer size is mainly determined by the number of segments in the database. For a Greenplum database with 2 segments, there will be 2 rows with a buffer size of 26. For PostgresSQL, there would be only one row with a buffer size of 52 since it is a single node database. For larger data sets, other factors go into computing buffers size besides number of segments. Here is the packed output table of training data for our simple example: 
      +SELECT rgb_shape, species_shape, buffer_id FROM image_data_packed ORDER BY buffer_id;
+
      + rgb_shape  | species_shape | buffer_id
+------------+---------------+-----------
+ {18,2,2,3} | {18,3}        |         0
+ {18,2,2,3} | {18,3}        |         1
+ {16,2,2,3} | {16,3}        |         2
+(3 rows)
+
      Review the output summary table: 
      +\x on
+SELECT * FROM image_data_packed_summary;
+
      +-[ RECORD 1 ]-----------+------------------
+source_table            | image_data
+output_table            | image_data_packed
+dependent_varname       | {species}
+independent_varname     | {rgb}
+dependent_vartype       | {text}
+species_class_values    | {bird,cat,dog}
+buffer_size             | 18
+normalizing_const       | 255
+num_classes             | {3}
+distribution_rules      | all_segments
+__internal_gpu_config__ | all_segments
+
      3. +
    3. Run the preprocessor for the validation dataset. In this example, we use the same images for validation to demonstrate, but normally validation data is different than training data: 
      +DROP TABLE IF EXISTS val_image_data_packed, val_image_data_packed_summary;
+SELECT madlib.validation_preprocessor_dl(
+      'image_data',             -- Source table
+      'val_image_data_packed',  -- Output table
+      'species',                -- Dependent variable
+      'rgb',                    -- Independent variable
+      'image_data_packed',      -- From training preprocessor step
+      NULL                      -- Buffer size
+      );
+
      We could choose to use a different buffer size compared to the training_preprocessor_dl run (but generally don't need to). Other parameters such as num_classes and normalizing_const that were passed to training_preprocessor_dl are automatically inferred using the image_data_packed param that is passed. Here is the packed output table of validation data for our simple example: 
      +SELECT rgb_shape, species_shape, buffer_id FROM val_image_data_packed ORDER BY buffer_id;
+
      + rgb_shape  | species_shape | buffer_id
+------------+---------------+-----------
+ {18,2,2,3} | {18,3}        |         0
+ {18,2,2,3} | {18,3}        |         1
+ {16,2,2,3} | {16,3}        |         2
+(3 rows)
+
      Review the output summary table: 
      +\x on
+SELECT * FROM val_image_data_packed_summary;
+
      +-[ RECORD 1 ]-----------+----------------------
+source_table            | image_data
+output_table            | val_image_data_packed
+dependent_varname       | {species}
+independent_varname     | {rgb}
+dependent_vartype       | {text}
+species_class_values    | {bird,cat,dog}
+buffer_size             | 18
+normalizing_const       | 255
+num_classes             | {3}
+distribution_rules      | all_segments
+__internal_gpu_config__ | all_segments
+
      4. +
    4. Load data in another format. Create an artificial 2x2 resolution color image data set with 3 possible classifications. The RGB values are unrolled into a flat array: 
      +DROP TABLE IF EXISTS image_data;
+CREATE TABLE image_data AS (
+SELECT ARRAY[
+        (random() * 256)::integer, -- R values
+        (random() * 256)::integer,
+        (random() * 256)::integer,
+        (random() * 256)::integer,
+        (random() * 256)::integer, -- G values
+        (random() * 256)::integer,
+        (random() * 256)::integer,
+        (random() * 256)::integer,
+        (random() * 256)::integer, -- B values
+        (random() * 256)::integer,
+        (random() * 256)::integer,
+        (random() * 256)::integer
+    ] as rgb, ('{cat,dog,bird}'::text[])[ceil(random()*3)] as species
+FROM generate_series(1, 52)
+);
+SELECT * FROM image_data;
+
      +                       rgb                        | species
+--------------------------------------------------+---------
+ {26,150,191,113,235,57,145,143,44,145,85,25}     | dog
+ {240,43,225,15,220,136,186,209,49,130,55,111}    | bird
+ {25,191,37,77,193,62,249,228,97,33,81,7}         | cat
+ {141,223,46,195,201,19,207,78,160,130,157,89}    | cat
+ {39,249,168,164,223,193,99,4,14,37,66,7}         | cat
+ {159,250,127,44,151,254,11,211,247,137,79,233}   | cat
+ {19,230,76,253,42,175,230,143,184,133,27,215}    | cat
+ {199,224,144,5,64,19,200,186,109,218,108,70}     | bird
+ {148,136,4,41,185,104,203,253,113,151,166,76}    | bird
+ {230,132,114,213,210,139,91,199,240,142,203,75}  | bird
+ {166,188,96,217,135,70,93,249,27,47,132,118}     | bird
+ {118,120,222,236,110,83,240,47,19,206,222,51}    | bird
+ {230,3,26,47,93,144,167,59,123,21,142,107}       | cat
+ {250,224,62,136,112,142,88,187,24,1,168,216}     | bird
+ {52,144,231,12,76,1,162,11,114,141,69,3}         | cat
+ {166,172,246,169,200,102,62,57,239,75,165,88}    | dog
+ {151,50,112,227,199,97,47,4,43,123,116,133}      | bird
+ {39,185,96,127,80,248,177,191,218,120,32,9}      | dog
+ {25,172,34,34,40,109,166,23,60,216,246,54}       | bird
+ {163,39,89,170,95,230,137,141,169,82,159,121}    | dog
+ {131,143,183,138,151,90,177,240,4,16,214,141}    | dog
+ {99,233,100,9,159,140,30,202,29,169,120,62}      | bird
+ {99,162,69,10,204,169,219,20,106,170,111,16}     | bird
+ {16,246,27,32,187,226,0,75,231,64,94,175}        | bird
+ {25,135,244,101,50,4,91,77,36,22,47,37}          | dog
+ {22,101,191,197,96,138,78,198,155,138,193,51}    | bird
+ {236,22,110,30,181,20,218,21,236,97,91,73}       | dog
+ {160,57,34,212,239,197,233,174,164,97,88,153}    | cat
+ {226,170,192,123,242,224,190,51,163,192,91,105}  | bird
+ {149,174,12,72,112,1,37,153,118,201,79,121}      | bird
+ {34,250,232,222,218,221,234,201,138,66,186,58}   | bird
+ {162,55,85,159,247,234,77,3,50,189,4,87}         | dog
+ {122,32,164,243,0,198,237,232,164,199,197,142}   | dog
+ {80,209,75,138,169,236,193,254,140,184,232,217}  | bird
+ {112,148,114,137,13,107,105,75,243,218,218,75}   | dog
+ {241,76,61,202,76,112,90,51,125,166,52,30}       | bird
+ {75,132,239,207,49,224,250,19,238,214,154,169}   | dog
+ {203,43,222,58,231,5,243,71,131,67,63,52}        | cat
+ {229,12,133,142,179,80,185,145,138,160,149,125}  | bird
+ {64,251,61,153,13,100,145,181,8,112,118,107}     | dog
+ {128,223,60,248,126,124,243,188,20,0,31,166}     | bird
+ {39,22,43,146,138,174,33,65,56,184,155,234}      | dog
+ {177,247,133,154,159,37,148,30,81,43,29,92}      | bird
+ {56,127,199,118,105,120,109,239,18,12,20,166}    | cat
+ {101,209,72,193,207,91,166,27,88,209,203,62}     | dog
+ {131,195,122,90,18,178,217,217,40,66,81,149}     | cat
+ {203,137,103,17,60,251,152,64,36,81,168,239}     | cat
+ {239,97,10,20,194,32,121,129,228,217,11,50}      | dog
+ {117,4,193,192,223,176,33,232,196,226,8,61}      | dog
+ {162,21,190,223,120,170,245,230,200,170,250,163} | bird
+ {32,67,65,195,2,39,198,28,86,35,172,254}         | dog
+ {39,19,236,146,87,140,203,121,96,187,62,73}      | dog
+(52 rows)
+
      5. +
    5. Run the preprocessor for training image data: 
      +DROP TABLE IF EXISTS image_data_packed, image_data_packed_summary;
+SELECT madlib.training_preprocessor_dl('image_data',         -- Source table
+                                        'image_data_packed',  -- Output table
+                                        'species',            -- Dependent variable
+                                        'rgb',                -- Independent variable
+                                        NULL,                 -- Buffer size
+                                        255                   -- Normalizing constant
+                                        );
+
      Here is a sample of the packed output table: 
      +SELECT rgb_shape, species_shape, buffer_id FROM image_data_packed ORDER BY buffer_id;
+
      + rgb_shape | species_shape | buffer_id
+-----------+---------------+-----------
+ {18,12}   | {18,3}        |         0
+ {18,12}   | {18,3}        |         1
+ {16,12}   | {16,3}        |         2
+(3 rows)
+
      6. +
    6. Run the preprocessor for the validation dataset. In this example, we use the same images for validation to demonstrate, but normally validation data is different than training data: 
      +DROP TABLE IF EXISTS val_image_data_packed, val_image_data_packed_summary;
+SELECT madlib.validation_preprocessor_dl(
+    'image_data',             -- Source table
+    'val_image_data_packed',  -- Output table
+    'species',                -- Dependent variable
+    'rgb',                    -- Independent variable
+    'image_data_packed',      -- From training preprocessor step
+    NULL                      -- Buffer size
+    );
+
      Here is a sample of the packed output summary table: 
      +SELECT rgb_shape, species_shape, buffer_id FROM val_image_data_packed ORDER BY buffer_id;
+
      + rgb_shape | species_shape | buffer_id
+-----------+---------------+-----------
+ {18,12}   | {18,3}        |         0
+ {18,12}   | {18,3}        |         1
+ {16,12}   | {16,3}        |         2
+(3 rows)
+
      7. +
    7. Generally the default buffer size will work well, but if you have occasion to change it: 
      +DROP TABLE IF EXISTS image_data_packed, image_data_packed_summary;
+SELECT madlib.training_preprocessor_dl('image_data',         -- Source table
+                                       'image_data_packed',  -- Output table
+                                       'species',            -- Dependent variable
+                                       'rgb',                -- Independent variable
+                                        10,                   -- Buffer size
+                                        255                   -- Normalizing constant
+                                        );
+SELECT rgb_shape, species_shape, buffer_id FROM image_data_packed ORDER BY buffer_id;
+
      + rgb_shape | species_shape | buffer_id
+-----------+---------------+-----------
+ {9,12}    | {9,3}         |         0
+ {9,12}    | {9,3}         |         1
+ {9,12}    | {9,3}         |         2
+ {9,12}    | {9,3}         |         3
+ {9,12}    | {9,3}         |         4
+ {7,12}    | {7,3}         |         5
+(6 rows)
+
      Review the output summary table: 
      +\x on
+SELECT * FROM image_data_packed_summary;
+
      +-[ RECORD 1 ]-----------+------------------
+source_table            | image_data
+output_table            | image_data_packed
+dependent_varname       | {species}
+independent_varname     | {rgb}
+dependent_vartype       | {text}
+species_class_values    | {bird,cat,dog}
+buffer_size             | 9
+normalizing_const       | 255
+num_classes             | {3}
+distribution_rules      | all_segments
+__internal_gpu_config__ | all_segments
+
      8. +
    8. Run the preprocessor for image data with num_classes greater than 3 (distinct class values found in table): 
      +DROP TABLE IF EXISTS image_data_packed, image_data_packed_summary;
+SELECT madlib.training_preprocessor_dl('image_data',         -- Source table
+                                        'image_data_packed',  -- Output table
+                                        'species',            -- Dependent variable
+                                        'rgb',                -- Independent variable
+                                        NULL,                 -- Buffer size
+                                        255,                  -- Normalizing constant
+                                        ARRAY[5]              -- Number of desired class values
+                                        );
+
      Here is a sample of the packed output table with the padded 1-hot vector: 
      +SELECT rgb_shape, species_shape, buffer_id FROM image_data_packed ORDER BY buffer_id;
+
      + rgb_shape | species_shape | buffer_id
+-----------+---------------+-----------
+ {18,12}   | {18,5}        |         0
+ {18,12}   | {18,5}        |         1
+ {16,12}   | {16,5}        |         2
+(3 rows)
+
      Review the output summary table: 
      +\x on
+SELECT * FROM image_data_packed_summary;
+
      +-[ RECORD 1 ]-----------+-------------------------
+source_table            | image_data
+output_table            | image_data_packed
+dependent_varname       | {species}
+independent_varname     | {rgb}
+dependent_vartype       | {text}
+species_class_values    | {bird,cat,dog,NULL,NULL}
+buffer_size             | 18
+normalizing_const       | 255
+num_classes             | {5}
+distribution_rules      | all_segments
+__internal_gpu_config__ | all_segments
+
      9. +
    9. Using distribution rules to specify how to distribute the 'output_table'. This is important for how the fit function will use resources on the cluster. To distribute to all segments on hosts with GPUs attached: 
      +DROP TABLE IF EXISTS image_data_packed, image_data_packed_summary;
+SELECT madlib.training_preprocessor_dl('image_data',          -- Source table
+                                        'image_data_packed',  -- Output table
+                                        'species',            -- Dependent variable
+                                        'rgb',                -- Independent variable
+                                        NULL,                 -- Buffer size
+                                        255,                  -- Normalizing constant
+                                        NULL,                 -- Number of classes
+                                        'gpu_segments'        -- Distribution rules
+                                        );
+\x on
+SELECT * FROM image_data_packed_summary;
+
      +-[ RECORD 1 ]-----------+------------------
+source_table            | image_data
+output_table            | image_data_packed
+dependent_varname       | {species}
+independent_varname     | {rgb}
+dependent_vartype       | {text}
+species_class_values    | {bird,cat,dog}
+buffer_size             | 26
+normalizing_const       | 255
+num_classes             | {3}
+distribution_rules      | {2,3,4,5}
+__internal_gpu_config__ | {0,1,2,3}
+
      To distribute to only specified segments, create a distribution table with a column called 'dbid' that lists the segments you want: 
      +DROP TABLE IF EXISTS segments_to_use;
+CREATE TABLE segments_to_use(
+    dbid INTEGER,
+    hostname TEXT
+);
+INSERT INTO segments_to_use VALUES
+(2, 'hostname-01'),
+(3, 'hostname-01');
+DROP TABLE IF EXISTS image_data_packed, image_data_packed_summary;
+SELECT madlib.training_preprocessor_dl('image_data',          -- Source table
+                                        'image_data_packed',  -- Output table
+                                        'species',            -- Dependent variable
+                                        'rgb',                -- Independent variable
+                                        NULL,                 -- Buffer size
+                                        255,                  -- Normalizing constant
+                                        NULL,                 -- Number of classes
+                                        'segments_to_use'     -- Distribution rules
+                                        );
+\x on
+SELECT * FROM image_data_packed_summary;
+
      +-[ RECORD 1 ]-----------+------------------
+source_table            | image_data
+output_table            | image_data_packed
+dependent_varname       | {species}
+independent_varname     | {rgb}
+dependent_vartype       | {text}
+species_class_values    | {bird,cat,dog}
+buffer_size             | 26
+normalizing_const       | 255
+num_classes             | {3}
+distribution_rules      | {2,3}
+__internal_gpu_config__ | {0,1}
+
      10. +
    +
    +

    References
    +

    [1] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent, Geoffrey Hinton with Nitish Srivastava and Kevin Swersky, http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

    +

    [2] Greenplum 'gp_segment_configuration' table https://gpdb.docs.pivotal.io/latest/ref_guide/system_catalogs/gp_segment_configuration.html

    +

    Related Topics
    +

    training_preprocessor_dl()

    +

    validation_preprocessor_dl()

    +

    gpu_configuration()

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__keras.html b/docs/docs/v2.1.0/group__grp__keras.html new file mode 100644 index 00000000..062abd94 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__keras.html @@ -0,0 +1,1328 @@ + + + + + + + + +MADlib: Train Single Model + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Train Single Model
    Deep Learning
    +
    +
    +
    Contents +

    This module allows you to use SQL to call deep learning models designed in Keras [1], which is a high-level neural network API written in Python.

    +

    Keras can run on top of different backends and the one that is currently supported by MADlib is TensorFlow [2]. The implementation in MADlib is designed to train a single model across multiple segments (workers) in Greenplum database. (PostgreSQL is also supported.) Alternatively, to train multiple models at the same time for model architecture search or hyperparameter tuning, you can use the methods in Train Multiple Models.

    +

    The main use case supported is classification using sequential models, which are made up of a linear stack of layers. This includes multilayer perceptrons (MLPs) and convolutional neural networks (CNNs). Regression is not currently supported.

    +

    Before using Keras in MADlib you will need to preprocess your training and evaluation datasets by using the method called Preprocess Data which is a utility that prepares data for use by models that support mini-batch as an optimization option. This is a one-time operation and you would only need to re-run the preprocessor if your input data has changed. The advantage of using mini-batching is that it can perform better than stochastic gradient descent because it uses more than one training example at a time, typically resulting faster and smoother convergence [3].

    +

    You can also do inference on models that have not been trained in MADlib, but rather imported from an external source. This is described in the section called "Predict BYOM" below, where "BYOM" stands for "Bring Your Own Model."

    +

    Note that the following MADlib functions are targeting a specific TensorFlow kernel version (1.14). Using a newer or older version may or may not work as intended.

    +

    MADlib's deep learning methods are designed to use the TensorFlow package and its built in Keras functions. To ensure consistency, please use tensorflow.keras objects (models, layers, etc.) instead of importing Keras and using its objects.

    +
    Note
    CUDA GPU memory cannot be released until the process holding it is terminated. When a MADlib deep learning function is called with GPUs, Greenplum internally creates a process (called a slice) which calls TensorFlow to do the computation. This process holds the GPU memory until one of the following two things happen: query finishes and user logs out of the Postgres client/session; or, query finishes and user waits for the timeout set by gp_vmem_idle_resource_timeout. The default value for this timeout is 18 sec [8]. So the recommendation is: log out/reconnect to the session after every GPU query; or wait for gp_vmem_idle_resource_timeout before you run another GPU query (you can also set it to a lower value).
    +

    Fit
    The fit (training) function has the following format:
    +
    +madlib_keras_fit(
+    source_table,
+    model,
+    model_arch_table,
+    model_id,
+    compile_params,
+    fit_params,
+    num_iterations,
+    use_gpus,
+    validation_table,
+    metrics_compute_frequency,
+    warm_start,
+    name,
+    description,
+    object_table
+    )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the training data. This is the name of the output table from the data preprocessor. Independent and dependent variables are specified in the preprocessor step which is why you do not need to explictly state them here as part of the fit function.

    +

    +
    +
    model
    +

    TEXT. Name of the output table containing the model. Details of the output table are shown below.

    +

    +
    +
    model_arch_table
    +

    TEXT. Name of the table containing the model architecture and (optionally) initial weights to use for training.

    +

    +
    +
    model_id
    +

    INTEGER. This is the id in 'model_arch_table' containing the model architecture and (optionally) initial weights to use for training.

    +

    +
    +
    compile_params
    +

    TEXT. Parameters passed to the compile method of the Keras model class [4]. These parameters will be passed through as is so they must conform to the Keras API definition. As an example, you might use something like: loss='categorical_crossentropy', optimizer='adam', metrics=['acc']. The mandatory parameters that must be specified are 'optimizer' and 'loss'. Others are optional and will use the default values as per Keras if not specified here. Also, when specifying 'loss' and 'metrics' do not include the module and submodule prefixes like loss='losses.categorical_crossentropy' or optimizer='keras.optmizers.adam'.

    +
    Note
      +
    • Custom loss functions and custom metrics can be used as defined in Define Custom Functions. List the custom function name and provide the name of the table where the serialized Python objects reside using the parameter 'object_table' below.
      • +
    • The following loss function is not supported: sparse_categorical_crossentropy. The following metrics are not supported: sparse_categorical_accuracy, sparse_top_k_categorical_accuracy.
      • +
    • The Keras accuracy parameter top_k_categorical_accuracy returns top 5 accuracy by default. If you want a different top k value, use the helper function Top k Accuracy Function to create a custom Python function to compute the top k accuracy that you want.
      • +
    +
    +

    +
    +
    fit_params
    +

    TEXT. Parameters passed to the fit method of the Keras model class [4]. These will be passed through as is so they must conform to the Keras API definition. As an example, you might use something like: batch_size=128, epochs=4. There are no mandatory parameters so if you specify NULL, it will use all default values as per Keras.

    +
    Note
    Callbacks are not currently supported except for TensorBoard which you can specify in the usual way, e.g., callbacks=[TensorBoard(log_dir="/tmp/logs/fit")]
    +
    +
    num_iterations
    +

    INTEGER. Number of iterations to train.

    +

    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.

    +
    Note
    This parameter must not conflict with how the distribution rules are set in the preprocessor function. For example, if you set a distribution rule to use certain segments on hosts that do not have GPUs attached, you will get an error if you set ‘use_gpus’ to TRUE. Also, we have seen some memory related issues when segments share GPU resources. For example, if you have 1 GPU per segment host and your cluster has 4 segments per segment host, it means that all 4 segments will share the same GPU on each host. The current recommended configuration is 1 GPU per segment.
    +
    +
    validation_table (optional)
    +

    TEXT, default: none. Name of the table containing the validation dataset. Note that the validation dataset must be preprocessed in the same way as the training dataset, so this is the name of the output table from running the data preprocessor on the validation dataset. Using a validation dataset can mean a longer training time, depending on its size. This can be controlled using the 'metrics_compute_frequency' paremeter described below.

    +

    +
    +
    metrics_compute_frequency (optional)
    +

    INTEGER, default: once at the end of training after 'num_iterations'. Frequency to compute per-iteration metrics for the training dataset and validation dataset (if specified). There can be considerable cost to computing metrics every iteration, especially if the training dataset is large. This parameter is a way of controlling the frequency of those computations. For example, if you specify 5, then metrics will be computed every 5 iterations as well as at the end of training after 'num_iterations'. If you use the default, metrics will be computed only once after 'num_iterations' have completed.

    +

    +
    +
    warm_start (optional)
    +

    BOOLEAN, default: FALSE. Initalize weights with the coefficients from the last call of the fit function. If set to TRUE, weights will be initialized from the model table generated by the previous training run.

    +
    Note
    The warm start feature works based on the name of the model output table from a previous training run. When using warm start, do not drop the model output table or the model output summary table before calling the fit function, since these are needed to obtain the weights from the previous run. If you are not using warm start, the model output table and the model output table summary must be dropped in the usual way before calling the training function.
    +
    +
    name (optional)
    +

    TEXT, default: NULL. Free text string to identify a name, if desired.

    +

    +
    +
    description (optional)
    +

    TEXT, default: NULL. Free text string to provide a description, if desired.

    +

    +
    +
    object_table (optional)
    +
    TEXT, default: NULL. Name of the table that contains the custom functions. Note that this table must be created using the Define Custom Functions method. Do not qualify with a schema name, since schema will be automatically pulled from the function definition.
    +
    +

    Output tables
    + The model table produced by fit contains the following columns:

    + + + + +
    model_weights BYTEA8. Byte array containing the weights of the neural net.
    model_arch TEXT. A JSON representation of the model architecture used in training.
    +

    A summary table named <model>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    source_table Source table used for training.
    model Model output table produced by training.
    dependent_varname Dependent variable column from the original source table in the data preprocessing step.
    independent_varname Independent variables column from the original source table in the data preprocessing step.
    model_arch_table Name of the table containing the model architecture and (optionally) the initial model weights.
    model_id The id of the model in the model architecture table used for training.
    compile_params Compile parameters passed to Keras.
    fit_params Fit parameters passed to Keras.
    num_iterations Number of iterations of training completed.
    validation_table Name of the table containing the validation dataset (if specified).
    metrics_compute_frequency Frequency that per-iteration metrics are computed for the training dataset and validation dataset.
    name Name of the training run (free text).
    description Description of the training run (free text).
    model_type General identifier for type of model trained. Currently says 'madlib_keras'.
    model_size Size of the model in KB. Models are stored in 'bytea' data format which is used for binary strings in PostgreSQL type databases.
    start_training_time Timestamp for start of training.
    end_training_time Timestamp for end of training.
    metrics_elapsed_time Array of elapsed time for metric computations as per the 'metrics_compute_frequency' parameter. Useful for drawing a curve showing loss, accuracy or other metrics as a function of time. For example, if 'metrics_compute_frequency=5' this would be an array of elapsed time for every 5th iteration, plus the last iteration. Note that this field reports the time for training + validation, if there is a validation table provided.
    madlib_version Version of MADlib used.
    num_classes Count of distinct classes values used for each dependent variable.
    dependent_vartype Data type for each dependent variable.
    normalizing_constant Normalizing constant used from the data preprocessing step.
    metrics_type Metric specified in the 'compile_params'.
    loss_type Loss specified in the 'compile_params'.
    training_metrics_final Final value of the training metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
    training_loss_final Final value of the training loss after all iterations have completed.
    training_metrics Array of training metrics as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of metrics for every 5th iteration, plus the last iteration.
    training_loss Array of training losses as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of losses for every 5th iteration, plus the last iteration.
    validation_metrics_final Final value of the validation metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
    validation_loss_final Final value of the validation loss after all iterations have completed.
    validation_metrics Array of validation metrics as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of metrics for every 5th iteration, plus the last iteration.
    validation_loss Array of validation losses as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of losses for every 5th iteration, plus the last iteration.
    metrics_iters Array indicating the iterations for which metrics are calculated, as derived from the parameters 'num_iterations' and 'metrics_compute_frequency'. For example, if 'num_iterations=5' and 'metrics_compute_frequency=2', then 'metrics_iters' value would be {2,4,5} indicating that metrics were computed at iterations 2, 4 and 5 (at the end). If 'num_iterations=5' and 'metrics_compute_frequency=1', then 'metrics_iters' value would be {1,2,3,4,5} indicating that metrics were computed at every iteration.
    <dependent_varname>_class_values Array of class values used for a particular dependent variable. A column will be generated for each dependent variable.
    +

    Evaluate
    The evaluation function has the following format:
    +
    +madlib_keras_evaluate(
+    model_table,
+    test_table,
+    output_table,
+    use_gpus
+    )
+

    Arguments

    +
    model_table
    +

    TEXT. Name of the table containing the model to use for validation.

    +

    +
    +
    test_table
    +

    TEXT. Name of the table containing the evaluation dataset. Note that test/validation data must be preprocessed in the same way as the training dataset, so this is the name of the output table from the data preprocessor. Independent and dependent variables are specified in the preprocessor step which is why you do not need to explictly state them here as part of the fit function.

    +

    +
    +
    output_table
    +
    TEXT. Name of table that validation output will be written to. Table contains: + + + + + + + + +
    loss Loss value on evaluation dataset, where 'loss_type' below identifies the type of loss.
    metric Metric value on evaluation dataset, where 'metrics_type' below identifies the type of metric.
    metrics_type Type of metric function that was used in the training step. (It means you cannot have a different metric in evaluate compared to training.)
    loss_type

    Type of loss function that was used in the training step. (It means you cannot have a different loss in evaluate compared to training.)

    +

    +
    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.

    +
    Note
    This parameter must not conflict with how the distribution rules are set in the preprocessor function. For example, if you set a distribution rule to use certain segments on hosts that do not have GPUs attached, you will get an error if you set ‘use_gpus’ to TRUE. Also, we have seen some memory related issues when segments share GPU resources. For example, if you have 1 GPU per segment host and your cluster has 4 segments per segment host, it means that all 4 segments will share the same GPU on each host. The current recommended configuration is 1 GPU per segment.
    +
    +
    +

    Predict
    The prediction function has the following format: 
    +madlib_keras_predict(
+    model_table,
+    test_table,
+    id_col,
+    independent_varname,
+    output_table,
+    pred_type,
+    use_gpus
+    )
+
    +

    Arguments

    +
    model_table
    +

    TEXT. Name of the table containing the model to use for prediction.

    +

    +
    +
    test_table
    +

    TEXT. Name of the table containing the dataset to predict on. Note that test data is not preprocessed (unlike fit and evaluate) so put one test image per row for prediction. Also see the comment below for the 'independent_varname' parameter regarding normalization.

    +

    +

    +
    +
    id_col
    +

    TEXT. Name of the id column in the test data table.

    +

    +
    +
    independent_varname
    +

    TEXT. Column with independent variables in the test table. If a 'normalizing_const' is specified when preprocessing the training dataset, this same normalization will be applied to the independent variables used in predict. In the case that there are multiple independent variables, representing a multi-input neural network, put the columns as a comma separated list, e.g., 'indep_var1, indep_var2, indep_var3' in the same way as was done in the preprocessor step for the training data.

    +

    +
    +
    output_table
    +
    TEXT. Name of the table that prediction output will be written to. Table contains: + + + + + + + + + + +
    id Gives the 'id' for each prediction, corresponding to each row from the test_table.
    class_name Name of variable being predicted.
    class_value Estimated class value.
    prob Probability of a given class value.
    rank

    The rank of a given class based on the ordering of probabilities.

    +

    +
    +
    +
    pred_type (optional)
    +

    TEXT or INTEGER or DOUBLE PRECISION default: 'prob'. The type and range of output desired. This parameter allows the following options.

      +
    • 'response': the actual prediction
      • +
    • 'prob': the probability value for each class
      • +
    • 0<value<1: the lower limit for the probability (double precision)
      • +
    • 1<=value: the lower limit for the rank of the prediction (integer)
      • +
    +

    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Flag to enable GPU support for training neural network. The number of GPUs to use is determined by the parameters passed to the preprocessor.

    +
    Note
    We have seen some memory related issues when segments share GPU resources. For example, if you provide 1 GPU and your database cluster is set up to have 4 segments per segment host, it means that all 4 segments on a segment host will share the same GPU. The current recommended configuration is 1 GPU per segment.
    +
    +
    +

    Predict BYOM (bring your own model)
    The predict BYOM function allows you to do inference on models that have not been trained on MADlib, but rather imported from elsewhere. It has the following format: 
    +madlib_keras_predict_byom(
+    model_arch_table,
+    model_id,
+    test_table,
+    id_col,
+    independent_varname,
+    output_table,
+    pred_type,
+    use_gpus,
+    class_values,
+    normalizing_const,
+    dependent_count
+    )
+
    +

    Arguments

    +
    model_arch_table
    +

    TEXT. Name of the architecture table containing the model to use for prediction. The model weights and architecture can be loaded to this table by using the Define Model Architectures function.

    +

    +
    +
    model_id
    +

    INTEGER. This is the id in 'model_arch_table' containing the model architecture and model weights to use for prediction.

    +

    +
    +
    test_table
    +

    TEXT. Name of the table containing the dataset to predict on. Note that test data is not preprocessed (unlike fit and evaluate) so put one test image per row for prediction. Set the 'normalizing_const' below for the independent variable if necessary.

    +

    +
    +
    id_col
    +

    TEXT. Name of the id column in the test data table.

    +

    +
    +
    independent_varname
    +

    TEXT. Column with independent variables in the test table. Set the 'normalizing_const' below if necessary.

    +

    +
    +
    output_table
    +
    TEXT. Name of the table that prediction output will be written to. Table contains: + + + + + + + + + + +
    id Gives the 'id' for each prediction, corresponding to each row from the test_table.
    class_name The estimated variable.
    class_value The estimated class for classification.
    prob Probability of a given class.
    rank

    The rank of a given class based on the ordering of probabilities.

    +

    +
    +
    +
    pred_type (optional)
    +

    TEXT, default: 'response'. The type of output desired, where 'response' gives the actual prediction and 'prob' gives the probability value for each class.

    +

    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Flag to enable GPU support for training neural network. The number of GPUs to use is determined by the parameters passed to the preprocessor.

    +
    Note
    We have seen some memory related issues when segments share GPU resources. For example, if you provide 1 GPU and your database cluster is set up to have 4 segments per segment host, it means that all 4 segments on a segment host will share the same GPU. The current recommended configuration is 1 GPU per segment.
    +
    +
    class_values (optional)
    +

    TEXT[], default: NULL. Two dimensional list of class labels that were used while training the model for each dependent variable.

    +
    Note
    If you specify the class values parameter, it must reflect how the dependent variable was 1-hot encoded for training. If you accidently pick another order that does not match the 1-hot encoding, the predictions would be wrong.
    +
    +
    normalizing_const (optional)
    +

    DOUBLE PRECISION, default: 1.0. The normalizing constant to divide each value in the 'independent_varname' array by. For example, you would use 255 for this value if the image data is in the form 0-255.

    +

    +
    +
    dependent_count (optional)
    +
    INTEGER, default: 1. The number of dependent variables in the model.
    +
    +

    Examples
    +
    Note
    Deep learning works best on very large datasets, but that is not convenient for a quick introduction to the syntax. So in this example we use an MLP on the well known iris data set from https://archive.ics.uci.edu/ml/datasets/iris. For more realistic examples with images please refer to the deep learning notebooks at https://github.com/apache/madlib-site/tree/asf-site/community-artifacts.
    +

    Classification

    +
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS iris_data;
+CREATE TABLE iris_data(
+    id serial,
+    attributes numeric[],
+    class_text varchar
+);
+INSERT INTO iris_data(id, attributes, class_text) VALUES
+(1,ARRAY[5.1,3.5,1.4,0.2],'Iris-setosa'),
+(2,ARRAY[4.9,3.0,1.4,0.2],'Iris-setosa'),
+(3,ARRAY[4.7,3.2,1.3,0.2],'Iris-setosa'),
+(4,ARRAY[4.6,3.1,1.5,0.2],'Iris-setosa'),
+(5,ARRAY[5.0,3.6,1.4,0.2],'Iris-setosa'),
+(6,ARRAY[5.4,3.9,1.7,0.4],'Iris-setosa'),
+(7,ARRAY[4.6,3.4,1.4,0.3],'Iris-setosa'),
+(8,ARRAY[5.0,3.4,1.5,0.2],'Iris-setosa'),
+(9,ARRAY[4.4,2.9,1.4,0.2],'Iris-setosa'),
+(10,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(11,ARRAY[5.4,3.7,1.5,0.2],'Iris-setosa'),
+(12,ARRAY[4.8,3.4,1.6,0.2],'Iris-setosa'),
+(13,ARRAY[4.8,3.0,1.4,0.1],'Iris-setosa'),
+(14,ARRAY[4.3,3.0,1.1,0.1],'Iris-setosa'),
+(15,ARRAY[5.8,4.0,1.2,0.2],'Iris-setosa'),
+(16,ARRAY[5.7,4.4,1.5,0.4],'Iris-setosa'),
+(17,ARRAY[5.4,3.9,1.3,0.4],'Iris-setosa'),
+(18,ARRAY[5.1,3.5,1.4,0.3],'Iris-setosa'),
+(19,ARRAY[5.7,3.8,1.7,0.3],'Iris-setosa'),
+(20,ARRAY[5.1,3.8,1.5,0.3],'Iris-setosa'),
+(21,ARRAY[5.4,3.4,1.7,0.2],'Iris-setosa'),
+(22,ARRAY[5.1,3.7,1.5,0.4],'Iris-setosa'),
+(23,ARRAY[4.6,3.6,1.0,0.2],'Iris-setosa'),
+(24,ARRAY[5.1,3.3,1.7,0.5],'Iris-setosa'),
+(25,ARRAY[4.8,3.4,1.9,0.2],'Iris-setosa'),
+(26,ARRAY[5.0,3.0,1.6,0.2],'Iris-setosa'),
+(27,ARRAY[5.0,3.4,1.6,0.4],'Iris-setosa'),
+(28,ARRAY[5.2,3.5,1.5,0.2],'Iris-setosa'),
+(29,ARRAY[5.2,3.4,1.4,0.2],'Iris-setosa'),
+(30,ARRAY[4.7,3.2,1.6,0.2],'Iris-setosa'),
+(31,ARRAY[4.8,3.1,1.6,0.2],'Iris-setosa'),
+(32,ARRAY[5.4,3.4,1.5,0.4],'Iris-setosa'),
+(33,ARRAY[5.2,4.1,1.5,0.1],'Iris-setosa'),
+(34,ARRAY[5.5,4.2,1.4,0.2],'Iris-setosa'),
+(35,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(36,ARRAY[5.0,3.2,1.2,0.2],'Iris-setosa'),
+(37,ARRAY[5.5,3.5,1.3,0.2],'Iris-setosa'),
+(38,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(39,ARRAY[4.4,3.0,1.3,0.2],'Iris-setosa'),
+(40,ARRAY[5.1,3.4,1.5,0.2],'Iris-setosa'),
+(41,ARRAY[5.0,3.5,1.3,0.3],'Iris-setosa'),
+(42,ARRAY[4.5,2.3,1.3,0.3],'Iris-setosa'),
+(43,ARRAY[4.4,3.2,1.3,0.2],'Iris-setosa'),
+(44,ARRAY[5.0,3.5,1.6,0.6],'Iris-setosa'),
+(45,ARRAY[5.1,3.8,1.9,0.4],'Iris-setosa'),
+(46,ARRAY[4.8,3.0,1.4,0.3],'Iris-setosa'),
+(47,ARRAY[5.1,3.8,1.6,0.2],'Iris-setosa'),
+(48,ARRAY[4.6,3.2,1.4,0.2],'Iris-setosa'),
+(49,ARRAY[5.3,3.7,1.5,0.2],'Iris-setosa'),
+(50,ARRAY[5.0,3.3,1.4,0.2],'Iris-setosa'),
+(51,ARRAY[7.0,3.2,4.7,1.4],'Iris-versicolor'),
+(52,ARRAY[6.4,3.2,4.5,1.5],'Iris-versicolor'),
+(53,ARRAY[6.9,3.1,4.9,1.5],'Iris-versicolor'),
+(54,ARRAY[5.5,2.3,4.0,1.3],'Iris-versicolor'),
+(55,ARRAY[6.5,2.8,4.6,1.5],'Iris-versicolor'),
+(56,ARRAY[5.7,2.8,4.5,1.3],'Iris-versicolor'),
+(57,ARRAY[6.3,3.3,4.7,1.6],'Iris-versicolor'),
+(58,ARRAY[4.9,2.4,3.3,1.0],'Iris-versicolor'),
+(59,ARRAY[6.6,2.9,4.6,1.3],'Iris-versicolor'),
+(60,ARRAY[5.2,2.7,3.9,1.4],'Iris-versicolor'),
+(61,ARRAY[5.0,2.0,3.5,1.0],'Iris-versicolor'),
+(62,ARRAY[5.9,3.0,4.2,1.5],'Iris-versicolor'),
+(63,ARRAY[6.0,2.2,4.0,1.0],'Iris-versicolor'),
+(64,ARRAY[6.1,2.9,4.7,1.4],'Iris-versicolor'),
+(65,ARRAY[5.6,2.9,3.6,1.3],'Iris-versicolor'),
+(66,ARRAY[6.7,3.1,4.4,1.4],'Iris-versicolor'),
+(67,ARRAY[5.6,3.0,4.5,1.5],'Iris-versicolor'),
+(68,ARRAY[5.8,2.7,4.1,1.0],'Iris-versicolor'),
+(69,ARRAY[6.2,2.2,4.5,1.5],'Iris-versicolor'),
+(70,ARRAY[5.6,2.5,3.9,1.1],'Iris-versicolor'),
+(71,ARRAY[5.9,3.2,4.8,1.8],'Iris-versicolor'),
+(72,ARRAY[6.1,2.8,4.0,1.3],'Iris-versicolor'),
+(73,ARRAY[6.3,2.5,4.9,1.5],'Iris-versicolor'),
+(74,ARRAY[6.1,2.8,4.7,1.2],'Iris-versicolor'),
+(75,ARRAY[6.4,2.9,4.3,1.3],'Iris-versicolor'),
+(76,ARRAY[6.6,3.0,4.4,1.4],'Iris-versicolor'),
+(77,ARRAY[6.8,2.8,4.8,1.4],'Iris-versicolor'),
+(78,ARRAY[6.7,3.0,5.0,1.7],'Iris-versicolor'),
+(79,ARRAY[6.0,2.9,4.5,1.5],'Iris-versicolor'),
+(80,ARRAY[5.7,2.6,3.5,1.0],'Iris-versicolor'),
+(81,ARRAY[5.5,2.4,3.8,1.1],'Iris-versicolor'),
+(82,ARRAY[5.5,2.4,3.7,1.0],'Iris-versicolor'),
+(83,ARRAY[5.8,2.7,3.9,1.2],'Iris-versicolor'),
+(84,ARRAY[6.0,2.7,5.1,1.6],'Iris-versicolor'),
+(85,ARRAY[5.4,3.0,4.5,1.5],'Iris-versicolor'),
+(86,ARRAY[6.0,3.4,4.5,1.6],'Iris-versicolor'),
+(87,ARRAY[6.7,3.1,4.7,1.5],'Iris-versicolor'),
+(88,ARRAY[6.3,2.3,4.4,1.3],'Iris-versicolor'),
+(89,ARRAY[5.6,3.0,4.1,1.3],'Iris-versicolor'),
+(90,ARRAY[5.5,2.5,4.0,1.3],'Iris-versicolor'),
+(91,ARRAY[5.5,2.6,4.4,1.2],'Iris-versicolor'),
+(92,ARRAY[6.1,3.0,4.6,1.4],'Iris-versicolor'),
+(93,ARRAY[5.8,2.6,4.0,1.2],'Iris-versicolor'),
+(94,ARRAY[5.0,2.3,3.3,1.0],'Iris-versicolor'),
+(95,ARRAY[5.6,2.7,4.2,1.3],'Iris-versicolor'),
+(96,ARRAY[5.7,3.0,4.2,1.2],'Iris-versicolor'),
+(97,ARRAY[5.7,2.9,4.2,1.3],'Iris-versicolor'),
+(98,ARRAY[6.2,2.9,4.3,1.3],'Iris-versicolor'),
+(99,ARRAY[5.1,2.5,3.0,1.1],'Iris-versicolor'),
+(100,ARRAY[5.7,2.8,4.1,1.3],'Iris-versicolor'),
+(101,ARRAY[6.3,3.3,6.0,2.5],'Iris-virginica'),
+(102,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
+(103,ARRAY[7.1,3.0,5.9,2.1],'Iris-virginica'),
+(104,ARRAY[6.3,2.9,5.6,1.8],'Iris-virginica'),
+(105,ARRAY[6.5,3.0,5.8,2.2],'Iris-virginica'),
+(106,ARRAY[7.6,3.0,6.6,2.1],'Iris-virginica'),
+(107,ARRAY[4.9,2.5,4.5,1.7],'Iris-virginica'),
+(108,ARRAY[7.3,2.9,6.3,1.8],'Iris-virginica'),
+(109,ARRAY[6.7,2.5,5.8,1.8],'Iris-virginica'),
+(110,ARRAY[7.2,3.6,6.1,2.5],'Iris-virginica'),
+(111,ARRAY[6.5,3.2,5.1,2.0],'Iris-virginica'),
+(112,ARRAY[6.4,2.7,5.3,1.9],'Iris-virginica'),
+(113,ARRAY[6.8,3.0,5.5,2.1],'Iris-virginica'),
+(114,ARRAY[5.7,2.5,5.0,2.0],'Iris-virginica'),
+(115,ARRAY[5.8,2.8,5.1,2.4],'Iris-virginica'),
+(116,ARRAY[6.4,3.2,5.3,2.3],'Iris-virginica'),
+(117,ARRAY[6.5,3.0,5.5,1.8],'Iris-virginica'),
+(118,ARRAY[7.7,3.8,6.7,2.2],'Iris-virginica'),
+(119,ARRAY[7.7,2.6,6.9,2.3],'Iris-virginica'),
+(120,ARRAY[6.0,2.2,5.0,1.5],'Iris-virginica'),
+(121,ARRAY[6.9,3.2,5.7,2.3],'Iris-virginica'),
+(122,ARRAY[5.6,2.8,4.9,2.0],'Iris-virginica'),
+(123,ARRAY[7.7,2.8,6.7,2.0],'Iris-virginica'),
+(124,ARRAY[6.3,2.7,4.9,1.8],'Iris-virginica'),
+(125,ARRAY[6.7,3.3,5.7,2.1],'Iris-virginica'),
+(126,ARRAY[7.2,3.2,6.0,1.8],'Iris-virginica'),
+(127,ARRAY[6.2,2.8,4.8,1.8],'Iris-virginica'),
+(128,ARRAY[6.1,3.0,4.9,1.8],'Iris-virginica'),
+(129,ARRAY[6.4,2.8,5.6,2.1],'Iris-virginica'),
+(130,ARRAY[7.2,3.0,5.8,1.6],'Iris-virginica'),
+(131,ARRAY[7.4,2.8,6.1,1.9],'Iris-virginica'),
+(132,ARRAY[7.9,3.8,6.4,2.0],'Iris-virginica'),
+(133,ARRAY[6.4,2.8,5.6,2.2],'Iris-virginica'),
+(134,ARRAY[6.3,2.8,5.1,1.5],'Iris-virginica'),
+(135,ARRAY[6.1,2.6,5.6,1.4],'Iris-virginica'),
+(136,ARRAY[7.7,3.0,6.1,2.3],'Iris-virginica'),
+(137,ARRAY[6.3,3.4,5.6,2.4],'Iris-virginica'),
+(138,ARRAY[6.4,3.1,5.5,1.8],'Iris-virginica'),
+(139,ARRAY[6.0,3.0,4.8,1.8],'Iris-virginica'),
+(140,ARRAY[6.9,3.1,5.4,2.1],'Iris-virginica'),
+(141,ARRAY[6.7,3.1,5.6,2.4],'Iris-virginica'),
+(142,ARRAY[6.9,3.1,5.1,2.3],'Iris-virginica'),
+(143,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
+(144,ARRAY[6.8,3.2,5.9,2.3],'Iris-virginica'),
+(145,ARRAY[6.7,3.3,5.7,2.5],'Iris-virginica'),
+(146,ARRAY[6.7,3.0,5.2,2.3],'Iris-virginica'),
+(147,ARRAY[6.3,2.5,5.0,1.9],'Iris-virginica'),
+(148,ARRAY[6.5,3.0,5.2,2.0],'Iris-virginica'),
+(149,ARRAY[6.2,3.4,5.4,2.3],'Iris-virginica'),
+(150,ARRAY[5.9,3.0,5.1,1.8],'Iris-virginica');
+
      Create a test/validation dataset from the training data: 
      +DROP TABLE IF EXISTS iris_train, iris_test;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.train_test_split('iris_data',     -- Source table
+                               'iris',          -- Output table root name
+                                0.8,            -- Train proportion
+                                NULL,           -- Test proportion (0.2)
+                                NULL,           -- Strata definition
+                                NULL,           -- Output all columns
+                                NULL,           -- Sample without replacement
+                                TRUE            -- Separate output tables
+                              );
+SELECT COUNT(*) FROM iris_train;
+
      + count
+------+
+   120
+
      2. +
    2. Call the preprocessor for deep learning. For the training dataset: 
      +DROP TABLE IF EXISTS iris_train_packed, iris_train_packed_summary;
+SELECT madlib.training_preprocessor_dl('iris_train',         -- Source table
+                                       'iris_train_packed',  -- Output table
+                                       'class_text',         -- Dependent variable
+                                       'attributes'          -- Independent variable
+                                        );
+\x on
+SELECT * FROM iris_train_packed_summary;
+
      +-[ RECORD 1 ]-----------+---------------------------------------------
+source_table            | iris_train
+output_table            | iris_train_packed
+dependent_varname       | {class_text}
+independent_varname     | {attributes}
+dependent_vartype       | {"character varying"}
+class_text_class_values | {Iris-setosa,Iris-versicolor,Iris-virginica}
+buffer_size             | 40
+normalizing_const       | 1
+num_classes             | {3}
+distribution_rules      | all_segments
+__internal_gpu_config__ | all_segments
+
      For the validation dataset: 
      +DROP TABLE IF EXISTS iris_test_packed, iris_test_packed_summary;
+SELECT madlib.validation_preprocessor_dl('iris_test',          -- Source table
+                                         'iris_test_packed',   -- Output table
+                                         'class_text',         -- Dependent variable
+                                         'attributes',         -- Independent variable
+                                         'iris_train_packed'   -- From training preprocessor step
+                                          );
+SELECT * FROM iris_test_packed_summary;
+
      +-[ RECORD 1 ]-----------+---------------------------------------------
+source_table            | iris_test
+output_table            | iris_test_packed
+dependent_varname       | {class_text}
+independent_varname     | {attributes}
+dependent_vartype       | {"character varying"}
+class_text_class_values | {Iris-setosa,Iris-versicolor,Iris-virginica}
+buffer_size             | 10
+normalizing_const       | 1
+num_classes             | {3}
+distribution_rules      | all_segments
+__internal_gpu_config__ | all_segments
+
      3. +
    3. Define and load model architecture. Use Keras to define the model architecture: 
      +import keras
+from tensorflow.keras.models import Sequential
+from tensorflow.keras.layers import Dense
+model_simple = Sequential()
+model_simple.add(Dense(10, activation='relu', input_shape=(4,)))
+model_simple.add(Dense(10, activation='relu'))
+model_simple.add(Dense(3, activation='softmax'))
+model_simple.summary()
+
      _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_1 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_2 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_3 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 193
+Trainable params: 193
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model_simple.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      Load into model architecture table: 
      +DROP TABLE IF EXISTS model_arch_library;
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,  -- JSON blob
+                               NULL,                  -- Weights
+                               'Sophie',              -- Name
+                               'A simple model'       -- Descr
+);
+
      4. +
    4. Train model and view summary table: 
      +DROP TABLE IF EXISTS iris_model, iris_model_summary;
+SELECT madlib.madlib_keras_fit('iris_train_packed',   -- source table
+                               'iris_model',          -- model output table
+                               'model_arch_library',  -- model arch table
+                                1,                    -- model arch id
+                                $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- compile_params
+                                $$ batch_size=5, epochs=3 $$,  -- fit_params
+                                10                    -- num_iterations
+                              );
+SELECT * FROM iris_model_summary;
+
      +-[ RECORD 1 ]-------------+--------------------------------------------------------------------------
+source_table              | iris_train_packed
+model                     | iris_model
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_id                  | 1
+compile_params            |  loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy']
+fit_params                |  batch_size=5, epochs=3
+num_iterations            | 10
+validation_table          |
+object_table              |
+metrics_compute_frequency | 10
+name                      |
+description               |
+model_type                | madlib_keras
+model_size                | 0.7900390625
+start_training_time       | 2021-02-01 15:58:43.760568
+end_training_time         | 2021-02-01 15:58:44.470054
+metrics_elapsed_time      | {0.709463119506836}
+madlib_version            | 2.1.0
+num_classes               | {3}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_type              | {accuracy}
+loss_type                 | categorical_crossentropy
+training_metrics_final    | 0.800000011920929
+training_loss_final       | 0.519745767116547
+training_metrics          | {0.800000011920929}
+training_loss             | {0.519745767116547}
+validation_metrics_final  |
+validation_loss_final     |
+validation_metrics        |
+validation_loss           |
+metrics_iters             | {10}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+
      5. +
    5. Use the test dataset to evaluate the model we built above: 
      +\x off
+DROP TABLE IF EXISTS iris_validate;
+SELECT madlib.madlib_keras_evaluate('iris_model',       -- model
+                                   'iris_test_packed',  -- test table
+                                   'iris_validate'      -- output table
+                                   );
+SELECT * FROM iris_validate;
+
      +       loss        |      metric       | metrics_type |        loss_type
+-------------------+-------------------+--------------+--------------------------
+ 0.566911578178406 | 0.699999988079071 | {accuracy}   | categorical_crossentropy
+(1 row)
+
      6. +
    6. Predict. We will use the validation dataset for prediction as well, which is not usual but serves to show the syntax. The prediction is in the 'estimated_class_text' column: 
      +DROP TABLE IF EXISTS iris_predict;
+SELECT madlib.madlib_keras_predict('iris_model', -- model
+                                   'iris_test',  -- test_table
+                                   'id',  -- id column
+                                   'attributes', -- independent var
+                                   'iris_predict'  -- output table
+                                   );
+SELECT * FROM iris_predict ORDER BY id, rank;
+
      + id  | class_name |   class_value   |    prob     | rank
+-----+------------+-----------------+-------------+------
+   4 | class_text | Iris-setosa     |   0.7689959 |    1
+   4 | class_text | Iris-virginica  |  0.15600422 |    2
+   4 | class_text | Iris-versicolor |  0.07499986 |    3
+   9 | class_text | Iris-setosa     |   0.7642913 |    1
+   9 | class_text | Iris-virginica  |  0.15844841 |    2
+   9 | class_text | Iris-versicolor | 0.077260315 |    3
+  13 | class_text | Iris-setosa     |   0.8160971 |    1
+  13 | class_text | Iris-virginica  |  0.13053566 |    2
+  13 | class_text | Iris-versicolor |  0.05336728 |    3
+  14 | class_text | Iris-setosa     |    0.804419 |    1
+  14 | class_text | Iris-virginica  |  0.13591427 |    2
+  14 | class_text | Iris-versicolor |  0.05966685 |    3
+  15 | class_text | Iris-setosa     |  0.88610095 |    1
+  15 | class_text | Iris-virginica  |  0.08893245 |    2
+  15 | class_text | Iris-versicolor | 0.024966586 |    3
+  25 | class_text | Iris-setosa     |  0.68195176 |    1
+  25 | class_text | Iris-virginica  |  0.20334557 |    2
+  25 | class_text | Iris-versicolor | 0.114702694 |    3
+  34 | class_text | Iris-setosa     |   0.8619849 |    1
+  34 | class_text | Iris-virginica  |   0.1032386 |    2
+  34 | class_text | Iris-versicolor | 0.034776475 |    3
+  36 | class_text | Iris-setosa     |  0.84423053 |    1
+  36 | class_text | Iris-virginica  | 0.114072084 |    2
+  36 | class_text | Iris-versicolor |  0.04169741 |    3
+  39 | class_text | Iris-setosa     |  0.79559565 |    1
+  39 | class_text | Iris-virginica  |  0.13950573 |    2
+  39 | class_text | Iris-versicolor | 0.064898595 |    3
+  48 | class_text | Iris-setosa     |   0.8010248 |    1
+  48 | class_text | Iris-virginica  |  0.13615999 |    2
+  48 | class_text | Iris-versicolor |  0.06281526 |    3
+  56 | class_text | Iris-versicolor |  0.47732472 |    1
+  56 | class_text | Iris-virginica  |  0.46635315 |    2
+  56 | class_text | Iris-setosa     | 0.056322116 |    3
+  63 | class_text | Iris-virginica  |   0.5329179 |    1
+  63 | class_text | Iris-versicolor |  0.38090497 |    2
+  63 | class_text | Iris-setosa     | 0.086177126 |    3
+  65 | class_text | Iris-virginica  |   0.4516514 |    1
+  65 | class_text | Iris-versicolor |   0.4330772 |    2
+  65 | class_text | Iris-setosa     |  0.11527142 |    3
+  69 | class_text | Iris-virginica  |  0.57348573 |    1
+  69 | class_text | Iris-versicolor |  0.36967018 |    2
+  69 | class_text | Iris-setosa     |  0.05684407 |    3
+  72 | class_text | Iris-virginica  |   0.4918356 |    1
+  72 | class_text | Iris-versicolor |  0.42640963 |    2
+  72 | class_text | Iris-setosa     |  0.08175478 |    3
+  73 | class_text | Iris-virginica  |   0.5534297 |    1
+  73 | class_text | Iris-versicolor |  0.39819974 |    2
+  73 | class_text | Iris-setosa     |  0.04837051 |    3
+  75 | class_text | Iris-virginica  |   0.4986787 |    1
+  75 | class_text | Iris-versicolor |  0.43546444 |    2
+  75 | class_text | Iris-setosa     |  0.06585683 |    3
+  82 | class_text | Iris-virginica  |  0.47533202 |    1
+  82 | class_text | Iris-versicolor |  0.43122545 |    2
+  82 | class_text | Iris-setosa     |  0.09344252 |    3
+  90 | class_text | Iris-virginica  |  0.47962278 |    1
+  90 | class_text | Iris-versicolor |  0.45068985 |    2
+  90 | class_text | Iris-setosa     |  0.06968742 |    3
+  91 | class_text | Iris-virginica  |  0.47005868 |    1
+  91 | class_text | Iris-versicolor |   0.4696341 |    2
+  91 | class_text | Iris-setosa     | 0.060307216 |    3
+  97 | class_text | Iris-versicolor |  0.49070656 |    1
+  97 | class_text | Iris-virginica  |  0.44852367 |    2
+  97 | class_text | Iris-setosa     | 0.060769808 |    3
+ 100 | class_text | Iris-versicolor |  0.47884703 |    1
+ 100 | class_text | Iris-virginica  |   0.4577389 |    2
+ 100 | class_text | Iris-setosa     |  0.06341412 |    3
+ 102 | class_text | Iris-virginica  |   0.5396443 |    1
+ 102 | class_text | Iris-versicolor |  0.40945858 |    2
+ 102 | class_text | Iris-setosa     | 0.050897114 |    3
+ 109 | class_text | Iris-virginica  |  0.61228466 |    1
+ 109 | class_text | Iris-versicolor |   0.3522025 |    2
+ 109 | class_text | Iris-setosa     |  0.03551281 |    3
+ 114 | class_text | Iris-virginica  |    0.562418 |    1
+ 114 | class_text | Iris-versicolor |  0.38269255 |    2
+ 114 | class_text | Iris-setosa     |  0.05488944 |    3
+ 128 | class_text | Iris-virginica  |  0.50814027 |    1
+ 128 | class_text | Iris-versicolor |  0.44240898 |    2
+ 128 | class_text | Iris-setosa     |  0.04945076 |    3
+ 138 | class_text | Iris-virginica  |  0.52319044 |    1
+ 138 | class_text | Iris-versicolor |  0.43786547 |    2
+ 138 | class_text | Iris-setosa     |  0.03894412 |    3
+ 140 | class_text | Iris-virginica  |   0.5677875 |    1
+ 140 | class_text | Iris-versicolor |   0.3936515 |    2
+ 140 | class_text | Iris-setosa     | 0.038560882 |    3
+ 141 | class_text | Iris-virginica  |  0.58414406 |    1
+ 141 | class_text | Iris-versicolor |   0.3770253 |    2
+ 141 | class_text | Iris-setosa     |  0.03883058 |    3
+ 150 | class_text | Iris-virginica  |   0.5025033 |    1
+ 150 | class_text | Iris-versicolor |   0.4495215 |    2
+ 150 | class_text | Iris-setosa     | 0.047975186 |    3
+(90 rows)
+
      Count missclassifications: 
      +SELECT COUNT(*) FROM iris_predict JOIN iris_test USING (id)
+WHERE iris_predict.class_value != iris_test.class_text AND iris_predict.rank = 1;
+
      + count
+-------+
+     9
+(1 row)
+
      Accuracy: 
      +SELECT round(count(*)*100/(150*0.2),2) as test_accuracy_percent from
+    (select iris_test.class_text as actual, iris_predict.class_value as estimated
+     from iris_predict inner join iris_test
+     on iris_test.id=iris_predict.id where iris_predict.rank = 1) q
+WHERE q.actual=q.estimated;
+
      + test_accuracy_percent
+-----------------------+
+                 70.00
+(1 row)
+
      7. +
    7. Predict BYOM. We will use the validation dataset for prediction as well, which is not usual but serves to show the syntax. See Define Model Architectures for details on how to load the model architecture and weights. In this example we will use weights we already have: 
      +UPDATE model_arch_library
+SET model_weights = iris_model.model_weights
+FROM iris_model
+WHERE model_arch_library.model_id = 1;
+
      Now train using a model from the model architecture table directly without referencing the model table from the MADlib training. Note that if you specify the class values parameter as we do below, it must reflect how the dependent variable was 1-hot encoded for training. In this example the 'training_preprocessor_dl()' in Step 2 above encoded in the order {'Iris-setosa', 'Iris-versicolor', 'Iris-virginica'} so this is the order we pass in the parameter. If we accidently pick another order that does not match the 1-hot encoding, the predictions would be wrong. 
      +DROP TABLE IF EXISTS iris_predict_byom;
+SELECT madlib.madlib_keras_predict_byom('model_arch_library',  -- model arch table
+                                         1,                    -- model arch id
+                                        'iris_test',           -- test_table
+                                        'id',                  -- id column
+                                        'attributes',          -- independent var
+                                        'iris_predict_byom',   -- output table
+                                        'response',            -- prediction type
+                                         FALSE,                -- use GPUs
+                                         ARRAY[ARRAY['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']], -- class values
+                                         1.0                   -- normalizing const
+                                   );
+SELECT * FROM iris_predict_byom ORDER BY id;
+
      The prediction is in the 'estimated_dependent_var' column: 
      + id  |  class_name   |   class_value   |    prob
+-----+---------------+-----------------+------------
+   4 | dependent_var | Iris-setosa     |  0.7689959
+   9 | dependent_var | Iris-setosa     |  0.7642913
+  13 | dependent_var | Iris-setosa     |  0.8160971
+  14 | dependent_var | Iris-setosa     |   0.804419
+  15 | dependent_var | Iris-setosa     | 0.88610095
+  25 | dependent_var | Iris-setosa     | 0.68195176
+  34 | dependent_var | Iris-setosa     |  0.8619849
+  36 | dependent_var | Iris-setosa     | 0.84423053
+  39 | dependent_var | Iris-setosa     | 0.79559565
+  48 | dependent_var | Iris-setosa     |  0.8010248
+  56 | dependent_var | Iris-versicolor | 0.47732472
+  63 | dependent_var | Iris-virginica  |  0.5329179
+  65 | dependent_var | Iris-virginica  |  0.4516514
+  69 | dependent_var | Iris-virginica  | 0.57348573
+  72 | dependent_var | Iris-virginica  |  0.4918356
+  73 | dependent_var | Iris-virginica  |  0.5534297
+  75 | dependent_var | Iris-virginica  |  0.4986787
+  82 | dependent_var | Iris-virginica  | 0.47533202
+  90 | dependent_var | Iris-virginica  | 0.47962278
+  91 | dependent_var | Iris-virginica  | 0.47005868
+  97 | dependent_var | Iris-versicolor | 0.49070656
+ 100 | dependent_var | Iris-versicolor | 0.47884703
+ 102 | dependent_var | Iris-virginica  |  0.5396443
+ 109 | dependent_var | Iris-virginica  | 0.61228466
+ 114 | dependent_var | Iris-virginica  |   0.562418
+ 128 | dependent_var | Iris-virginica  | 0.50814027
+ 138 | dependent_var | Iris-virginica  | 0.52319044
+ 140 | dependent_var | Iris-virginica  |  0.5677875
+ 141 | dependent_var | Iris-virginica  | 0.58414406
+ 150 | dependent_var | Iris-virginica  |  0.5025033
+(30 rows)
+
      Count missclassifications: 
      +SELECT COUNT(*) FROM iris_predict_byom JOIN iris_test USING (id)
+WHERE iris_predict_byom.class_value != iris_test.class_text;
+
      + count
+-------+
+     9
+(1 row)
+
      Accuracy: 
      +SELECT round(count(*)*100/(150*0.2),2) as test_accuracy_percent from
+    (select iris_test.class_text as actual, iris_predict_byom.class_value as estimated
+     from iris_predict_byom inner join iris_test
+     on iris_test.id=iris_predict_byom.id) q
+WHERE q.actual=q.estimated;
+
      + test_accuracy_percent
+-----------------------+
+                 70.00
+(1 row)
+
      8. +
    +

    Classification with Other Parameters

    +
      +
    1. Validation dataset. Now use a validation dataset and compute metrics every 3rd iteration using the 'metrics_compute_frequency' parameter. This can help reduce run time if you do not need metrics computed at every iteration. 
      +DROP TABLE IF EXISTS iris_model, iris_model_summary;
+SELECT madlib.madlib_keras_fit('iris_train_packed',   -- source table
+                               'iris_model',          -- model output table
+                               'model_arch_library',  -- model arch table
+                                1,                    -- model arch id
+                                $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- compile_params
+                                $$ batch_size=5, epochs=3 $$,  -- fit_params
+                                10,                   -- num_iterations
+                                FALSE,                -- use GPUs
+                                'iris_test_packed',   -- validation dataset
+                                3,                    -- metrics compute frequency
+                                FALSE,                -- warm start
+                               'Sophie L.',           -- name
+                               'Simple MLP for iris dataset'  -- description
+                              );
+\x on
+SELECT * FROM iris_model_summary;
+
      +-[ RECORD 1 ]-------------+--------------------------------------------------------------------------
+source_table              | iris_train_packed
+model                     | iris_model
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_id                  | 1
+compile_params            |  loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy']
+fit_params                |  batch_size=5, epochs=3
+num_iterations            | 10
+validation_table          | iris_test_packed
+object_table              |
+metrics_compute_frequency | 3
+name                      | Sophie L.
+description               | Simple MLP for iris dataset
+model_type                | madlib_keras
+model_size                | 0.7900390625
+start_training_time       | 2021-01-29 14:41:16.943861
+end_training_time         | 2021-01-29 14:41:19.478149
+metrics_elapsed_time      | {2.3377411365509,2.42358803749084,2.49885511398315,2.53427410125732}
+madlib_version            | 2.1.0
+num_classes               | {3}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_type              | {accuracy}
+loss_type                 | categorical_crossentropy
+training_metrics_final    | 0.883333325386047
+training_loss_final       | 0.584357917308807
+training_metrics          | {0.733333349227905,0.774999976158142,0.883333325386047,0.883333325386047}
+training_loss             | {0.765825688838959,0.664925456047058,0.605871021747589,0.584357917308807}
+validation_metrics_final  | 0.899999976158142
+validation_loss_final     | 0.590348184108734
+validation_metrics        | {0.699999988079071,0.866666674613953,0.899999976158142,0.899999976158142}
+validation_loss           | {0.81381630897522,0.691304981708527,0.616305589675903,0.590348184108734}
+metrics_iters             | {3,6,9,10}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+
      2. +
    2. Predict probabilities for each class: 
      +DROP TABLE IF EXISTS iris_predict;
+SELECT madlib.madlib_keras_predict('iris_model',      -- model
+                                   'iris_test',       -- test_table
+                                   'id',              -- id column
+                                   'attributes',      -- independent var
+                                   'iris_predict',    -- output table
+                                   'prob'             -- response type
+                                   );
+\x off
+SELECT * FROM iris_predict ORDER BY id;
+
      + id  | class_name |   class_value   |    prob     | rank
+-----+------------+-----------------+-------------+------
+   4 | class_text | Iris-versicolor |  0.34548566 |    2
+   4 | class_text | Iris-setosa     |  0.57626975 |    1
+   4 | class_text | Iris-virginica  |  0.07824467 |    3
+   7 | class_text | Iris-versicolor |  0.34442508 |    2
+   7 | class_text | Iris-setosa     |  0.57735515 |    1
+   7 | class_text | Iris-virginica  | 0.078219764 |    3
+   9 | class_text | Iris-versicolor |   0.3453845 |    2
+   9 | class_text | Iris-virginica  |  0.08293749 |    3
+   9 | class_text | Iris-setosa     |  0.57167804 |    1
+  12 | class_text | Iris-versicolor |  0.34616387 |    2
+  12 | class_text | Iris-setosa     |   0.5793855 |    1
+  12 | class_text | Iris-virginica  | 0.074450605 |    3
+  18 | class_text | Iris-versicolor |  0.34597218 |    2
+  18 | class_text | Iris-virginica  |  0.07100027 |    3
+  18 | class_text | Iris-setosa     |  0.58302754 |    1
+  20 | class_text | Iris-versicolor |  0.34480608 |    2
+  20 | class_text | Iris-setosa     |   0.5856424 |    1
+  20 | class_text | Iris-virginica  |  0.06955151 |    3
+  24 | class_text | Iris-versicolor |  0.38339624 |    2
+  24 | class_text | Iris-setosa     |   0.5330486 |    1
+  24 | class_text | Iris-virginica  | 0.083555184 |    3
+  30 | class_text | Iris-versicolor |  0.35101113 |    2
+  30 | class_text | Iris-setosa     |  0.56958234 |    1
+  30 | class_text | Iris-virginica  |  0.07940655 |    3
+  31 | class_text | Iris-versicolor |   0.3503181 |    2
+  31 | class_text | Iris-setosa     |   0.5733414 |    1
+  31 | class_text | Iris-virginica  |  0.07634052 |    3
+  33 | class_text | Iris-versicolor |  0.34489658 |    2
+  33 | class_text | Iris-setosa     |   0.5847962 |    1
+  33 | class_text | Iris-virginica  |  0.07030724 |    3
+  35 | class_text | Iris-versicolor |  0.34719768 |    2
+  35 | class_text | Iris-setosa     |    0.577414 |    1
+  35 | class_text | Iris-virginica  |  0.07538838 |    3
+  40 | class_text | Iris-versicolor |   0.3464746 |    2
+  40 | class_text | Iris-setosa     |  0.58250487 |    1
+  40 | class_text | Iris-virginica  | 0.071020484 |    3
+  41 | class_text | Iris-versicolor |  0.34581655 |    2
+  41 | class_text | Iris-setosa     |   0.5805128 |    1
+  41 | class_text | Iris-virginica  |  0.07367061 |    3
+  45 | class_text | Iris-versicolor |  0.38146245 |    2
+  45 | class_text | Iris-setosa     |  0.52559936 |    1
+  45 | class_text | Iris-virginica  |  0.09293811 |    3
+  51 | class_text | Iris-virginica  |  0.41811863 |    2
+  51 | class_text | Iris-setosa     |  0.07617204 |    3
+  51 | class_text | Iris-versicolor |   0.5057093 |    1
+  53 | class_text | Iris-virginica  |  0.47048044 |    2
+  53 | class_text | Iris-versicolor |  0.47150916 |    1
+  53 | class_text | Iris-setosa     | 0.058010455 |    3
+  57 | class_text | Iris-versicolor |   0.4443615 |    2
+  57 | class_text | Iris-setosa     | 0.055230834 |    3
+  57 | class_text | Iris-virginica  |   0.5004077 |    1
+  58 | class_text | Iris-virginica  |  0.35905617 |    2
+  58 | class_text | Iris-setosa     |  0.15329117 |    3
+  58 | class_text | Iris-versicolor |   0.4876526 |    1
+  69 | class_text | Iris-versicolor |   0.4485282 |    2
+  69 | class_text | Iris-virginica  |   0.4913048 |    1
+  69 | class_text | Iris-setosa     | 0.060167026 |    3
+  72 | class_text | Iris-virginica  |  0.38764492 |    2
+  72 | class_text | Iris-versicolor |   0.5052213 |    1
+  72 | class_text | Iris-setosa     |  0.10713379 |    3
+  74 | class_text | Iris-versicolor |  0.44894043 |    2
+  74 | class_text | Iris-setosa     |  0.06307102 |    3
+  74 | class_text | Iris-virginica  |  0.48798853 |    1
+  93 | class_text | Iris-virginica  |  0.40836224 |    2
+  93 | class_text | Iris-setosa     | 0.102442265 |    3
+  93 | class_text | Iris-versicolor |  0.48919544 |    1
+  94 | class_text | Iris-virginica  |  0.35238466 |    2
+  94 | class_text | Iris-versicolor |  0.49192256 |    1
+  94 | class_text | Iris-setosa     |  0.15569273 |    3
+ 110 | class_text | Iris-versicolor |   0.2917817 |    2
+ 110 | class_text | Iris-virginica  |   0.6972358 |    1
+ 110 | class_text | Iris-setosa     | 0.010982483 |    3
+ 113 | class_text | Iris-versicolor |  0.35037678 |    2
+ 113 | class_text | Iris-setosa     | 0.021288367 |    3
+ 113 | class_text | Iris-virginica  |   0.6283349 |    1
+ 117 | class_text | Iris-versicolor |  0.35009244 |    2
+ 117 | class_text | Iris-virginica  |   0.6264066 |    1
+ 117 | class_text | Iris-setosa     | 0.023500985 |    3
+ 123 | class_text | Iris-versicolor |   0.2849912 |    2
+ 123 | class_text | Iris-virginica  |  0.70571697 |    1
+ 123 | class_text | Iris-setosa     | 0.009291774 |    3
+ 127 | class_text | Iris-versicolor |   0.4041788 |    2
+ 127 | class_text | Iris-virginica  |  0.55537915 |    1
+ 127 | class_text | Iris-setosa     | 0.040441982 |    3
+ 130 | class_text | Iris-versicolor |  0.38396156 |    2
+ 130 | class_text | Iris-virginica  |  0.59018326 |    1
+ 130 | class_text | Iris-setosa     | 0.025855187 |    3
+ 143 | class_text | Iris-versicolor |  0.33123586 |    2
+ 143 | class_text | Iris-virginica  |   0.6445185 |    1
+ 143 | class_text | Iris-setosa     | 0.024245638 |    3
+(30 rows)
+
      3. +
    3. Warm start. Next, use the warm_start parameter to continue learning, using the coefficients from the run above. Note that we don't drop the model table or model summary table: 
      +SELECT madlib.madlib_keras_fit('iris_train_packed',   -- source table
+                               'iris_model',          -- model output table
+                               'model_arch_library',  -- model arch table
+                                1,                    -- model arch id
+                                $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- compile_params
+                                $$ batch_size=5, epochs=3 $$,  -- fit_params
+                                5,                   -- num_iterations
+                                FALSE,               -- use GPUs
+                                'iris_test_packed',   -- validation dataset
+                                1,                    -- metrics compute frequency
+                                TRUE,                 -- warm start
+                               'Sophie L.',           -- name
+                               'Simple MLP for iris dataset'  -- description
+                              );
+\x on
+SELECT * FROM iris_model_summary;
+
      +-[ RECORD 1 ]-------------+--------------------------------------------------------------------------------------------
+source_table              | iris_train_packed
+model                     | iris_model
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_id                  | 1
+compile_params            |  loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy']
+fit_params                |  batch_size=5, epochs=3
+num_iterations            | 5
+validation_table          | iris_test_packed
+object_table              |
+metrics_compute_frequency | 1
+name                      | Sophie L.
+description               | Simple MLP for iris dataset
+model_type                | madlib_keras
+model_size                | 0.7900390625
+start_training_time       | 2021-01-29 14:42:28.780276
+end_training_time         | 2021-01-29 14:42:31.177561
+metrics_elapsed_time      | {2.24628114700317,2.28473520278931,2.32178020477295,2.35844302177429,2.39726710319519}
+madlib_version            | 2.1.0
+num_classes               | {3}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_type              | {accuracy}
+loss_type                 | categorical_crossentropy
+training_metrics_final    | 0.916666686534882
+training_loss_final       | 0.456518471240997
+training_metrics          | {0.883333325386047,0.891666650772095,0.908333361148834,0.916666686534882,0.916666686534882}
+training_loss             | {0.559914350509644,0.537041485309601,0.513083755970001,0.47985765337944,0.456518471240997}
+validation_metrics_final  | 0.966666638851166
+validation_loss_final     | 0.432968735694885
+validation_metrics        | {0.899999976158142,0.899999976158142,0.933333337306976,0.966666638851166,0.966666638851166}
+validation_loss           | {0.558336615562439,0.529355347156525,0.496939331293106,0.462678134441376,0.432968735694885}
+metrics_iters             | {1,2,3,4,5}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+
      Note that the loss and accuracy values pick up from where the previous run left off.
      4. +
    +

    Transfer Learning

    +

    Here we want to start with initial weights from a pre-trained model rather than training from scratch. We also want to use a model architecture with the earlier feature layer(s) frozen to save on training time. The example below is somewhat contrived but gives you the idea of the steps.

    +
      +
    1. Define and load a model architecture with the 1st hidden layer frozen:
      2. +
    +
    +model_transfer = Sequential()
+model_transfer.add(Dense(10, activation='relu', input_shape=(4,), trainable=False))
+model_transfer.add(Dense(10, activation='relu'))
+model_transfer.add(Dense(3, activation='softmax'))
+model_simple.summary()
+
    _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_1 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_2 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_3 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 193
+Trainable params: 143
+Non-trainable params: 50
+
    
+

    Export the model to JSON: 

    +model_simple.to_json()
+
    +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": false, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+

    Load into model architecture table: 

    +SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": false, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,  -- JSON blob
+                               NULL,                  -- Weights
+                               'Maria',               -- Name
+                               'A transfer model'     -- Descr
+);
+

    Fetch the weights from a previous MADlib run. (Normally these would be downloaded from a source that trained the same model architecture on a related dataset.) 

    +UPDATE model_arch_library
+SET model_weights = iris_model.model_weights
+FROM iris_model
+WHERE model_arch_library.model_id = 2;
+

    Now train the model using the transfer model and the pre-trained weights: 

    +DROP TABLE IF EXISTS iris_model, iris_model_summary;
+SELECT madlib.madlib_keras_fit('iris_train_packed',   -- source table
+                               'iris_model',          -- model output table
+                               'model_arch_library',  -- model arch table
+                                2,                    -- model arch id
+                                $$ loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy'] $$,  -- compile_params
+                                $$ batch_size=5, epochs=3 $$,  -- fit_params
+                                10                    -- num_iterations
+                              );
+\x on
+SELECT * FROM iris_model_summary;
+
    +-[ RECORD 1 ]-------------+--------------------------------------------------------------------------
+source_table              | iris_train_packed
+model                     | iris_model
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_id                  | 2
+compile_params            |  loss='categorical_crossentropy', optimizer='adam', metrics=['categorical_accuracy']
+fit_params                |  batch_size=5, epochs=3
+num_iterations            | 10
+validation_table          |
+object_table              |
+metrics_compute_frequency | 10
+name                      |
+description               |
+model_type                | madlib_keras
+model_size                | 0.7900390625
+start_training_time       | 2021-01-29 14:44:51.176983
+end_training_time         | 2021-01-29 14:44:53.666457
+metrics_elapsed_time      | {2.48945999145508}
+madlib_version            | 2.1.0
+num_classes               | {3}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_type              | {accuracy}
+loss_type                 | categorical_crossentropy
+training_metrics_final    | 0.949999988079071
+training_loss_final       | 0.340020209550858
+training_metrics          | {0.949999988079071}
+training_loss             | {0.340020209550858}
+validation_metrics_final  |
+validation_loss_final     |
+validation_metrics        |
+validation_loss           |
+metrics_iters             | {10}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+

    Notes
    +
      +
    1. Refer to the deep learning section of the Apache MADlib wiki [5] for important information including supported libraries and versions.
      2. +
    2. Classification is currently supported, not regression.
      3. +
    3. Reminder about the distinction between warm start and transfer learning. Warm start uses model state (weights) from the model output table from a previous training run - set the 'warm_start' parameter to TRUE in the fit function. Transfer learning uses initial model state (weights) stored in the 'model_arch_table' - in this case set the 'warm_start' parameter to FALSE in the fit function.
      4. +
    +

    Technical Background
    +

    For an introduction to deep learning foundations, including MLP and CNN, refer to [6].

    +

    This module trains a single large model across the database cluster using the bulk synchronous parallel (BSP) approach, with model averaging [7].

    +

    On the effect of database cluster size: as the database cluster size increases, the per iteration loss will be higher since the model only sees 1/n of the data, where n is the number of segments. However, each iteration runs faster than single node because it is only traversing 1/n of the data. For highly non-convex solution spaces, convergence behavior may diminish as cluster size increases. Ensure that each segment has sufficient volume of data and examples of each class value.

    +

    Alternatively, to train multiple models at the same time for model architecture search or hyperparameter tuning, you can use the methods in Train Multiple Models, which does not do model averaging and hence may have better covergence efficiency.

    +

    Literature
    +

    [1] https://keras.io/

    +

    [2] https://www.tensorflow.org/

    +

    [3] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent, Geoffrey Hinton with Nitish Srivastava and Kevin Swersky, http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

    +

    [4] https://keras.io/models/model/

    +

    [5] Deep learning section of Apache MADlib wiki, https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning

    +

    [6] Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville, MIT Press, 2016.

    +

    [7] "Resource-Efficient and Reproducible Model Selection on Deep Learning Systems," Supun Nakandala, Yuhao Zhang, and Arun Kumar, Technical Report, Computer Science and Engineering, University of California, San Diego https://adalabucsd.github.io/papers/TR_2019_Cerebro.pdf.

    +

    [8] Greenplum Database server configuration parameters https://gpdb.docs.pivotal.io/latest/ref_guide/config_params/guc-list.html

    +

    Related Topics
    +

    File madlib_keras.sql_in documenting the training, evaluate and predict functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__keras__model__arch.html b/docs/docs/v2.1.0/group__grp__keras__model__arch.html new file mode 100644 index 00000000..53c0a934 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__keras__model__arch.html @@ -0,0 +1,350 @@ + + + + + + + + +MADlib: Define Model Architectures + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Define Model Architectures
    Deep Learning » Model Preparation
    +
    +
    +
    Contents +

    This function loads model architectures and weights into a table for use by deep learning algorithms.

    +

    Model architecture is in JSON form and model weights are in the form of PostgreSQL binary data types (bytea). If the output table already exists, a new row is inserted into the table so it can act as a repository for multiple model architectures and weights.

    +

    There is also a function to delete a model from the table.

    +

    MADlib's deep learning methods are designed to use the TensorFlow package and its built in Keras functions. To ensure consistency, please use tensorflow.keras objects (models, layers, etc.) instead of importing Keras and using its objects.

    +

    Load Model
    +
    +load_keras_model(
+    keras_model_arch_table,
+    model_arch,
+    model_weights,
+    name,
+    description
+    )
+

    Arguments

    +
    keras_model_arch_table
    +

    VARCHAR. Output table to load keras model architecture and weights.

    +

    +
    +
    model_arch
    +

    JSON. JSON of the model architecture to load.

    Note
    Please note that every input layer must have the 'input_shape' stated explicitly in the model architecture. MADlib has this requirement because, in some cases, the JSON representation may not have the input shape by default and it has to be read from the JSON for fit() type functions.
    +

    +
    +
    model_weights (optional)
    +

    bytea. Model weights to load as a PostgreSQL binary data type.

    +

    +
    +
    name (optional)
    +

    TEXT, default: NULL. Free text string to provide a name, if desired.

    +

    +
    +
    description (optional)
    +

    TEXT, default: NULL. Free text string to provide a description, if desired.

    +

    +
    +
    +

    Output table
    + The output table contains the following columns:

    + + + + + + + + + + + + +
    model_id SERIAL PRIMARY KEY. Model ID.
    model_arch JSON. JSON blob of the model architecture.
    model_weights BYTEA. Weights of the model which may be used for warm start or transfer learning. Weights are stored as a PostgreSQL binary data type.
    name TEXT. Name of model (free text).
    description TEXT. Description of model (free text).
    __internal_madlib_id__ TEXT. Unique id for model arch. This is an id used internally be MADlib.
    +

    Delete Model
    +
    +delete_keras_model(
+    keras_model_arch_table
+    model_id
+)
+

    Arguments

    +
    keras_model_arch_table
    +

    VARCHAR. Table containing model architectures and weights.

    +

    +
    +
    model_id
    +
    INTEGER. The id of the model to be deleted.
    +
    +

    Examples
      +
    1. Define model architecture. Use tensorflow.keras to define the model architecture: 
      +import keras
+from tensorflow.keras.models import Sequential
+from tensorflow.keras.layers import Dense
+model_simple = Sequential()
+model_simple.add(Dense(10, activation='relu', input_shape=(4,)))
+model_simple.add(Dense(10, activation='relu'))
+model_simple.add(Dense(3, activation='softmax'))
+model_simple.summary()
+
      _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_1 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_2 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_3 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 193
+Trainable params: 193
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model_simple.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      2. +
    2. Load into model architecture table: 
      +DROP TABLE IF EXISTS model_arch_library;
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,  -- JSON blob
+                               NULL,                  -- Weights
+                               'Sophie',              -- Name
+                               'A simple model'       -- Descr
+);
+SELECT COUNT(*) FROM model_arch_library;
+
      + count
+-------+
+     1
+
      Load another model architecture: 
      +SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,  -- JSON blob
+                               NULL,                  -- Weights
+                               'Maria',               -- Name
+                               'Also a simple model'  -- Descr
+);
+SELECT COUNT(*) FROM model_arch_library;
+
      + count
+-------+
+     2
+
      3. +
    3. Load model weights. To load weights from previous MADlib run, use UPDATE to load directly into the table. For example, if 'model_weights' are the weights in the output table 'iris_model' from a previous run of 'madlib_keras_fit()' : 
      +UPDATE model_arch_library SET model_weights = model_weights FROM iris_model WHERE model_id = 2;
+SELECT model_id, name, description, (model_weights IS NOT NULL) AS has_model_weights FROM model_arch_library ORDER BY model_id;
+
      + model_id |  name  |     description     | has_model_weights 
+----------+--------+---------------------+-------------------
+        1 | Sophie | A simple model      | f
+        2 | Maria  | Also a simple model | t
+
      4. +
    4. To load weights from tensorflow.keras using a PL/Python function, we need to flatten then serialize the weights to store as a PostgreSQL binary data type. Byte format is more efficient on space and memory compared to a numeric array. The model weights will be de-serialized when passed to Keras functions. 
      +CREATE OR REPLACE FUNCTION load_weights() RETURNS VOID AS
+$$
+import keras
+from tensorflow.keras.layers import *
+from tensorflow.keras import Sequential
+import numpy as np
+import plpy
+#
+# create model
+model = Sequential()
+model.add(Dense(10, activation='relu', input_shape=(4,)))
+model.add(Dense(10, activation='relu'))
+model.add(Dense(3, activation='softmax'))
+#
+# get weights, flatten and serialize
+weights = model.get_weights()
+weights_flat = [w.flatten() for w in weights]
+weights1d =  np.concatenate(weights_flat).ravel()
+weights_bytea = weights1d.tostring()
+#
+# load query
+load_query = plpy.prepare("""SELECT madlib.load_keras_model(
+                        'model_arch_library',
+                        $1, $2)
+                    """, ['json','bytea'])
+plpy.execute(load_query, [model.to_json(), weights_bytea])
+$$ language plpython3u;
+-- Call load function
+SELECT load_weights();
+SELECT model_id, name, description, (model_weights IS NOT NULL) AS has_model_weights FROM model_arch_library ORDER BY model_id;
+
      + model_id |  name  |     description     | has_model_weights 
+----------+--------+---------------------+-------------------
+        1 | Sophie | A simple model      | f
+        2 | Maria  | Also a simple model | t
+        3 | Ella   | Model x             | t
+
      5. +
    5. Load weights from tensorflow.keras using psycopg2. (Psycopg is a PostgreSQL database adapter for the Python programming language.) As above we need to flatten then serialize the weights to store as a PostgreSQL binary data type. Note that the psycopg2.Binary function used below will increase the size of the Python object for the weights, so if your model is large it might be better to use a PL/Python function as above. 
      +import psycopg2
+import psycopg2 as p2
+conn = p2.connect('postgresql://gpadmin@35.239.240.26:5432/madlib')
+cur = conn.cursor()
+from tensorflow.keras.layers import *
+from tensorflow.keras import Sequential
+import numpy as np
+#
+# create model
+model = Sequential()
+model.add(Dense(10, activation='relu', input_shape=(4,)))
+model.add(Dense(10, activation='relu'))
+model.add(Dense(3, activation='softmax'))
+#
+# get weights, flatten and serialize
+weights = model.get_weights()
+weights_flat = [w.flatten() for w in weights]
+weights1d =  np.concatenate(weights_flat).ravel()
+weights_bytea = psycopg2.Binary(weights1d.tostring())
+#
+# load query
+query = "SELECT madlib.load_keras_model('model_arch_library', %s,%s)"
+cur.execute(query,[model.to_json(),weights_bytea])
+conn.commit()
+SELECT model_id, name, description, (model_weights IS NOT NULL) AS has_model_weights FROM model_arch_library ORDER BY model_id;
+
      + model_id |  name  |     description     | has_model_weights 
+----------+--------+---------------------+-------------------
+        1 | Sophie | A simple model      | f
+        2 | Maria  | Also a simple model | t
+        3 | Ella   | Model x             | t
+        4 | Grace  | Model y             | t
+
      6. +
    6. Delete one of the models: 
      +SELECT madlib.delete_keras_model('model_arch_library',   -- Output table
+                                  1                      -- Model id
+                                );
+SELECT model_id, name, description, (model_weights IS NOT NULL) AS has_model_weights FROM model_arch_library ORDER BY model_id;
+
      + model_id | name  |     description     | has_model_weights 
+----------+-------+---------------------+-------------------
+        2 | Maria | Also a simple model | t
+        3 | Ella  | Model x             | t
+        4 | Grace | Model y             | t
+
      7. +
    +
    +

    Related Topics
    +

    See keras_model_arch_table.sql_in

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__keras__run__model__selection.html b/docs/docs/v2.1.0/group__grp__keras__run__model__selection.html new file mode 100644 index 00000000..9acf8bdd --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__keras__run__model__selection.html @@ -0,0 +1,1112 @@ + + + + + + + + +MADlib: Train Model Configurations + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Train Model Configurations
    Deep Learning » Train Multiple Models
    +
    +
    +
    Contents +

    This module allows you to explore network architectures and hyperparameters by training many models a time across the database cluster.

    +

    The aim is to support efficient empirical comparison of multiple training configurations. This process is called model selection, and the implementation here is based on a parallel execution strategy called model hopper parallelism (MOP) [1,2].

    +

    Models are designed in Keras [3], which is a high-level neural network API written in Python. It can run on top of different backends and the one that is currently supported by MADlib is TensorFlow [4].

    +

    The main use case is classification using sequential models, which are made up of a linear stack of layers. This includes multilayer perceptrons (MLPs) and convolutional neural networks (CNNs). Regression is not currently supported.

    +

    Before using this model selection method, you will need to Prepocess Data which prepares data for use by models that support mini-batch as an optimization option. This is a one-time operation and you would only need to re-run the preprocessor if your input data has changed. The advantage of using mini-batching is that it can perform better than stochastic gradient descent because it uses more than one training example at a time, typically resulting faster and smoother convergence [5].

    +

    You can set up the models and hyperparameters to try with the Define Model Configurations function to define the unique combinations of model architectures, compile and fit parameters.

    +
    Note
    1. If 'madlib_keras_fit_multiple_model()' is running on GPDB 5 and some versions of GPDB 6, the database will keep adding to the disk space (in proportion to model size) and will only release the disk space once the fit multiple query has completed execution. This is not the case for GPDB 6.5.0+ where disk space is released during the fit multiple query.
    +
    +2. CUDA GPU memory cannot be released until the process holding it is terminated. When a MADlib deep learning function is called with GPUs, Greenplum internally creates a process (called a slice) which calls TensorFlow to do the computation. This process holds the GPU memory until one of the following two things happen: query finishes and user logs out of the Postgres client/session; or, query finishes and user waits for the timeout set by gp_vmem_idle_resource_timeout. The default value for this timeout is 18 sec [8]. So the recommendation is: log out/reconnect to the session after every GPU query; or wait for gp_vmem_idle_resource_timeout before you run another GPU query (you can also set it to a lower value).
    +
    +3. This method does not currently support multi-input or multi-output neural networks.
    +

    Fit
    The fit (training) function has the following format:
    +
    +madlib_keras_fit_multiple_model(
+    source_table,
+    model_output_table,
+    model_selection_table,
+    num_iterations,
+    use_gpus,
+    validation_table,
+    metrics_compute_frequency,
+    warm_start,
+    name,
+    description,
+    use_caching
+    )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the training data. This is the name of the output table from the data preprocessor. Independent and dependent variables are specified in the preprocessor step which is why you do not need to explictly state them here as part of the fit function.

    +

    +
    +
    model_output_table
    +
    TEXT. Name of the output table containing the multiple models created.
    Note
    pg_temp is not allowed as an output table schema for fit multiple. Details of output tables are shown below.
    +
    +
    model_selection_table
    +

    TEXT. Name of the table containing model selection parameters to be tried. Here we mean both hyper-parameter tuning and model architecture search.

    +

    +
    +
    num_iterations
    +

    INTEGER. Number of iterations to train.

    +
    Note
    This parameter is different than the number of passes over the dataset, which is commonly referred to as the number of epochs. Since MADlib operates in a distributed system, the number of epochs is actually equal to this parameter 'num_iterations' X 'epochs' as specified in the Keras fit parameter.
    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.

    +
    Note
    This parameter must not conflict with how the distribution rules are set in the preprocessor function. For example, if you set a distribution rule to use certain segments on hosts that do not have GPUs attached, you will get an error if you set ‘use_gpus’ to TRUE. Also, we have seen some memory related issues when segments share GPU resources. For example, if you have 1 GPU per segment host and your cluster has 4 segments per segment host, it means that all 4 segments will share the same GPU on each host. The current recommended configuration is 1 GPU per segment.
    +
    +
    validation_table (optional)
    +

    TEXT, default: none. Name of the table containing the validation dataset. Note that the validation dataset must be preprocessed in the same way as the training dataset, so this is the name of the output table from running the data preprocessor on the validation dataset. Using a validation dataset can mean a longer training time, depending on its size. This can be controlled using the 'metrics_compute_frequency' parameter described below.

    +

    +
    +
    metrics_compute_frequency (optional)
    +

    INTEGER, default: once at the end of training after 'num_iterations'. Frequency to compute per-iteration metrics for the training dataset and validation dataset (if specified). There can be considerable cost to computing metrics every iteration, especially if the training dataset is large. This parameter is a way of controlling the frequency of those computations. For example, if you specify 5, then metrics will be computed every 5 iterations as well as at the end of training after 'num_iterations'. If you use the default, metrics will be computed only once after 'num_iterations' have completed.

    +

    +
    +
    warm_start (optional)
    +

    BOOLEAN, default: FALSE. Initalize weights with the coefficients from the last call to the fit function. If set to TRUE, weights will be initialized from the model table generated by the previous training run.

    +
    Note
    The warm start feature works based on the name of the model output table from a previous training run. When using warm start, do not drop the model output table or the model output summary table before calling the fit function, since these are needed to obtain the weights from the previous run. If you are not using warm start, the model output table and the model output table summary must be dropped in the usual way before calling the training function.
    +
    +
    name (optional)
    +

    TEXT, default: NULL. Free text string to identify a name, if desired.

    +

    +
    +
    description (optional)
    +

    TEXT, default: NULL. Free text string to provide a description, if desired.

    +

    +
    +
    use_caching (optional)
    +

    BOOLEAN, default: FALSE. Use caching of data in memory on the segment in order to speed up processing.

    +
    Note
    When set to TRUE, byte arrays on each segment are maintained in cache (SD). This can speed up training significantly, however the memory usage per segment increases. In effect, it requires enough available memory on a segment so that all training data residing on that segment can be read into memory.
    +
    +
    +

    Output tables
    + The model output table produced by fit contains the following columns. There is one row per model as per the rows in the 'model_selection_table':

    + + + + + + +
    mst_key INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters, as defined in the 'model_selection_table'.
    model_weights BYTEA8. Byte array containing the weights of the neural net.
    model_arch TEXT. A JSON representation of the model architecture used in training.
    +

    An info table named <model_output_table>_info is also created, which has the following columns. There is one row per model as per the rows in the 'model_selection_table':

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    mst_key INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters, as defined in the 'model_selection_table'.
    model_id INTEGER. ID that defines model in the 'model_arch_table'.
    compile_params Compile parameters passed to Keras.
    fit_params Fit parameters passed to Keras.
    model_type General identifier for type of model trained. Currently says 'madlib_keras'.
    model_size Size of the model in KB. Models are stored in 'bytea' data format which is used for binary strings in PostgreSQL type databases.
    metrics_elapsed_time Array of elapsed time for metric computations as per the 'metrics_compute_frequency' parameter. Useful for drawing a curve showing loss, accuracy or other metrics as a function of time. For example, if 'metrics_compute_frequency=5' this would be an array of elapsed time for every 5th iteration, plus the last iteration. Note that this field reports the time for training + validation if there is a validation table provided.
    metrics_type Metric specified in the 'compile_params'.
    loss_type Loss specified in the 'compile_params'.
    training_metrics_final Final value of the training metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
    training_loss_final Final value of the training loss after all iterations have completed.
    training_metrics Array of training metrics as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of metrics for every 5th iteration, plus the last iteration.
    training_loss Array of training losses as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of losses for every 5th iteration, plus the last iteration.
    validation_metrics_final Final value of the validation metric after all iterations have completed. The metric reported is the one specified in the 'metrics_type' parameter.
    validation_loss_final Final value of the validation loss after all iterations have completed.
    validation_metrics Array of validation metrics as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of metrics for every 5th iteration, plus the last iteration.
    validation_loss

    Array of validation losses as per the 'metrics_compute_frequency' parameter. For example, if 'metrics_compute_frequency=5' this would be an array of losses for every 5th iteration, plus the last iteration.

    +

    +
    +

    A summary table named <model>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    source_table Source table used for training.
    validation_table Name of the table containing the validation dataset (if specified).
    model Name of the output table containing the model for each model selection tuple.
    model_info Name of the output table containing the model performance and other info for each model selection tuple.
    dependent_varname Dependent variable column from the original source table in the data preprocessing step.
    independent_varname Independent variables column from the original source table in the data preprocessing step.
    model_arch_table Name of the table containing the model architecture and (optionally) the initial model weights.
    num_iterations Number of iterations of training completed.
    metrics_compute_frequency Frequency that per-iteration metrics are computed for the training dataset and validation datasets.
    warm_start Indicates whether warm start used or not.
    name Name of the training run (free text).
    description Description of the training run (free text).
    start_training_time Timestamp for start of training.
    end_training_time Timestamp for end of training.
    madlib_version Version of MADlib used.
    num_classes Count of distinct classes values used.
    <dependent_varname>_class_values Array of actual class values used for a particular dependent variable. A column will be generated for each dependent variable.
    dependent_vartype Data type of the dependent variable.
    normalizing_constant Normalizing constant used from the data preprocessing step.
    metrics_iters Array indicating the iterations for which metrics are calculated, as derived from the parameters 'num_iterations' and 'metrics_compute_frequency'. For example, if 'num_iterations=5' and 'metrics_compute_frequency=2', then 'metrics_iters' value would be {2,4,5} indicating that metrics were computed at iterations 2, 4 and 5 (at the end). If 'num_iterations=5' and 'metrics_compute_frequency=1', then 'metrics_iters' value would be {1,2,3,4,5} indicating that metrics were computed at every iteration.
    +

    Evaluate
    The evaluation function has the following format:
    +
    +madlib_keras_evaluate(
+    model_table,
+    test_table,
+    output_table,
+    use_gpus,
+    mst_key
+    )
+

    Arguments

    +
    model_table
    +

    TEXT. Name of the table containing the model to use for validation.

    +

    +
    +
    test_table
    +

    TEXT. Name of the table containing the evaluation dataset. Note that test/validation data must be preprocessed in the same way as the training dataset, so this is the name of the output table from the data preprocessor. Independent and dependent variables are specified in the preprocessor step which is why you do not need to explictly state them here as part of the fit function.

    +

    +
    +
    output_table
    +
    TEXT. Name of table that validation output will be written to. Table contains: + + + + + + + + +
    loss Loss value on evaluation dataset, where 'loss_type' below identifies the type of loss.
    metric Metric value on evaluation dataset, where 'metrics_type' below identifies the type of metric.
    metrics_type Type of metric used that was used in the training step. (It means you cannot have a different metric in evaluate compared to training.)
    loss_type

    Type of loss function that was used in the training step. (It means you cannot have a different loss in evaluate compared to training.)

    +

    +
    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for training the neural network. Set to TRUE to use GPUs.

    +
    Note
    This parameter must not conflict with how the distribution rules are set in the preprocessor function. For example, if you set a distribution rule to use certain segments on hosts that do not have GPUs attached, you will get an error if you set ‘use_gpus’ to TRUE. Also, we have seen some memory related issues when segments share GPU resources. For example, if you have 1 GPU per segment host and your cluster has 4 segments per segment host, it means that all 4 segments will share the same GPU on each host. The current recommended configuration is 1 GPU per segment.
    +
    +
    mst_key (optional)
    +
    INTEGER, default: NULL. ID that defines a unique tuple for model architecture-compile parameters-fit parameters as defined in the model selection table.
    +
    +

    Predict
    The prediction function has the following format: 
    +madlib_keras_predict(
+    model_table,
+    test_table,
+    id_col,
+    independent_varname,
+    output_table,
+    pred_type,
+    use_gpus,    
+    mst_key
+    )
+
    +

    Arguments

    +
    model_table
    +

    TEXT. Name of the table containing the model to use for prediction.

    +

    +
    +
    test_table
    +

    TEXT. Name of the table containing the dataset to predict on. Note that test data is not preprocessed (unlike fit and evaluate) so put one test image per row for prediction. Also see the comment below for the 'independent_varname' parameter regarding normalization.

    +

    +

    +
    +
    id_col
    +

    TEXT. Name of the id column in the test data table.

    +

    +
    +
    independent_varname
    +

    TEXT. Column with independent variables in the test table. If a 'normalizing_const' is specified when preprocessing the training dataset, this same normalization will be applied to the independent variables used in predict.

    +

    +
    +
    output_table
    +
    TEXT. Name of the table that prediction output will be written to. Table contains: + + + + + + + + + + +
    id Gives the 'id' for each prediction, corresponding to each row from the test_table.
    class_name The estimated variable.
    class_value The estimated class for classification.
    prob Probability of a given class.
    rank

    The rank of a given class based on the ordering of probabilities.

    +

    +
    +
    +
    pred_type (optional)
    +

    TEXT or INTEGER or DOUBLE PRECISION default: 'prob'. The type and range of output desired. This parameter allows the following options.

      +
    • 'response': the actual prediction
      • +
    • 'prob': the probability value for each class
      • +
    • 0<value<1: the lower limit for the probability (double precision)
      • +
    • 1<=value: the lower limit for the rank of the prediction (integer)
      • +
    +

    +
    +
    use_gpus (optional)
    +

    BOOLEAN, default: FALSE (i.e., CPU). Determines whether GPUs are to be used for prediction/inference. Set to TRUE to use GPUs.

    +
    Note
    The prediction function uses the whole cluster. If you are using GPUs, it requires that GPUs are attached to all hosts, and that there are the same number of GPUs on each host (homogeneous cluster). This is different from the fit() and evaluate() functions that support GPUs on only some of the hosts (heterogeneous cluster). Therefore, if you have GPUs only on some of the hosts, or an uneven numbers of GPUs per host, then set this parameter to FALSE to use CPUs.
    +
    +
    mst_key (optional)
    +
    INTEGER, default: NULL. ID that defines a unique tuple for model architecture-compile parameters-fit parameters as defined in the model selection table.
    +
    +

    Examples
    +
    Note
    Deep learning works best on very large datasets, but that is not convenient for a quick introduction to the syntax. So in this example we use an MLP on the well known iris data set from https://archive.ics.uci.edu/ml/datasets/iris. For more realistic examples with images please refer to the deep learning notebooks at https://github.com/apache/madlib-site/tree/asf-site/community-artifacts.
    +

    Classification

    +
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS iris_data;
+CREATE TABLE iris_data(
+    id serial,
+    attributes numeric[],
+    class_text varchar
+);
+INSERT INTO iris_data(id, attributes, class_text) VALUES
+(1,ARRAY[5.1,3.5,1.4,0.2],'Iris-setosa'),
+(2,ARRAY[4.9,3.0,1.4,0.2],'Iris-setosa'),
+(3,ARRAY[4.7,3.2,1.3,0.2],'Iris-setosa'),
+(4,ARRAY[4.6,3.1,1.5,0.2],'Iris-setosa'),
+(5,ARRAY[5.0,3.6,1.4,0.2],'Iris-setosa'),
+(6,ARRAY[5.4,3.9,1.7,0.4],'Iris-setosa'),
+(7,ARRAY[4.6,3.4,1.4,0.3],'Iris-setosa'),
+(8,ARRAY[5.0,3.4,1.5,0.2],'Iris-setosa'),
+(9,ARRAY[4.4,2.9,1.4,0.2],'Iris-setosa'),
+(10,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(11,ARRAY[5.4,3.7,1.5,0.2],'Iris-setosa'),
+(12,ARRAY[4.8,3.4,1.6,0.2],'Iris-setosa'),
+(13,ARRAY[4.8,3.0,1.4,0.1],'Iris-setosa'),
+(14,ARRAY[4.3,3.0,1.1,0.1],'Iris-setosa'),
+(15,ARRAY[5.8,4.0,1.2,0.2],'Iris-setosa'),
+(16,ARRAY[5.7,4.4,1.5,0.4],'Iris-setosa'),
+(17,ARRAY[5.4,3.9,1.3,0.4],'Iris-setosa'),
+(18,ARRAY[5.1,3.5,1.4,0.3],'Iris-setosa'),
+(19,ARRAY[5.7,3.8,1.7,0.3],'Iris-setosa'),
+(20,ARRAY[5.1,3.8,1.5,0.3],'Iris-setosa'),
+(21,ARRAY[5.4,3.4,1.7,0.2],'Iris-setosa'),
+(22,ARRAY[5.1,3.7,1.5,0.4],'Iris-setosa'),
+(23,ARRAY[4.6,3.6,1.0,0.2],'Iris-setosa'),
+(24,ARRAY[5.1,3.3,1.7,0.5],'Iris-setosa'),
+(25,ARRAY[4.8,3.4,1.9,0.2],'Iris-setosa'),
+(26,ARRAY[5.0,3.0,1.6,0.2],'Iris-setosa'),
+(27,ARRAY[5.0,3.4,1.6,0.4],'Iris-setosa'),
+(28,ARRAY[5.2,3.5,1.5,0.2],'Iris-setosa'),
+(29,ARRAY[5.2,3.4,1.4,0.2],'Iris-setosa'),
+(30,ARRAY[4.7,3.2,1.6,0.2],'Iris-setosa'),
+(31,ARRAY[4.8,3.1,1.6,0.2],'Iris-setosa'),
+(32,ARRAY[5.4,3.4,1.5,0.4],'Iris-setosa'),
+(33,ARRAY[5.2,4.1,1.5,0.1],'Iris-setosa'),
+(34,ARRAY[5.5,4.2,1.4,0.2],'Iris-setosa'),
+(35,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(36,ARRAY[5.0,3.2,1.2,0.2],'Iris-setosa'),
+(37,ARRAY[5.5,3.5,1.3,0.2],'Iris-setosa'),
+(38,ARRAY[4.9,3.1,1.5,0.1],'Iris-setosa'),
+(39,ARRAY[4.4,3.0,1.3,0.2],'Iris-setosa'),
+(40,ARRAY[5.1,3.4,1.5,0.2],'Iris-setosa'),
+(41,ARRAY[5.0,3.5,1.3,0.3],'Iris-setosa'),
+(42,ARRAY[4.5,2.3,1.3,0.3],'Iris-setosa'),
+(43,ARRAY[4.4,3.2,1.3,0.2],'Iris-setosa'),
+(44,ARRAY[5.0,3.5,1.6,0.6],'Iris-setosa'),
+(45,ARRAY[5.1,3.8,1.9,0.4],'Iris-setosa'),
+(46,ARRAY[4.8,3.0,1.4,0.3],'Iris-setosa'),
+(47,ARRAY[5.1,3.8,1.6,0.2],'Iris-setosa'),
+(48,ARRAY[4.6,3.2,1.4,0.2],'Iris-setosa'),
+(49,ARRAY[5.3,3.7,1.5,0.2],'Iris-setosa'),
+(50,ARRAY[5.0,3.3,1.4,0.2],'Iris-setosa'),
+(51,ARRAY[7.0,3.2,4.7,1.4],'Iris-versicolor'),
+(52,ARRAY[6.4,3.2,4.5,1.5],'Iris-versicolor'),
+(53,ARRAY[6.9,3.1,4.9,1.5],'Iris-versicolor'),
+(54,ARRAY[5.5,2.3,4.0,1.3],'Iris-versicolor'),
+(55,ARRAY[6.5,2.8,4.6,1.5],'Iris-versicolor'),
+(56,ARRAY[5.7,2.8,4.5,1.3],'Iris-versicolor'),
+(57,ARRAY[6.3,3.3,4.7,1.6],'Iris-versicolor'),
+(58,ARRAY[4.9,2.4,3.3,1.0],'Iris-versicolor'),
+(59,ARRAY[6.6,2.9,4.6,1.3],'Iris-versicolor'),
+(60,ARRAY[5.2,2.7,3.9,1.4],'Iris-versicolor'),
+(61,ARRAY[5.0,2.0,3.5,1.0],'Iris-versicolor'),
+(62,ARRAY[5.9,3.0,4.2,1.5],'Iris-versicolor'),
+(63,ARRAY[6.0,2.2,4.0,1.0],'Iris-versicolor'),
+(64,ARRAY[6.1,2.9,4.7,1.4],'Iris-versicolor'),
+(65,ARRAY[5.6,2.9,3.6,1.3],'Iris-versicolor'),
+(66,ARRAY[6.7,3.1,4.4,1.4],'Iris-versicolor'),
+(67,ARRAY[5.6,3.0,4.5,1.5],'Iris-versicolor'),
+(68,ARRAY[5.8,2.7,4.1,1.0],'Iris-versicolor'),
+(69,ARRAY[6.2,2.2,4.5,1.5],'Iris-versicolor'),
+(70,ARRAY[5.6,2.5,3.9,1.1],'Iris-versicolor'),
+(71,ARRAY[5.9,3.2,4.8,1.8],'Iris-versicolor'),
+(72,ARRAY[6.1,2.8,4.0,1.3],'Iris-versicolor'),
+(73,ARRAY[6.3,2.5,4.9,1.5],'Iris-versicolor'),
+(74,ARRAY[6.1,2.8,4.7,1.2],'Iris-versicolor'),
+(75,ARRAY[6.4,2.9,4.3,1.3],'Iris-versicolor'),
+(76,ARRAY[6.6,3.0,4.4,1.4],'Iris-versicolor'),
+(77,ARRAY[6.8,2.8,4.8,1.4],'Iris-versicolor'),
+(78,ARRAY[6.7,3.0,5.0,1.7],'Iris-versicolor'),
+(79,ARRAY[6.0,2.9,4.5,1.5],'Iris-versicolor'),
+(80,ARRAY[5.7,2.6,3.5,1.0],'Iris-versicolor'),
+(81,ARRAY[5.5,2.4,3.8,1.1],'Iris-versicolor'),
+(82,ARRAY[5.5,2.4,3.7,1.0],'Iris-versicolor'),
+(83,ARRAY[5.8,2.7,3.9,1.2],'Iris-versicolor'),
+(84,ARRAY[6.0,2.7,5.1,1.6],'Iris-versicolor'),
+(85,ARRAY[5.4,3.0,4.5,1.5],'Iris-versicolor'),
+(86,ARRAY[6.0,3.4,4.5,1.6],'Iris-versicolor'),
+(87,ARRAY[6.7,3.1,4.7,1.5],'Iris-versicolor'),
+(88,ARRAY[6.3,2.3,4.4,1.3],'Iris-versicolor'),
+(89,ARRAY[5.6,3.0,4.1,1.3],'Iris-versicolor'),
+(90,ARRAY[5.5,2.5,4.0,1.3],'Iris-versicolor'),
+(91,ARRAY[5.5,2.6,4.4,1.2],'Iris-versicolor'),
+(92,ARRAY[6.1,3.0,4.6,1.4],'Iris-versicolor'),
+(93,ARRAY[5.8,2.6,4.0,1.2],'Iris-versicolor'),
+(94,ARRAY[5.0,2.3,3.3,1.0],'Iris-versicolor'),
+(95,ARRAY[5.6,2.7,4.2,1.3],'Iris-versicolor'),
+(96,ARRAY[5.7,3.0,4.2,1.2],'Iris-versicolor'),
+(97,ARRAY[5.7,2.9,4.2,1.3],'Iris-versicolor'),
+(98,ARRAY[6.2,2.9,4.3,1.3],'Iris-versicolor'),
+(99,ARRAY[5.1,2.5,3.0,1.1],'Iris-versicolor'),
+(100,ARRAY[5.7,2.8,4.1,1.3],'Iris-versicolor'),
+(101,ARRAY[6.3,3.3,6.0,2.5],'Iris-virginica'),
+(102,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
+(103,ARRAY[7.1,3.0,5.9,2.1],'Iris-virginica'),
+(104,ARRAY[6.3,2.9,5.6,1.8],'Iris-virginica'),
+(105,ARRAY[6.5,3.0,5.8,2.2],'Iris-virginica'),
+(106,ARRAY[7.6,3.0,6.6,2.1],'Iris-virginica'),
+(107,ARRAY[4.9,2.5,4.5,1.7],'Iris-virginica'),
+(108,ARRAY[7.3,2.9,6.3,1.8],'Iris-virginica'),
+(109,ARRAY[6.7,2.5,5.8,1.8],'Iris-virginica'),
+(110,ARRAY[7.2,3.6,6.1,2.5],'Iris-virginica'),
+(111,ARRAY[6.5,3.2,5.1,2.0],'Iris-virginica'),
+(112,ARRAY[6.4,2.7,5.3,1.9],'Iris-virginica'),
+(113,ARRAY[6.8,3.0,5.5,2.1],'Iris-virginica'),
+(114,ARRAY[5.7,2.5,5.0,2.0],'Iris-virginica'),
+(115,ARRAY[5.8,2.8,5.1,2.4],'Iris-virginica'),
+(116,ARRAY[6.4,3.2,5.3,2.3],'Iris-virginica'),
+(117,ARRAY[6.5,3.0,5.5,1.8],'Iris-virginica'),
+(118,ARRAY[7.7,3.8,6.7,2.2],'Iris-virginica'),
+(119,ARRAY[7.7,2.6,6.9,2.3],'Iris-virginica'),
+(120,ARRAY[6.0,2.2,5.0,1.5],'Iris-virginica'),
+(121,ARRAY[6.9,3.2,5.7,2.3],'Iris-virginica'),
+(122,ARRAY[5.6,2.8,4.9,2.0],'Iris-virginica'),
+(123,ARRAY[7.7,2.8,6.7,2.0],'Iris-virginica'),
+(124,ARRAY[6.3,2.7,4.9,1.8],'Iris-virginica'),
+(125,ARRAY[6.7,3.3,5.7,2.1],'Iris-virginica'),
+(126,ARRAY[7.2,3.2,6.0,1.8],'Iris-virginica'),
+(127,ARRAY[6.2,2.8,4.8,1.8],'Iris-virginica'),
+(128,ARRAY[6.1,3.0,4.9,1.8],'Iris-virginica'),
+(129,ARRAY[6.4,2.8,5.6,2.1],'Iris-virginica'),
+(130,ARRAY[7.2,3.0,5.8,1.6],'Iris-virginica'),
+(131,ARRAY[7.4,2.8,6.1,1.9],'Iris-virginica'),
+(132,ARRAY[7.9,3.8,6.4,2.0],'Iris-virginica'),
+(133,ARRAY[6.4,2.8,5.6,2.2],'Iris-virginica'),
+(134,ARRAY[6.3,2.8,5.1,1.5],'Iris-virginica'),
+(135,ARRAY[6.1,2.6,5.6,1.4],'Iris-virginica'),
+(136,ARRAY[7.7,3.0,6.1,2.3],'Iris-virginica'),
+(137,ARRAY[6.3,3.4,5.6,2.4],'Iris-virginica'),
+(138,ARRAY[6.4,3.1,5.5,1.8],'Iris-virginica'),
+(139,ARRAY[6.0,3.0,4.8,1.8],'Iris-virginica'),
+(140,ARRAY[6.9,3.1,5.4,2.1],'Iris-virginica'),
+(141,ARRAY[6.7,3.1,5.6,2.4],'Iris-virginica'),
+(142,ARRAY[6.9,3.1,5.1,2.3],'Iris-virginica'),
+(143,ARRAY[5.8,2.7,5.1,1.9],'Iris-virginica'),
+(144,ARRAY[6.8,3.2,5.9,2.3],'Iris-virginica'),
+(145,ARRAY[6.7,3.3,5.7,2.5],'Iris-virginica'),
+(146,ARRAY[6.7,3.0,5.2,2.3],'Iris-virginica'),
+(147,ARRAY[6.3,2.5,5.0,1.9],'Iris-virginica'),
+(148,ARRAY[6.5,3.0,5.2,2.0],'Iris-virginica'),
+(149,ARRAY[6.2,3.4,5.4,2.3],'Iris-virginica'),
+(150,ARRAY[5.9,3.0,5.1,1.8],'Iris-virginica');
+
      Create a test/validation dataset from the training data: 
      +DROP TABLE IF EXISTS iris_train, iris_test;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.train_test_split('iris_data',     -- Source table
+                               'iris',          -- Output table root name
+                                0.8,            -- Train proportion
+                                NULL,           -- Test proportion (0.2)
+                                NULL,           -- Strata definition
+                                NULL,           -- Output all columns
+                                NULL,           -- Sample without replacement
+                                TRUE            -- Separate output tables
+                              );
+SELECT COUNT(*) FROM iris_train;
+
      + count
+------+
+   120
+
      2. +
    2. Call the preprocessor for deep learning. For the training dataset: 
      +\x on
+DROP TABLE IF EXISTS iris_train_packed, iris_train_packed_summary;
+SELECT madlib.training_preprocessor_dl('iris_train',         -- Source table
+                                       'iris_train_packed',  -- Output table
+                                       'class_text',         -- Dependent variable
+                                       'attributes'          -- Independent variable
+                                        );
+SELECT * FROM iris_train_packed_summary;
+
      +-[ RECORD 1 ]-------+---------------------------------------------
+source_table        | iris_train
+output_table        | iris_train_packed
+dependent_varname   | class_text
+independent_varname | attributes
+dependent_vartype   | character varying
+class_values        | {Iris-setosa,Iris-versicolor,Iris-virginica}
+buffer_size         | 60
+normalizing_const   | 1.0
+num_classes         | 3
+
      For the validation dataset: 
      +DROP TABLE IF EXISTS iris_test_packed, iris_test_packed_summary;
+SELECT madlib.validation_preprocessor_dl('iris_test',          -- Source table
+                                         'iris_test_packed',   -- Output table
+                                         'class_text',         -- Dependent variable
+                                         'attributes',         -- Independent variable
+                                         'iris_train_packed'   -- From training preprocessor step
+                                          );
+SELECT * FROM iris_test_packed_summary;
+
      +-[ RECORD 1 ]-------+---------------------------------------------
+source_table        | iris_test
+output_table        | iris_test_packed
+dependent_varname   | class_text
+independent_varname | attributes
+dependent_vartype   | character varying
+class_values        | {Iris-setosa,Iris-versicolor,Iris-virginica}
+buffer_size         | 15
+normalizing_const   | 1.0
+num_classes         | 3
+
      3. +
    3. Define and load model architecture. Use Keras to define the model architecture with 1 hidden layer: 
      +import keras
+from tensorflow.keras.models import Sequential
+from tensorflow.keras.layers import Dense
+model1 = Sequential()
+model1.add(Dense(10, activation='relu', input_shape=(4,)))
+model1.add(Dense(10, activation='relu'))
+model1.add(Dense(3, activation='softmax'))
+model1.summary()
+
      _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_1 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_2 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_3 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 193
+Trainable params: 193
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model1.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      Define model architecture with 2 hidden layers: 
      +model2 = Sequential()
+model2.add(Dense(10, activation='relu', input_shape=(4,)))
+model2.add(Dense(10, activation='relu'))
+model2.add(Dense(10, activation='relu'))
+model2.add(Dense(3, activation='softmax'))
+model2.summary()
+
      Layer (type)                 Output Shape              Param #
+=================================================================
+dense_4 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_5 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_6 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_7 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 303
+Trainable params: 303
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model2.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      Load into model architecture table: 
      +DROP TABLE IF EXISTS model_arch_library;
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,         -- JSON blob
+                               NULL,                  -- Weights
+                               'Sophie',              -- Name
+                               'MLP with 1 hidden layer'       -- Descr
+);
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,         -- JSON blob
+                               NULL,                  -- Weights
+                               'Maria',               -- Name
+                               'MLP with 2 hidden layers'       -- Descr
+);
+
      4. +
    4. Generate model configurations using grid search. The output table for grid search contains the unique combinations of model architectures, compile and fit parameters. 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [ {'optimizer': ['Adam'], 'lr': [0.001, 0.01, 0.1]} ],
+                                             'metrics': ['accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [4, 8],
+                                           'epochs': [1]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'grid'               -- search_type
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                 compile_params                                  |      fit_params       
+---------+----------+---------------------------------------------------------------------------------+-----------------------
+       1 |        1 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=4
+       2 |        1 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=8
+       3 |        1 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=4
+       4 |        1 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=8
+       5 |        1 | optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=4
+       6 |        1 | optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=8
+       7 |        2 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=4
+       8 |        2 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=1,batch_size=8
+       9 |        2 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=4
+      10 |        2 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=1,batch_size=8
+      11 |        2 | optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=4
+      12 |        2 | optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=1,batch_size=8
+(12 rows)
+
      This is the name of the model architecture table that corresponds to the model selection table: 
      +SELECT * FROM mst_table_summary;
+
      +  model_arch_table  | object_table 
+--------------------+--------------
+ model_arch_library | 
+
      5. +
    5. Train multiple models. 
      +DROP TABLE IF EXISTS iris_multi_model, iris_multi_model_summary, iris_multi_model_info;
+SELECT madlib.madlib_keras_fit_multiple_model('iris_train_packed',    -- source_table
+                                              'iris_multi_model',     -- model_output_table
+                                              'mst_table',            -- model_selection_table
+                                              10,                     -- num_iterations
+                                              FALSE                   -- use gpus
+                                             );
+
      View the model summary: 
      +SELECT * FROM iris_multi_model_summary;
+
      +source_table              | iris_train_packed
+validation_table          | 
+model                     | iris_multi_model
+model_info                | iris_multi_model_info
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_selection_table     | mst_table
+object_table              | 
+num_iterations            | 10
+metrics_compute_frequency | 10
+warm_start                | f
+name                      | 
+description               | 
+start_training_time       | 2021-02-05 00:40:42.695613
+end_training_time         | 2021-02-05 00:42:20.796712
+madlib_version            | 2.1.0
+num_classes               | {1}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_iters             | {10}
+
      View results for each model: 
      +SELECT * FROM iris_multi_model_info ORDER BY training_metrics_final DESC, training_loss_final;
+
      +  mst_key | model_id |                                 compile_params                                  |      fit_params       |  model_type  | model_size | metrics_elapsed_time | metrics_type |        loss_type         | training_metrics_final | training_loss_final |  training_metrics   |    training_loss     | validation_metrics_final | validation_loss_final | validation_metrics | validation_loss 
+---------+----------+---------------------------------------------------------------------------------+-----------------------+--------------+------------+----------------------+--------------+--------------------------+------------------------+---------------------+---------------------+----------------------+--------------------------+-----------------------+--------------------+-----------------
+       2 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {96.2744579315186}   | {accuracy}   | categorical_crossentropy |      0.966666638851166 |  0.0771341994404793 | {0.966666638851166} | {0.0771341994404793} |                          |                       |                    |
+       3 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {95.0798950195312}   | {accuracy}   | categorical_crossentropy |      0.958333313465118 |    0.14112713932991 | {0.958333313465118} | {0.14112713932991}   |                          |                       |                    |
+      10 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {95.7743279933929}   | {accuracy}   | categorical_crossentropy |      0.949999988079071 |   0.126085489988327 | {0.949999988079071} | {0.126085489988327}  |                          |                       |                    |
+       5 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {97.8191220760345}   | {accuracy}   | categorical_crossentropy |      0.866666674613953 |   0.459462374448776 | {0.866666674613953} | {0.459462374448776}  |                          |                       |                    |
+       4 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {96.7445840835571}   | {accuracy}   | categorical_crossentropy |      0.858333349227905 |   0.279698997735977 | {0.858333349227905} | {0.279698997735977}  |                          |                       |                    |
+       9 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {95.3640351295471}   | {accuracy}   | categorical_crossentropy |      0.824999988079071 |   0.325970768928528 | {0.824999988079071} | {0.325970768928528}  |                          |                       |                    |
+       7 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {94.8350050449371}   | {accuracy}   | categorical_crossentropy |      0.800000011920929 |   0.458843886852264 | {0.800000011920929} | {0.458843886852264}  |                          |                       |                    |
+      12 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {96.0411529541016}   | {accuracy}   | categorical_crossentropy |      0.783333361148834 |   0.766786217689514 | {0.783333361148834} | {0.766786217689514}  |                          |                       |                    |
+      11 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {98.098680973053}    | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.607033967971802 | {0.683333337306976} | {0.607033967971802}  |                          |                       |                    |
+       6 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {96.5071561336517}   | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.704851150512695 | {0.683333337306976} | {0.704851150512695}  |                          |                       |                    |
+       8 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {97.4749901294708}   | {accuracy}   | categorical_crossentropy |      0.641666650772095 |   0.473412454128265 | {0.641666650772095} | {0.473412454128265}  |                          |                       |                    |
+       1 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {96.9749960899353}   | {accuracy}   | categorical_crossentropy |      0.358333319425583 |    1.09744954109192 | {0.358333319425583} | {1.09744954109192}   |                          |                       |                    |
+(12 rows)
+
      6. +
    6. Evaluate. Now run evaluate using models we built above: 
      +DROP TABLE IF EXISTS iris_validate;
+SELECT madlib.madlib_keras_evaluate('iris_multi_model',  -- model
+                                    'iris_test_packed',  -- test table
+                                    'iris_validate',     -- output table
+                                     NULL,               -- use gpus
+                                     3                   -- mst_key to use
+                                   );
+SELECT * FROM iris_validate;
+
      +        loss        | metric | metrics_type |        loss_type         
+--------------------+--------+--------------+--------------------------
+ 0.0789926201105118 |      1 | {accuracy}   | categorical_crossentropy
+
      7. +
    7. Predict. Now predict using one of the models we built. We will use the validation data set for prediction as well, which is not usual but serves to show the syntax. The prediction is in the estimated_class_text column: 
      +DROP TABLE IF EXISTS iris_predict;
+SELECT madlib.madlib_keras_predict('iris_multi_model', -- model
+                                   'iris_test',        -- test_table
+                                   'id',               -- id column
+                                   'attributes',       -- independent var
+                                   'iris_predict',     -- output table
+                                    'response',        -- prediction type
+                                    FALSE,             -- use gpus
+                                    3                  -- mst_key to use
+                                   );
+SELECT * FROM iris_predict ORDER BY id;
+
      + id  | class_name |   class_value   |    prob    
+-----+------------+-----------------+------------
+   8 | class_text | Iris-setosa     |  0.9979984
+  15 | class_text | Iris-setosa     | 0.99929357
+  20 | class_text | Iris-setosa     |  0.9985701
+  21 | class_text | Iris-setosa     |  0.9984106
+  22 | class_text | Iris-setosa     |  0.9983991
+  27 | class_text | Iris-setosa     | 0.99763095
+  28 | class_text | Iris-setosa     |   0.998376
+  33 | class_text | Iris-setosa     | 0.99901116
+  37 | class_text | Iris-setosa     | 0.99871385
+  38 | class_text | Iris-setosa     | 0.99740535
+  46 | class_text | Iris-setosa     |  0.9968368
+  51 | class_text | Iris-versicolor | 0.93798196
+  57 | class_text | Iris-versicolor | 0.73391247
+  58 | class_text | Iris-versicolor |  0.9449931
+  59 | class_text | Iris-versicolor |  0.8938894
+  64 | class_text | Iris-versicolor |  0.6563309
+  65 | class_text | Iris-versicolor | 0.95828146
+  72 | class_text | Iris-versicolor |    0.94206
+  75 | class_text | Iris-versicolor | 0.93305194
+  87 | class_text | Iris-versicolor |  0.8458596
+  95 | class_text | Iris-versicolor | 0.76850986
+  97 | class_text | Iris-versicolor |  0.8467575
+  98 | class_text | Iris-versicolor |  0.9081358
+ 120 | class_text | Iris-virginica  | 0.86913925
+ 121 | class_text | Iris-virginica  | 0.96328884
+ 122 | class_text | Iris-virginica  |  0.9474733
+ 123 | class_text | Iris-virginica  | 0.97997576
+ 140 | class_text | Iris-virginica  |  0.8721462
+ 144 | class_text | Iris-virginica  |  0.9745266
+ 147 | class_text | Iris-virginica  |  0.8978669
+(30 rows)
+
      Count missclassifications: 
      +SELECT COUNT(*) FROM iris_predict JOIN iris_test USING (id) 
+WHERE iris_predict.class_value != iris_test.class_text;
+
      + count 
+-------+
+     0
+
      Accuracy: 
      +SELECT round(count(*)*100/(150*0.2),2) as test_accuracy_percent from
+    (select iris_test.class_text as actual, iris_predict.class_value as estimated
+     from iris_predict inner join iris_test
+     on iris_test.id=iris_predict.id) q
+WHERE q.actual=q.estimated;
+
      + test_accuracy_percent 
+-----------------------+
+                100.00
+
      8. +
    +

    Classification with Other Parameters

    +
      +
    1. Validation dataset. Now use a validation dataset and compute metrics every 3rd iteration using the 'metrics_compute_frequency' parameter. This can help reduce run time if you do not need metrics computed at every iteration. Also turn on caching. 
      +DROP TABLE IF EXISTS iris_multi_model, iris_multi_model_summary, iris_multi_model_info;
+SELECT madlib.madlib_keras_fit_multiple_model('iris_train_packed',    -- source_table
+                                              'iris_multi_model',     -- model_output_table
+                                              'mst_table',            -- model_selection_table
+                                               10,                     -- num_iterations
+                                               FALSE,                 -- use gpus
+                                              'iris_test_packed',     -- validation dataset
+                                               3,                     -- metrics compute frequency
+                                               FALSE,                 -- warm start
+                                              'Sophie L.',            -- name
+                                              'Model selection for iris dataset',  -- description
+                                               TRUE                   -- use caching
+                                             );
+
      View the model summary: 
      +SELECT * FROM iris_multi_model_summary;
+
      +-[ RECORD 1 ]-------------+---------------------------------------------
+source_table              | iris_train_packed
+validation_table          | iris_test_packed
+model                     | iris_multi_model
+model_info                | iris_multi_model_info
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_selection_table     | mst_table
+object_table              | 
+num_iterations            | 10
+metrics_compute_frequency | 3
+warm_start                | f
+name                      | Sophie L.
+description               | Model selection for iris dataset
+start_training_time       | 2021-02-05 01:03:11.337798
+end_training_time         | 2021-02-05 01:05:14.988912
+madlib_version            | 2.1.0
+num_classes               | {1}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_iters             | {3,6,9,10}
+
      View results for each model: 
      +SELECT * FROM iris_multi_model_info ORDER BY training_metrics_final DESC, training_loss_final;
+
      + ---------+----------+---------------------------------------------------------------------------------+-----------------------+--------------+------------+-----------------------------------------------------------------------+--------------+--------------------------+------------------------+---------------------+---------------------------------------------------------------------------+---------------------------------------------------------------------------+--------------------------+-----------------------+---------------------------------------------------------------------------+------------------------------------------------------------------------------
+      10 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {34.347088098526,69.4049510955811,105.285098075867,121.389348983765}  | {accuracy}   | categorical_crossentropy |      0.975000023841858 |   0.166684880852699 | {0.949999988079071,0.949999988079071,0.908333361148834,0.975000023841858} | {0.615781545639038,0.269571483135223,0.242876216769218,0.166684880852699} |                        1 |     0.107727721333504 | {1,1,0.966666638851166,1}                                                 | {0.620104968547821,0.227639734745026,0.155238434672356,0.107727721333504}
+       3 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {33.7874810695648,68.735356092453,104.679323911667,120.741965055466}  | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.151768147945404 | {0.958333313465118,0.816666662693024,0.941666662693024,0.958333313465118} | {0.232924744486809,0.356248170137405,0.160927340388298,0.151768147945404} |                        1 |    0.0933234840631485 | {1,0.866666674613953,0.966666638851166,1}                                 | {0.197644680738449,0.244517579674721,0.0969053283333778,0.0933234840631485}
+       4 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {35.5827050209045,70.4194140434265,106.230206012726,122.374103069305} | {accuracy}   | categorical_crossentropy |      0.941666662693024 |   0.146068558096886 | {0.824999988079071,0.958333313465118,0.941666662693024,0.941666662693024} | {0.339193284511566,0.171411842107773,0.154963329434395,0.146068558096886} |                        1 |    0.0618178397417068 | {0.933333337306976,1,1,1}                                                 | {0.302341401576996,0.0991373136639595,0.0709080845117569,0.0618178397417068}
+       5 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {36.3988909721375,71.1546559333801,107.219161987305,123.366652965546} | {accuracy}   | categorical_crossentropy |      0.908333361148834 |   0.656857788562775 | {0.358333319425583,0.683333337306976,0.766666650772095,0.908333361148834} | {0.996901094913483,0.852809607982635,0.694450318813324,0.656857788562775} |        0.899999976158142 |     0.630161166191101 | {0.233333334326744,0.600000023841858,0.633333325386047,0.899999976158142} | {1.05581676959991,0.876067101955414,0.700714349746704,0.630161166191101}
+       2 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {35.0734770298004,69.949450969696,105.773796081543,121.901873111725}  | {accuracy}   | categorical_crossentropy |      0.866666674613953 |    0.26227542757988 | {0.558333337306976,0.683333337306976,0.708333313465118,0.866666674613953} | {0.755041897296906,0.551798105239868,0.504159986972809,0.26227542757988}  |        0.899999976158142 |     0.156955525279045 | {0.633333325386047,0.600000023841858,0.633333325386047,0.899999976158142} | {0.663675665855408,0.674827337265015,0.613502621650696,0.156955525279045}
+       6 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {35.3355600833893,70.1827409267426,106.000793933868,122.135368108749} | {accuracy}   | categorical_crossentropy |      0.858333349227905 |   0.403681367635727 | {0.708333313465118,0.850000023841858,0.783333361148834,0.858333349227905} | {0.609176814556122,0.488206028938293,0.425172030925751,0.403681367635727} |        0.899999976158142 |     0.393621385097504 | {0.600000023841858,0.833333313465118,0.800000011920929,0.899999976158142} | {0.624664425849915,0.48302897810936,0.428876429796219,0.393621385097504}
+       9 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {34.0762810707092,69.0332140922546,105.02664899826,121.034147024155}  | {accuracy}   | categorical_crossentropy |      0.816666662693024 |    0.40071240067482 | {0.716666638851166,0.975000023841858,0.941666662693024,0.816666662693024} | {0.530809044837952,0.112755678594112,0.178483173251152,0.40071240067482}  |        0.899999976158142 |     0.160617485642433 | {0.666666686534882,1,1,0.899999976158142}                                 | {0.510058879852295,0.0435655005276203,0.0271952152252197,0.160617485642433}
+      11 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {36.664577960968,71.4262120723724,107.501835107803,123.646811962128}  | {accuracy}   | categorical_crossentropy |      0.816666662693024 |   0.683901190757751 | {0.358333319425583,0.574999988079071,0.758333325386047,0.816666662693024} | {0.969602465629578,0.828204095363617,0.7138671875,0.683901190757751}      |        0.833333313465118 |     0.720155417919159 | {0.233333334326744,0.466666668653488,0.666666686534882,0.833333313465118} | {1.04192113876343,0.878720223903656,0.755707621574402,0.720155417919159}
+       1 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {35.8240220546722,70.6528959274292,106.680663108826,122.609847068787} | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.479730814695358 | {0.675000011920929,0.683333337306976,0.683333337306976,0.683333337306976} | {0.507641136646271,0.467351347208023,0.507468938827515,0.479730814695358} |        0.600000023841858 |     0.503782331943512 | {0.600000023841858,0.600000023841858,0.600000023841858,0.600000023841858} | {0.504352450370789,0.448328793048859,0.561446607112885,0.503782331943512}
+       7 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {33.5537171363831,68.2605030536652,104.443753004074,120.498863935471} | {accuracy}   | categorical_crossentropy |      0.683333337306976 |   0.940275907516479 | {0.733333349227905,0.641666650772095,0.933333337306976,0.683333337306976} | {0.419289141893387,0.746466338634491,0.25556743144989,0.940275907516479}  |        0.600000023841858 |       1.1002448797226 | {0.633333325386047,0.766666650772095,0.966666638851166,0.600000023841858} | {0.457020550966263,0.510054171085358,0.249405279755592,1.1002448797226}
+      12 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {34.8103830814362,69.698233127594,105.547440052032,121.659696102142}  | {accuracy}   | categorical_crossentropy |      0.633333325386047 |   0.711242735385895 | {0.458333343267441,0.5,0.683333337306976,0.633333325386047}               | {1.71241450309753,0.98362809419632,0.776128530502319,0.711242735385895}   |        0.566666662693024 |     0.721668004989624 | {0.433333337306976,0.5,0.600000023841858,0.566666662693024}               | {1.30801546573639,0.950868666172028,0.841940879821777,0.721668004989624}
+       8 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {36.0954039096832,70.921669960022,106.977710008621,123.112148046494}  | {accuracy}   | categorical_crossentropy |      0.358333319425583 |    1.10370969772339 | {0.324999988079071,0.358333319425583,0.358333319425583,0.358333319425583} | {1.10047388076782,1.09791541099548,1.09736382961273,1.10370969772339}     |        0.233333334326744 |      1.11518168449402 | {0.366666674613953,0.233333334326744,0.233333334326744,0.233333334326744} | {1.09480428695679,1.1150735616684,1.10827457904816,1.11518168449402}
+(12 rows)
+
      2. +
    2. Predict probabilities for each class: 
      +DROP TABLE IF EXISTS iris_predict;
+SELECT madlib.madlib_keras_predict('iris_multi_model', -- model
+                                   'iris_test',        -- test_table
+                                   'id',               -- id column
+                                   'attributes',       -- independent var
+                                   'iris_predict',     -- output table
+                                    'prob',            -- prediction type
+                                    FALSE,             -- use gpus
+                                    3                  -- mst_key to use
+                                   );
+SELECT * FROM iris_predict ORDER BY id, rank;
+
      +-----+------------+-----------------+---------------+------
+   8 | class_text | Iris-setosa     |    0.99961567 |    1
+   8 | class_text | Iris-versicolor | 0.00038426166 |    2
+   8 | class_text | Iris-virginica  | 5.4132368e-08 |    3
+  15 | class_text | Iris-setosa     |     0.9999677 |    1
+  15 | class_text | Iris-versicolor |  3.235117e-05 |    2
+  15 | class_text | Iris-virginica  | 7.5747697e-10 |    3
+  20 | class_text | Iris-setosa     |    0.99956757 |    1
+  20 | class_text | Iris-versicolor |  0.0004323488 |    2
+  20 | class_text | Iris-virginica  | 6.8698306e-08 |    3
+  21 | class_text | Iris-setosa     |    0.99978334 |    1
+  21 | class_text | Iris-versicolor | 0.00021666527 |    2
+  21 | class_text | Iris-virginica  |  1.741537e-08 |    3
+  22 | class_text | Iris-setosa     |    0.99955314 |    1
+  22 | class_text | Iris-versicolor | 0.00044669537 |    2
+  22 | class_text | Iris-virginica  |  8.287442e-08 |    3
+  27 | class_text | Iris-setosa     |      0.999393 |    1
+  27 | class_text | Iris-versicolor | 0.00060693553 |    2
+  27 | class_text | Iris-virginica  | 1.4125514e-07 |    3
+  28 | class_text | Iris-setosa     |     0.9997589 |    1
+  28 | class_text | Iris-versicolor | 0.00024109415 |    2
+  28 | class_text | Iris-virginica  | 2.3418018e-08 |    3
+  33 | class_text | Iris-setosa     |    0.99966764 |    1
+  33 | class_text | Iris-versicolor | 0.00033237415 |    2
+  33 | class_text | Iris-virginica  | 3.2712443e-08 |    3
+  37 | class_text | Iris-setosa     |     0.9999347 |    1
+  37 | class_text | Iris-versicolor | 6.5290136e-05 |    2
+  37 | class_text | Iris-virginica  | 2.6893372e-09 |    3
+  38 | class_text | Iris-setosa     |    0.99963343 |    1
+  38 | class_text | Iris-versicolor |  0.0003665546 |    2
+  38 | class_text | Iris-virginica  | 4.7346873e-08 |    3
+  46 | class_text | Iris-setosa     |     0.9995722 |    1
+  46 | class_text | Iris-versicolor | 0.00042761036 |    2
+  46 | class_text | Iris-virginica  | 8.4179504e-08 |    3
+  51 | class_text | Iris-versicolor |     0.9678325 |    1
+  51 | class_text | Iris-virginica  |   0.031179406 |    2
+  51 | class_text | Iris-setosa     |  0.0009880556 |    3
+  57 | class_text | Iris-versicolor |     0.7971095 |    1
+  57 | class_text | Iris-virginica  |    0.20281655 |    2
+  57 | class_text | Iris-setosa     |  7.402597e-05 |    3
+  58 | class_text | Iris-versicolor |    0.93808955 |    1
+  58 | class_text | Iris-virginica  |   0.045088027 |    2
+  58 | class_text | Iris-setosa     |   0.016822474 |    3
+  59 | class_text | Iris-versicolor |    0.95377713 |    1
+  59 | class_text | Iris-virginica  |   0.045621604 |    2
+  59 | class_text | Iris-setosa     |  0.0006012956 |    3
+  64 | class_text | Iris-versicolor |     0.8078371 |    1
+  64 | class_text | Iris-virginica  |    0.19210756 |    2
+  64 | class_text | Iris-setosa     | 5.5370016e-05 |    3
+  65 | class_text | Iris-versicolor |      0.946594 |    1
+  65 | class_text | Iris-virginica  |    0.04081257 |    2
+  65 | class_text | Iris-setosa     |   0.012593448 |    3
+  72 | class_text | Iris-versicolor |     0.9616088 |    1
+  72 | class_text | Iris-virginica  |      0.033955 |    2
+  72 | class_text | Iris-setosa     |   0.004436169 |    3
+  75 | class_text | Iris-versicolor |    0.96245867 |    1
+  75 | class_text | Iris-virginica  |    0.03556654 |    2
+  75 | class_text | Iris-setosa     |  0.0019747794 |    3
+  87 | class_text | Iris-versicolor |     0.9264334 |    1
+  87 | class_text | Iris-virginica  |    0.07328824 |    2
+  87 | class_text | Iris-setosa     | 0.00027841402 |    3
+  95 | class_text | Iris-versicolor |    0.85156035 |    1
+  95 | class_text | Iris-virginica  |    0.14813933 |    2
+  95 | class_text | Iris-setosa     | 0.00030031145 |    3
+  97 | class_text | Iris-versicolor |    0.87470025 |    1
+  97 | class_text | Iris-virginica  |     0.1248041 |    2
+  97 | class_text | Iris-setosa     |  0.0004957556 |    3
+  98 | class_text | Iris-versicolor |     0.9439469 |    1
+  98 | class_text | Iris-virginica  |    0.05491364 |    2
+  98 | class_text | Iris-setosa     |   0.001139452 |    3
+ 120 | class_text | Iris-virginica  |    0.58107394 |    1
+ 120 | class_text | Iris-versicolor |    0.41892523 |    2
+ 120 | class_text | Iris-setosa     | 8.7891783e-07 |    3
+ 121 | class_text | Iris-virginica  |    0.90112364 |    1
+ 121 | class_text | Iris-versicolor |   0.098876335 |    2
+ 121 | class_text | Iris-setosa     | 5.8106266e-09 |    3
+ 122 | class_text | Iris-virginica  |     0.8664512 |    1
+ 122 | class_text | Iris-versicolor |    0.13354866 |    2
+ 122 | class_text | Iris-setosa     |  8.255242e-08 |    3
+ 123 | class_text | Iris-virginica  |    0.90162355 |    1
+ 123 | class_text | Iris-versicolor |    0.09837647 |    2
+ 123 | class_text | Iris-setosa     |  2.745874e-10 |    3
+ 140 | class_text | Iris-virginica  |     0.7306292 |    1
+ 140 | class_text | Iris-versicolor |     0.2693706 |    2
+ 140 | class_text | Iris-setosa     | 1.9480031e-07 |    3
+ 144 | class_text | Iris-virginica  |    0.92295665 |    1
+ 144 | class_text | Iris-versicolor |    0.07704339 |    2
+ 144 | class_text | Iris-setosa     | 1.6369142e-09 |    3
+ 147 | class_text | Iris-virginica  |    0.69545543 |    1
+ 147 | class_text | Iris-versicolor |    0.30454406 |    2
+ 147 | class_text | Iris-setosa     | 4.5714978e-07 |    3
+(90 rows)
+
      3. +
    3. Warm start. Next, use the warm_start parameter to continue learning, using the coefficients from the run above. Note that we don't drop the model table or model summary table: 
      +SELECT madlib.madlib_keras_fit_multiple_model('iris_train_packed',    -- source_table
+                                              'iris_multi_model',     -- model_output_table
+                                              'mst_table',            -- model_selection_table
+                                               3,                     -- num_iterations
+                                               FALSE,                 -- use gpus
+                                              'iris_test_packed',     -- validation dataset
+                                               1,                     -- metrics compute frequency
+                                               TRUE,                  -- warm start
+                                              'Sophie L.',            -- name
+                                              'Simple MLP for iris dataset',  -- description
+                                               TRUE                   -- use caching
+                                             );
+SELECT * FROM iris_multi_model_summary;
+
      +-[ RECORD 1 ]-------------+---------------------------------------------
+source_table              | iris_train_packed
+validation_table          | iris_test_packed
+model                     | iris_multi_model
+model_info                | iris_multi_model_info
+dependent_varname         | {class_text}
+independent_varname       | {attributes}
+model_arch_table          | model_arch_library
+model_selection_table     | mst_table
+object_table              | 
+num_iterations            | 3
+metrics_compute_frequency | 1
+warm_start                | t
+name                      | Sophie L.
+description               | Simple MLP for iris dataset
+start_training_time       | 2021-02-05 01:17:19.432839
+end_training_time         | 2021-02-05 01:18:09.062384
+madlib_version            | 2.1.0
+num_classes               | {1}
+class_text_class_values   | {Iris-setosa,Iris-versicolor,Iris-virginica}
+dependent_vartype         | {"character varying"}
+normalizing_const         | 1
+metrics_iters             | {1,2,3}
+
      View results for each model: 
      +SELECT * FROM iris_multi_model_info ORDER BY training_metrics_final DESC, training_loss_final;
+
      +  mst_key | model_id |                                 compile_params                                  |      fit_params       |  model_type  | model_size |                 metrics_elapsed_time                 | metrics_type |        loss_type         | training_metrics_final | training_loss_final |                    training_metrics                     |                      training_loss                      | validation_metrics_final | validation_loss_final |                   validation_metrics                    |                      validation_loss                      
+---------+----------+---------------------------------------------------------------------------------+-----------------------+--------------+------------+------------------------------------------------------+--------------+--------------------------+------------------------+---------------------+---------------------------------------------------------+---------------------------------------------------------+--------------------------+-----------------------+---------------------------------------------------------+-----------------------------------------------------------
+      10 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {15.5192940235138,31.2597029209137,47.3274641036987} | {accuracy}   | categorical_crossentropy |      0.966666638851166 |   0.122704714536667 | {0.925000011920929,0.808333337306976,0.966666638851166} | {0.172832280397415,0.354962348937988,0.122704714536667} |                        1 |    0.0603121444582939 | {1,0.866666674613953,1}                                 | {0.100369863212109,0.210344776511192,0.0603121444582939}
+       4 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {16.485249042511,32.207494020462,48.3005399703979}   | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.104984156787395 | {0.949999988079071,0.866666674613953,0.958333313465118} | {0.126872479915619,0.29683381319046,0.104984156787395}  |                        1 |    0.0291607566177845 | {1,0.933333337306976,1}                                 | {0.0433581434190273,0.127146035432816,0.0291607566177845}
+       3 |        1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {14.8933939933777,30.7211890220642,46.7588970661163} | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.107885278761387 | {0.941666662693024,0.966666638851166,0.958333313465118} | {0.155905768275261,0.129546254873276,0.107885278761387} |                        1 |    0.0387893654406071 | {1,1,1}                                                 | {0.087645135819912,0.0574964620172977,0.0387893654406071}
+       7 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {14.657429933548,30.4864449501038,46.5082159042358}  | {accuracy}   | categorical_crossentropy |      0.958333313465118 |   0.215500101447105 | {0.891666650772095,0.649999976158142,0.958333313465118} | {0.2352494597435,0.490339070558548,0.215500101447105}   |                        1 |     0.194652214646339 | {0.899999976158142,0.766666650772095,1}                 | {0.235657200217247,0.335934072732925,0.194652214646339}
+       6 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {16.2535049915314,31.9760749340057,48.0661840438843} | {accuracy}   | categorical_crossentropy |      0.941666662693024 |   0.354692339897156 | {0.975000023841858,0.908333361148834,0.941666662693024} | {0.38957467675209,0.367432981729507,0.354692339897156}  |                        1 |     0.321579396724701 | {1,0.966666638851166,1}                                 | {0.348732680082321,0.345716863870621,0.321579396724701}
+       2 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1 | madlib_keras | 0.75390625 | {16.0124208927155,31.7479128837585,47.8348250389099} | {accuracy}   | categorical_crossentropy |      0.933333337306976 |   0.238343968987465 | {0.975000023841858,0.975000023841858,0.933333337306976} | {0.17331151664257,0.0775784701108932,0.238343968987465} |        0.966666638851166 |     0.182112962007523 | {0.966666638851166,1,0.966666638851166}                 | {0.114220358431339,0.0159573350101709,0.182112962007523}
+       9 |        2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {15.1569800376892,30.9868409633636,47.0489699840546} | {accuracy}   | categorical_crossentropy |      0.908333361148834 |   0.254226505756378 | {0.858333349227905,0.833333313465118,0.908333361148834} | {0.450037389993668,0.500195503234863,0.254226505756378} |        0.966666638851166 |    0.0769383609294891 | {0.899999976158142,0.899999976158142,0.966666638851166} | {0.163723081350327,0.211927503347397,0.0769383609294891}
+      11 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 1.18359375 | {17.7095139026642,33.4267060756683,49.6263670921326} | {accuracy}   | categorical_crossentropy |      0.899999976158142 |   0.602623522281647 | {0.824999988079071,0.899999976158142,0.899999976158142} | {0.65915185213089,0.633350729942322,0.602623522281647}  |        0.899999976158142 |     0.626452326774597 | {0.833333313465118,0.899999976158142,0.899999976158142} | {0.695301294326782,0.661069989204407,0.626452326774597}
+       5 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {17.4354989528656,33.1478018760681,49.3430600166321} | {accuracy}   | categorical_crossentropy |      0.741666674613953 |   0.532543838024139 | {0.916666686534882,0.875,0.741666674613953}             | {0.610130310058594,0.571656167507172,0.532543838024139} |        0.633333325386047 |     0.540634453296661 | {0.966666638851166,0.899999976158142,0.633333325386047} | {0.601030588150024,0.567581355571747,0.540634453296661}
+      12 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {15.7747659683228,31.5215599536896,47.6013031005859} | {accuracy}   | categorical_crossentropy |      0.675000011920929 |   0.581513583660126 | {0.683333337306976,0.683333337306976,0.675000011920929} | {0.660648465156555,0.623969316482544,0.581513583660126} |        0.600000023841858 |     0.594986796379089 | {0.600000023841858,0.600000023841858,0.600000023841858} | {0.694275736808777,0.665920257568359,0.594986796379089}
+       1 |        1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1 | madlib_keras | 0.75390625 | {16.8983609676361,32.4361009597778,48.5357549190521} | {accuracy}   | categorical_crossentropy |      0.608333349227905 |   0.687089145183563 | {0.583333313465118,0.699999988079071,0.608333349227905} | {0.816642761230469,0.455933183431625,0.687089145183563} |        0.533333361148834 |     0.692391216754913 | {0.533333361148834,0.600000023841858,0.533333361148834} | {0.85290253162384,0.465981602668762,0.692391216754913}
+       8 |        2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1 | madlib_keras | 1.18359375 | {17.1899569034576,32.8988509178162,49.0880739688873} | {accuracy}   | categorical_crossentropy |      0.358333319425583 |    1.11154329776764 | {0.358333319425583,0.324999988079071,0.358333319425583} | {1.09858739376068,1.09980893135071,1.11154329776764}    |        0.233333334326744 |      1.16109442710876 | {0.233333334326744,0.366666674613953,0.233333334326744} | {1.12281405925751,1.10376691818237,1.16109442710876}
+(12 rows)
+
      Note that the loss and accuracy values pick up from where the previous run left off.
      4. +
    +

    Notes
    +
      +
    1. Refer to the deep learning section of the Apache MADlib wiki [6] for important information including supported libraries and versions.
      2. +
    2. Classification is currently supported, not regression.
      3. +
    3. Reminder about the distinction between warm start and transfer learning. Warm start uses model state (weights) from the model output table from a previous training run - set the 'warm_start' parameter to TRUE in the fit function. Transfer learning uses initial model state (weights) stored in the 'model_arch_table' - in this case set the 'warm_start' parameter to FALSE in the fit function.
      4. +
    4. Here are some more details on how warm start works. These details are mostly applicable when implementing autoML algorithms on top of MADlib's model selection. In short, the 'model_selection_table' dictates which models get trained and output to the 'model_output_table' and associated summary and info tables. When 'warm_start' is TRUE, models are built for each 'mst_key' in the 'model_selection_table'. If there are prior runs for an 'mst_key' then the weights from that run will be used. If there are no prior runs for an 'mst_key' then random initialization will be used. For example, let's say we start with 'mst_keys' of 1, 2, 3, and 4 in the 'model_selection_table'. We run fit once to get model and info tables for 1, 2, 3, and 4. Then we modify the 'model_selection_table' as part of an autoML scheme, in which we remove the 'mst_key' for 1 and add a new 'mst_key' for 5. Next we run fit with warm start. The result will be models created for 'mst_keys' of 2, 3, 4, and 5. Warm start will be used for 2, 3, and 4 (using prior run) and random initialization will be used for 5 (no prior run). The 'mst_key' of 1 will be dropped.
      5. +
    5. The 'num_iterations' parameter and the Keras fit parameter 'epochs' can substantially affect accuracy and run-time. In general, increasing the number of 'epochs' for a fixed 'num_iterations' will speed up training, but may result in lower accuracy. It's best to do some experimentation to find out what works for your models and dataset.
      6. +
    +

    Technical Background
    +

    For an introduction to deep learning foundations, including MLP and CNN, refer to [7].

    +

    This module trains many models a time across the database cluster in order to explore network architectures and hyperparameters. It uses model hopper parallelism (MOP) and has high convergence efficiency since it does not do model averaging [2].

    +

    On the effect of database cluster size: as the database cluster size increases, it will be faster to train a set of models, as long as you have at least as many model selection tuples as segments. This is because model state is "hopped" from segment to segment and training takes place in parallel [1,2]. If you have fewer model selection tuples to train than segments, then some segments may not be busy 100% of the time so speedup will not necessarily increase on a larger cluster. Inference (prediction) is an embarrassingly parallel operation so inference runtimes will be proportionally faster as the number of segments increases.

    +

    Literature
    +

    [1] "Cerebro: Efficient and Reproducible Model Selection on Deep Learning Systems," Supun Nakandala, Yuhao Zhang, and Arun Kumar, ACM SIGMOD 2019 DEEM Workshop, https://adalabucsd.github.io/papers/2019_Cerebro_DEEM.pdf

    +

    [2] "Cerebro: A Data System for Optimized Deep Learning Model Selection," Supun Nakandala, Yuhao Zhang, and Arun Kumar, Proceedings of the VLDB Endowment (2020), Vol. 13, No. 11 https://adalabucsd.github.io/papers/2020_Cerebro_VLDB.pdf

    +

    [3] https://keras.io/

    +

    [4] https://www.tensorflow.org/

    +

    [5] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent, Geoffrey Hinton with Nitish Srivastava and Kevin Swersky, http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

    +

    [6] Deep learning section of Apache MADlib wiki https://cwiki.apache.org/confluence/display/MADLIB/Deep+Learning

    +

    [7] Deep Learning, Ian Goodfellow, Yoshua Bengio and Aaron Courville, MIT Press, 2016.

    +

    [8] Greenplum Database server configuration parameters https://gpdb.docs.pivotal.io/latest/ref_guide/config_params/guc-list.html

    +

    Related Topics
    +

    File madlib_keras_fit_multiple_model.sql_in documents training, evaluate and predict functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__keras__setup__model__selection.html b/docs/docs/v2.1.0/group__grp__keras__setup__model__selection.html new file mode 100644 index 00000000..e565a38d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__keras__setup__model__selection.html @@ -0,0 +1,721 @@ + + + + + + + + +MADlib: Define Model Configurations + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Define Model Configurations
    Deep Learning » Train Multiple Models
    +
    +
    +
    Contents +

    This module generates model configurations using grid search or random search.

    +

    Once the configurations are defined, they can be used by the fit function in Train Model Configurations. By model configurations we mean both hyperparameters and model architectures. The output table from this module defines the combinations of model architectures, compile and fit parameters to be trained in parallel.

    +

    Generate Model Configurations
    +
    +generate_model_configs(
+    model_arch_table,
+    model_selection_table,
+    model_id_list,
+    compile_params_grid,
+    fit_params_grid,
+    search_type,
+    num_configs,
+    random_state,
+    object_table
+    )
+

    Arguments

    +
    model_arch_table
    +

    VARCHAR. Table containing model architectures and weights. For more information on this table refer to the module Define Model Architectures.

    +

    +
    +
    model_selection_table
    +

    VARCHAR. Model selection table created by this module. If this table already exists, it will be appended to. A summary table named <model_selection_table>_summary is also created. Contents of both output tables are described below.

    +

    +
    +
    model_id_list
    +

    INTEGER[]. Array of model IDs from the 'model_arch_table' to be included in the run combinations. For hyperparameter search, this will typically be one model ID. For model architecture search, this will be the different model IDs that you want to compare.

    +

    +
    +
    compile_params_grid
    +

    VARCHAR. String representation of a Python dictionary of compile parameters to be tested. Each entry of the dictionary should consist of keys as compile parameter names, and values as a Python list of compile parameter values to be passed to Keras. Also, optimizer parameters are a nested dictionary to allow different optimizer types to have different parameters or ranges of parameters. Here is an example:

    +
    +  $$
+    {'loss': ['categorical_crossentropy'],
+     'optimizer_params_list': [
+        {'optimizer': ['SGD'], 'lr': [0.0001, 0.001, 'log'], 'momentum': [0.95, 0.99, 'log_near_one']},
+        {'optimizer': ['Adam'], 'lr': [0.01, 0.1, 'log'], 'decay': [1e-6, 1e-4, 'log']}],
+     'metrics': ['accuracy']
+    }
+  $$
+

    The following types of sampling are supported: 'linear', 'log' and 'log_near_one'. The 'log_near_one' sampling is useful for exponentially weighted average types of parameters like momentum, which are very sensitive to changes near 1. It has the effect of producing more values near 1 than regular log-based sampling.

    +

    In the case of grid search, omit the sampling type and just put the grid points in the list.

    +
    Note
      +
    • Custom loss functions and custom metrics can be used as defined in Define Custom Functions. List the custom function name and provide the name of the table where the serialized Python objects reside using the parameter 'object_table' below.
      • +
    • The following loss function is not supported: sparse_categorical_crossentropy. The following metrics are not supported: sparse_categorical_accuracy, sparse_top_k_categorical_accuracy.
      • +
    • The Keras accuracy parameter top_k_categorical_accuracy returns top 5 accuracy by default. If you want a different top k value, use the helper function Top k Accuracy Function to create a custom Python function to compute the top k accuracy that you want.
      • +
    +
    +
    +
    fit_params_grid
    +

    VARCHAR. String representation of a Python dictionary of fit parameters to be tested. Each entry of the dictionary should consist of keys as fit parameter names, and values as a Python list of fit parameter values to be passed to Keras. Here is an example:

    +
    +  $$
+    {'batch_size': [32, 64, 128, 256],
+     'epochs': [10, 20, 30]
+    }
+  $$
+
    Note
    Callbacks are not currently supported except for TensorBoard which you can specify in the usual way, e.g., 'callbacks': ['[TensorBoard(log_dir="/tmp/logs/fit")]']
    +
    +
    search_type
    +

    VARCHAR, 'grid' or 'random'. Search strategy for generating model configurations. For grid search, will generate all combinations of model IDs + compile params + fit params. For random search, specify the number of configs you want to generate using the 'num_configs' parameter below. Note that you can also use short forms for the 'grid' or 'random' keywords, e.g.,'rand' or 'r' instead of writing out 'random' in full.

    +

    +
    +
    num_configs (optional)
    +

    INTEGER, default: NULL. Number of model configs to generate. Only applies when search_type='random'.

    +

    +
    +
    random_state (optional)
    +

    INTEGER, default: NULL. Pseudo random number generator state used for random uniform sampling from lists of possible values. Pass an integer for reproducible output across multiple function calls. Only applies when search_type='random'.

    +

    +
    +
    object_table (optional)
    +

    VARCHAR, default: NULL. Name of the table containing Python objects in the case that custom loss functions or custom metrics are specified in the 'compile_params_grid'. Note that this table has to be created by the Define Custom Functions method. It is not allowed to pass a schema name, since it will be automatically pulled from this functions associated madlib schema.

    +

    +
    +
    +

    Output table
    + The model selection output table contains the following columns:

    + + + + + + + + +
    mst_key INTEGER. ID that defines a unique tuple for model architecture-compile parameters-fit parameters.
    model_id VARCHAR. Model architecture ID from the 'model_arch_table'.
    compile_params VARCHAR. Keras compile parameters.
    fit_params VARCHAR. Keras fit parameters.
    +

    A summary table named <model_selection_table>_summary is also created, which contains the following column:

    + + + + +
    model_arch_table VARCHAR. Name of the model architecture table containing the model architecture IDs.
    object_table VARCHAR. Name of the object table containing the serialized Python objects for custom loss functions and custom metrics. If there are none, this field will be blank.
    +

    Load Model Selection Table [Deprecated]
    +

    This method is deprecated and replaced by the method 'generate_model_configs' described above.

    +
    +load_model_selection_table(
+    model_arch_table,
+    model_selection_table,
+    model_id_list,
+    compile_params_list,
+    fit_params_list,
+    object_table
+    )
+

    Arguments

    +
    model_arch_table
    +

    VARCHAR. Table containing model architectures and weights. For more information on this table refer to Define Model Architectures.

    +

    +
    +
    model_selection_table
    +

    VARCHAR. Model selection table created by this utility. A summary table named <model_selection_table>_summary is also created. Contents of both output tables are the same as described above for the method 'generate_model_configs'.

    +

    +
    +
    model_id_list
    +

    INTEGER[]. Array of model IDs from the 'model_arch_table' to be included in the run combinations. For hyperparameter search, this will typically be one model ID. For model architecture search, this will be the different model IDs that you want to test.

    +

    +
    +
    compile_params_list
    +

    VARCHAR[]. Array of compile parameters to be tested. Each element of the array should consist of a string of compile parameters exactly as it is to be passed to Keras. For custom loss functions or custom metrics, list the custom function name in the usual way, and also provide the name of the table where the serialized objects reside in the parameter 'object_table' below.

    +

    +
    +
    fit_params_list
    +

    VARCHAR[]. Array of fit parameters to be tested. Each element of the array should consist of a string of fit parameters exactly as it is to be passed to Keras. Callbacks are not currently supported except for TensorBoard which you can specify in the usual way, e.g., callbacks=[TensorBoard(log_dir="/tmp/logs/fit")]

    +

    +
    +
    object_table (optional)
    +

    VARCHAR, default: NULL. Name of the table containing Python objects in the case that custom loss functions or custom metrics are specified in the parameter 'compile_params_list'.

    +

    +
    +
    +

    Examples
      +
    1. The model selection table works in conjunction with a model architecture table, so we first create a model architecture table with two different models. Use Keras to define a model architecture with 1 hidden layer: 
      +from tensorflow.keras.models import Sequential
+from tensorflow.keras.layers import Dense
+model1 = Sequential()
+model1.add(Dense(10, activation='relu', input_shape=(4,)))
+model1.add(Dense(10, activation='relu'))
+model1.add(Dense(3, activation='softmax'))
+model1.summary()
+
      _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_1 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_2 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_3 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 193
+Trainable params: 193
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model1.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      Now use Keras to define a model architecture with 2 hidden layers: 
      +model2 = Sequential()
+model2.add(Dense(10, activation='relu', input_shape=(4,)))
+model2.add(Dense(10, activation='relu'))
+model2.add(Dense(10, activation='relu'))
+model2.add(Dense(3, activation='softmax'))
+model2.summary()
+
      _________________________________________________________________
+Layer (type)                 Output Shape              Param #
+=================================================================
+dense_4 (Dense)              (None, 10)                50
+_________________________________________________________________
+dense_5 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_6 (Dense)              (None, 10)                110
+_________________________________________________________________
+dense_7 (Dense)              (None, 3)                 33
+=================================================================
+Total params: 303
+Trainable params: 303
+Non-trainable params: 0
+
      
+
      Export the model to JSON: 
      +model2.to_json()
+
      +'{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}'
+
      2. +
    2. Load both models into the architecture table: 
      +DROP TABLE IF EXISTS model_arch_library;
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_1", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_2", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_3", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,         -- JSON blob
+                               NULL,                  -- Weights
+                               'Sophie',              -- Name
+                               'MLP with 1 hidden layer'       -- Descr
+);
+SELECT madlib.load_keras_model('model_arch_library',  -- Output table,
+$$
+{"class_name": "Sequential", "keras_version": "2.1.6", "config": [{"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_4", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "dtype": "float32", "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "batch_input_shape": [null, 4], "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_5", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_6", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "relu", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 10, "use_bias": true, "activity_regularizer": null}}, {"class_name": "Dense", "config": {"kernel_initializer": {"class_name": "VarianceScaling", "config": {"distribution": "uniform", "scale": 1.0, "seed": null, "mode": "fan_avg"}}, "name": "dense_7", "kernel_constraint": null, "bias_regularizer": null, "bias_constraint": null, "activation": "softmax", "trainable": true, "kernel_regularizer": null, "bias_initializer": {"class_name": "Zeros", "config": {}}, "units": 3, "use_bias": true, "activity_regularizer": null}}], "backend": "tensorflow"}
+$$
+::json,         -- JSON blob
+                               NULL,                  -- Weights
+                               'Maria',               -- Name
+                               'MLP with 2 hidden layers'       -- Descr
+);
+SELECT model_id, name, description FROM model_arch_library ORDER BY model_id;
+
      + model_id |  name  |       description
+----------+--------+--------------------------
+        1 | Sophie | MLP with 1 hidden layer
+        2 | Maria  | MLP with 2 hidden layers
+(2 rows)
+
      3. +
    3. Generate model configurations using grid search. The output table for grid search contains the unique combinations of model architectures, compile and fit parameters. 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [ {'optimizer': ['Adam', 'SGD'], 'lr': [0.001, 0.01]} ],
+                                             'metrics': ['accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'grid'               -- search_type
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                 compile_params                                  |        fit_params
+---------+----------+---------------------------------------------------------------------------------+--------------------------
+       1 |        1 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+       2 |        1 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+       3 |        1 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       4 |        1 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       5 |        1 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       6 |        1 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       7 |        1 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+       8 |        1 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+       9 |        2 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+      10 |        2 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      11 |        2 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      12 |        2 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      13 |        2 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      14 |        2 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      15 |        2 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      16 |        2 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+(16 rows)
+
      Note that above uses the same learning rate for the two optimizers. If you wanted to use different learning rates and different parameters for different optimizers (common): 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [
+                                                 {'optimizer': ['SGD']},
+                                                 {'optimizer': ['SGD'], 'lr': [0.0001, 0.001], 'momentum': [0.95]},
+                                                 {'optimizer': ['Adam'], 'lr': [0.01, 0.1], 'decay': [1e-4]}],
+                                             'metrics': ['accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'grid'               -- search_type
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                        compile_params                                         |        fit_params
+---------+----------+-----------------------------------------------------------------------------------------------+--------------------------
+       1 |        1 | optimizer='SGD()',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                        | epochs=10,batch_size=64
+       2 |        1 | optimizer='SGD()',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                        | epochs=10,batch_size=128
+       3 |        2 | optimizer='SGD()',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                        | epochs=10,batch_size=64
+       4 |        2 | optimizer='SGD()',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                        | epochs=10,batch_size=128
+       5 |        1 | optimizer='SGD(lr=0.0001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+       6 |        1 | optimizer='SGD(lr=0.0001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+       7 |        1 | optimizer='SGD(lr=0.001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       8 |        1 | optimizer='SGD(lr=0.001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       9 |        2 | optimizer='SGD(lr=0.0001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+      10 |        2 | optimizer='SGD(lr=0.0001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      11 |        2 | optimizer='SGD(lr=0.001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      12 |        2 | optimizer='SGD(lr=0.001,momentum=0.95)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      13 |        1 | optimizer='Adam(lr=0.01,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      14 |        1 | optimizer='Adam(lr=0.01,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+      15 |        1 | optimizer='Adam(lr=0.1,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'    | epochs=10,batch_size=64
+      16 |        1 | optimizer='Adam(lr=0.1,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'    | epochs=10,batch_size=128
+      17 |        2 | optimizer='Adam(lr=0.01,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      18 |        2 | optimizer='Adam(lr=0.01,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+      19 |        2 | optimizer='Adam(lr=0.1,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'    | epochs=10,batch_size=64
+      20 |        2 | optimizer='Adam(lr=0.1,decay=0.0001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'    | epochs=10,batch_size=128
+(20 rows)
+
      4. +
    4. Generate model configurations using random search. The output table for random search contains the specified number of model architectures, compile and fit parameters, sampled from the specified distributions. 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [
+                                                 {'optimizer': ['SGD'], 'lr': [0.0001, 0.001, 'log'], 'momentum': [0.95, 0.99, 'log_near_one']},
+                                                 {'optimizer': ['Adam'], 'lr': [0.01, 0.1, 'log'], 'decay': [1e-6, 1e-4, 'log']}],
+                                             'metrics': ['accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'random',            -- search_type
+                                         20
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                                       compile_params                                                        |        fit_params
+---------+----------+-----------------------------------------------------------------------------------------------------------------------------+--------------------------
+       1 |        1 | optimizer='SGD(lr=0.000195784477708685,momentum=0.9768159513291526)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+       2 |        2 | optimizer='SGD(lr=0.0002499200066875511,momentum=0.9807877269510826)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       3 |        1 | optimizer='SGD(lr=0.0009097798285407916,momentum=0.9706029152411938)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       4 |        1 | optimizer='SGD(lr=0.0001272842475986666,momentum=0.9858583458057799)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       5 |        1 | optimizer='SGD(lr=0.0001367874444015989,momentum=0.9772674033475668)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       6 |        2 | optimizer='SGD(lr=0.0002233708561319785,momentum=0.9743315606145182)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       7 |        1 | optimizer='SGD(lr=0.0009066689970530365,momentum=0.9835897505288803)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       8 |        1 | optimizer='SGD(lr=0.0007589416356572876,momentum=0.958751411608181)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+       9 |        2 | optimizer='Adam(lr=0.057814228170084386,decay=1.0641718595377929e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      10 |        1 | optimizer='Adam(lr=0.01927466297833838,decay=1.039476442716842e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+      11 |        2 | optimizer='Adam(lr=0.014718555287257804,decay=9.947768661882175e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      12 |        1 | optimizer='Adam(lr=0.010397686133595378,decay=2.5730580994358942e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      13 |        1 | optimizer='SGD(lr=0.0008624562426613621,momentum=0.989134963527059)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      14 |        2 | optimizer='SGD(lr=0.00010555974470031461,momentum=0.980489419269402)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      15 |        2 | optimizer='Adam(lr=0.05041699703418617,decay=4.685540619995589e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+      16 |        1 | optimizer='Adam(lr=0.034295140601304126,decay=1.6034699865163222e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+      17 |        1 | optimizer='Adam(lr=0.06888969005355218,decay=1.6318109152382423e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      18 |        2 | optimizer='SGD(lr=0.0008225712651952847,momentum=0.9819748008695103)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      19 |        1 | optimizer='Adam(lr=0.0819110285922332,decay=1.6912312124827899e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      20 |        1 | optimizer='Adam(lr=0.011688026325555774,decay=2.9315437856404027e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+(20 rows)
+
      5. +
    5. Incremental loading for more complex combinations. If it is easier to generate the model configurations incrementally rather than all at once, you can do that by not dropping the model selection table and associated summary table, in which case the new model configurations will be appended to the existing table. Here we combine two of the previous examples in to a single output table: 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [ {'optimizer': ['Adam', 'SGD'], 'lr': [0.001, 0.01]} ],
+                                             'metrics': ['accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'grid'               -- search_type
+                                         );
+
      Now add to the existing table and note that mst_key continues where it left off: 
      +SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [
+                                                 {'optimizer': ['SGD'], 'lr': [0.0001, 0.001, 'log'], 'momentum': [0.95, 0.99, 'log_near_one']},
+                                                 {'optimizer': ['Adam'], 'lr': [0.01, 0.1, 'log'], 'decay': [1e-6, 1e-4, 'log']}],
+                                             'metrics': ['accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'random',            -- search_type
+                                          20
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                                       compile_params                                                        |        fit_params
+---------+----------+-----------------------------------------------------------------------------------------------------------------------------+--------------------------
+       1 |        1 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                             | epochs=10,batch_size=64
+       2 |        1 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                             | epochs=10,batch_size=128
+       3 |        1 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=64
+       4 |        1 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=128
+       5 |        1 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=64
+       6 |        1 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=128
+       7 |        1 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                               | epochs=10,batch_size=64
+       8 |        1 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                               | epochs=10,batch_size=128
+       9 |        2 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                             | epochs=10,batch_size=64
+      10 |        2 | optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                             | epochs=10,batch_size=128
+      11 |        2 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=64
+      12 |        2 | optimizer='SGD(lr=0.001)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=128
+      13 |        2 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=64
+      14 |        2 | optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                              | epochs=10,batch_size=128
+      15 |        2 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                               | epochs=10,batch_size=64
+      16 |        2 | optimizer='SGD(lr=0.01)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'                                               | epochs=10,batch_size=128
+      17 |        2 | optimizer='SGD(lr=0.00013996842804647915,momentum=0.9677072493281305)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+      18 |        1 | optimizer='Adam(lr=0.04252873277972123,decay=9.503983307511243e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      19 |        2 | optimizer='Adam(lr=0.06666969394323848,decay=1.5626668941131748e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      20 |        2 | optimizer='SGD(lr=0.00016137313867804707,momentum=0.954293112127019)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      21 |        2 | optimizer='Adam(lr=0.019443570245321506,decay=1.2882524497407873e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+      22 |        2 | optimizer='Adam(lr=0.06302317748060839,decay=6.238009849562074e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+      23 |        2 | optimizer='SGD(lr=0.00010890482493011119,momentum=0.9826239169968034)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      24 |        1 | optimizer='SGD(lr=0.0009201966766121783,momentum=0.9896730563556151)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      25 |        2 | optimizer='SGD(lr=0.00028961522836420906,momentum=0.9859394149216544)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      26 |        1 | optimizer='SGD(lr=0.0001503249757866609,momentum=0.9777816636354879)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      27 |        2 | optimizer='SGD(lr=0.0008405326172626768,momentum=0.9538686498263182)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      28 |        1 | optimizer='SGD(lr=0.00011926989091387571,momentum=0.9876746918399469)',metrics=['categorical_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      29 |        1 | optimizer='Adam(lr=0.018794361633022855,decay=9.387826286694454e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      30 |        2 | optimizer='SGD(lr=0.0009692977025027591,momentum=0.9878758592330659)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      31 |        2 | optimizer='SGD(lr=0.0006671929498585603,momentum=0.9786502962872058)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      32 |        2 | optimizer='Adam(lr=0.03948766165185474,decay=3.056584635386748e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      33 |        2 | optimizer='Adam(lr=0.020343961099103417,decay=1.183810228780669e-05)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      34 |        1 | optimizer='Adam(lr=0.016854644990148417,decay=3.561117893117444e-06)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      35 |        2 | optimizer='SGD(lr=0.0004620089560788749,momentum=0.9887310587871919)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      36 |        1 | optimizer='SGD(lr=0.0002493912675066962,momentum=0.9892077270385708)',metrics=['categorical_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+(36 rows)
+
      6. +
    6. Create model selection table manually. If you want more control over the content of the model selection table, you could use grid or random search to generate a large number of combinations, then SELECT a subset of rows for training. Alternatively, you could manually create the model selection table and the associated summary table. Both must be created since they are needed by the multiple model fit module. For example, let's say we don't want all combinations but only want batch_size=4 for model_id=1 and batch_size=8 for model_id=2: 
      +DROP TABLE IF EXISTS mst_table_manual;
+CREATE TABLE mst_table_manual(
+    mst_key serial,
+    model_id integer,
+    compile_params varchar,
+    fit_params varchar
+);
+INSERT INTO mst_table_manual(model_id, compile_params, fit_params) VALUES
+(1, $$loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']$$, 'batch_size=4,epochs=1'),
+(1, $$loss='categorical_crossentropy',optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy']$$, 'batch_size=4,epochs=1'),
+(1, $$loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy']$$, 'batch_size=4,epochs=1'),
+(2, $$loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']$$, 'batch_size=8,epochs=1'),
+(2, $$loss='categorical_crossentropy',optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy']$$, 'batch_size=8,epochs=1'),
+(2, $$loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy']$$, 'batch_size=8,epochs=1');
+SELECT * FROM mst_table_manual ORDER BY mst_key;
+
      + mst_key | model_id      |                                 compile_params                                  |      fit_params
+---------+---------------+---------------------------------------------------------------------------------+-----------------------
+       1 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1
+       2 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy']  | batch_size=4,epochs=1
+       3 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1
+       4 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1
+       5 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy']  | batch_size=8,epochs=1
+       6 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1
+(6 rows)
+
      Create the summary table which must be named with the model selection output table appended by "_summary": 
      +DROP TABLE IF EXISTS mst_table_manual_summary;
+CREATE TABLE mst_table_manual_summary (
+    model_arch_table varchar
+);
+INSERT INTO mst_table_manual_summary(model_arch_table) VALUES
+('model_arch_library');
+SELECT * FROM mst_table_manual_summary;
+
      +  model_arch_table
+--------------------+
+ model_arch_library
+(1 row)
+
      7. +
    7. Custom loss functions and custom metrics. Let's say we have a table 'custom_function_table' that contains a custom loss function called 'my_custom_loss' and a custom accuracy function called 'my_custom_accuracy' based on Define Custom Functions. Generate the model configurations with: 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['my_custom_loss'],
+                                             'optimizer_params_list': [ {'optimizer': ['Adam', 'SGD'], 'lr': [0.001, 0.01]} ],
+                                             'metrics': ['my_custom_accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'grid',              -- search_type
+                                         NULL,                -- num_configs
+                                         NULL,                -- random_state
+                                         'custom_function_table'  -- table with custom functions
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                 compile_params                                  |        fit_params
+---------+----------+---------------------------------------------------------------------------------+--------------------------
+       1 |        1 | optimizer='Adam(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss' | epochs=10,batch_size=64
+       2 |        1 | optimizer='Adam(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss' | epochs=10,batch_size=128
+       3 |        1 | optimizer='SGD(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=64
+       4 |        1 | optimizer='SGD(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=128
+       5 |        1 | optimizer='Adam(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=64
+       6 |        1 | optimizer='Adam(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=128
+       7 |        1 | optimizer='SGD(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'   | epochs=10,batch_size=64
+       8 |        1 | optimizer='SGD(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'   | epochs=10,batch_size=128
+       9 |        2 | optimizer='Adam(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss' | epochs=10,batch_size=64
+      10 |        2 | optimizer='Adam(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss' | epochs=10,batch_size=128
+      11 |        2 | optimizer='SGD(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=64
+      12 |        2 | optimizer='SGD(lr=0.001)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=128
+      13 |        2 | optimizer='Adam(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=64
+      14 |        2 | optimizer='Adam(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'  | epochs=10,batch_size=128
+      15 |        2 | optimizer='SGD(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'   | epochs=10,batch_size=64
+      16 |        2 | optimizer='SGD(lr=0.01)',metrics=['my_custom_accuracy'],loss='my_custom_loss'   | epochs=10,batch_size=128
+(16 rows)
+
      Similarly, if you created a custom top k categorical accuracy function 'top_3_accuracy' in Define Custom Functions you can generate the model configurations as: 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.generate_model_configs(
+                                        'model_arch_library', -- model architecture table
+                                        'mst_table',          -- model selection table output
+                                         ARRAY[1,2],          -- model ids from model architecture table
+                                         $$
+                                            {'loss': ['categorical_crossentropy'],
+                                             'optimizer_params_list': [ {'optimizer': ['Adam', 'SGD'], 'lr': [0.001, 0.01]} ],
+                                             'metrics': ['top_3_accuracy']}
+                                         $$,                  -- compile_param_grid
+                                         $$
+                                         { 'batch_size': [64, 128],
+                                           'epochs': [10]
+                                         }
+                                         $$,                  -- fit_param_grid
+                                         'grid',              -- search_type
+                                         NULL,                -- num_configs
+                                         NULL,                -- random_state
+                                         'custom_function_table'  -- table with custom functions
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id |                                 compile_params                                  |        fit_params
+---------+----------+---------------------------------------------------------------------------------+--------------------------
+       1 |        1 | optimizer='Adam(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+       2 |        1 | optimizer='Adam(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+       3 |        1 | optimizer='SGD(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       4 |        1 | optimizer='SGD(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       5 |        1 | optimizer='Adam(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+       6 |        1 | optimizer='Adam(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+       7 |        1 | optimizer='SGD(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+       8 |        1 | optimizer='SGD(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+       9 |        2 | optimizer='Adam(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=64
+      10 |        2 | optimizer='Adam(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy' | epochs=10,batch_size=128
+      11 |        2 | optimizer='SGD(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      12 |        2 | optimizer='SGD(lr=0.001)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      13 |        2 | optimizer='Adam(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=64
+      14 |        2 | optimizer='Adam(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'  | epochs=10,batch_size=128
+      15 |        2 | optimizer='SGD(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=64
+      16 |        2 | optimizer='SGD(lr=0.01)',metrics=['top_3_accuracy'],loss='categorical_crossentropy'   | epochs=10,batch_size=128
+(16 rows)
+
      8. +
    8. [Deprecated] Load model selection table. This method is replaced by the 'generate_model_configs' method described above. Select the model(s) from the model architecture table that you want to run, along with the compile and fit parameters. Unique combinations will be created: 
      +DROP TABLE IF EXISTS mst_table, mst_table_summary;
+SELECT madlib.load_model_selection_table('model_arch_library', -- model architecture table
+                                         'mst_table',          -- model selection table output
+                                          ARRAY[1,2],              -- model ids from model architecture table
+                                          ARRAY[                   -- compile params
+                                              $$loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']$$,
+                                              $$loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy']$$,
+                                              $$loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy']$$
+                                          ],
+                                          ARRAY[                    -- fit params
+                                              $$batch_size=4,epochs=1$$,
+                                              $$batch_size=8,epochs=1$$
+                                          ]
+                                         );
+SELECT * FROM mst_table ORDER BY mst_key;
+
      + mst_key | model_id      |                                 compile_params                                  |      fit_params
+---------+---------------+---------------------------------------------------------------------------------+-----------------------
+       1 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1
+       2 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1
+       3 |             1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1
+       4 |             1 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1
+       5 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1
+       6 |             1 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1
+       7 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=4,epochs=1
+       8 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.1)',metrics=['categorical_accuracy']   | batch_size=8,epochs=1
+       9 |             2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1
+      10 |             2 | loss='categorical_crossentropy', optimizer='Adam(lr=0.01)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1
+      11 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=4,epochs=1
+      12 |             2 | loss='categorical_crossentropy',optimizer='Adam(lr=0.001)',metrics=['categorical_accuracy'] | batch_size=8,epochs=1
+(12 rows)
+
      The name of the model architecture table is stored in the summary table: 
      +SELECT * FROM mst_table_summary;
+
      +  model_arch_table
+--------------------+
+ model_arch_library
+(1 row)
+
      9. +
    +
    +

    Related Topics
    +

    See keras_model_arch_table.sql_in

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__kmeans.html b/docs/docs/v2.1.0/group__grp__kmeans.html new file mode 100644 index 00000000..77e2cedb --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__kmeans.html @@ -0,0 +1,757 @@ + + + + + + + + +MADlib: k-Means Clustering + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
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    + +
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    +
    k-Means Clustering
    Unsupervised Learning » Clustering
    +
    +
    +
    Contents +

    Clustering refers to the problem of partitioning a set of objects according to some problem-dependent measure of similarity. In the k-means variant, given \( n \) points \( x_1, \dots, x_n \in \mathbb R^d \), the goal is to position \( k \) centroids \( c_1, \dots, c_k \in \mathbb R^d \) so that the sum of distances between each point and its closest centroid is minimized. Each centroid represents a cluster that consists of all points to which this centroid is closest.

    +

    This module can compute clusters given the number of centroids k as an input, using a variety of seeding methods. It can also automatically select the best k value from a range of suggested k values, using the simplified silhouette method or the elbow method.

    +

    Clustering Function
    +

    The k-means algorithm can be invoked in different ways, depending on the source of the initial set of centroids:

    +
      +
    • Uniform random centroid seeding method. 
      +kmeans_random( rel_source,
+               expr_point,
+               k,
+               fn_dist,
+               agg_centroid,
+               max_num_iterations,
+               min_frac_reassigned
+             )
+
      • +
    • k-means++ centroid seeding method [1]. This method can speed up convergence by seeding centroids spread out over the whole range of the input points, while at the same time not being too susceptible to outliers. 
      +kmeanspp( rel_source,
+          expr_point,
+          k,
+          fn_dist,
+          agg_centroid,
+          max_num_iterations,
+          min_frac_reassigned,
+          seeding_sample_ratio
+        )
+
      • +
    • Supply an initial centroid set in a relation identified by the rel_initial_centroids argument, for the case where initial centroids are stored in a table. 
      +kmeans( rel_source,
+        expr_point,
+        rel_initial_centroids,
+        expr_centroid,
+        fn_dist,
+        agg_centroid,
+        max_num_iterations,
+        min_frac_reassigned
+      )
+
      • +
    • Provide an initial centroid set as an array expression in the initial_centroids argument. 
      +kmeans( rel_source,
+        expr_point,
+        initial_centroids,
+        fn_dist,
+        agg_centroid,
+        max_num_iterations,
+        min_frac_reassigned
+      )
+
      • +
    +

    Arguments

    +
    rel_source
    +

    TEXT. The name of the table containing the input data points. Data points and predefined centroids (if used) are expected to be stored row-wise, in a column of type SVEC (or any type convertible to SVEC, like FLOAT[] or INTEGER[]). Data points with non-finite values (NULL, NaN, infinity) in any component are skipped during analysis.

    +

    +
    +
    expr_point
    +

    TEXT. The name of the column with point coordinates or an array expression.

    +

    +
    +
    k
    +

    INTEGER. The number of centroids to calculate.

    +

    +
    +
    fn_dist (optional)
    +

    TEXT, default: 'squared_dist_norm2'. The name of the function to use to calculate the distance from a data point vector to a centroid vector. The following distance functions can be used (computation of barycenter/mean in parentheses):

      +
    • +dist_norm1: 1-norm/Manhattan (element-wise median). MADlib does not provide a median aggregate function for performance reasons.
      • +
    • +dist_norm2: 2-norm/Euclidean (element-wise mean)
      • +
    • +squared_dist_norm2: squared Euclidean distance (element-wise mean)
      • +
    • +dist_angle: angle (element-wise mean of normalized points)
      • +
    • +dist_tanimoto: tanimoto (element-wise mean of normalized points [5])
      • +
    • +user defined function with signature DOUBLE PRECISION[] x, DOUBLE PRECISION[] y -> DOUBLE PRECISION
      • +
    +

    +
    +
    agg_centroid (optional)
    +

    TEXT, default: 'avg'. The name of the aggregate function used to determine centroids. The following aggregate functions can be used:

    +

    +
    +
    max_num_iterations (optional)
    +

    INTEGER, default: 20. The maximum number of iterations to perform.

    +

    +
    +
    min_frac_reassigned (optional)
    +

    DOUBLE PRECISION, default: 0.001. The minimum fraction of centroids reassigned to continue iterating. When fewer than this fraction of centroids are reassigned in an iteration, the calculation completes.

    +

    +
    +
    seeding_sample_ratio (optional)
    +

    DOUBLE PRECISION, default: 1.0. The proportion of subsample of original dataset to use for kmeans++ centroid seeding method. Kmeans++ scans through the data sequentially 'k' times and can be too slow for big datasets. When 'seeding_sample_ratio' is greater than 0 (thresholded to be maximum value of 1.0), the seeding is run on a uniform random subsample of the data. Note: the final K-means algorithm is run on the complete dataset. This parameter only builds a subsample for the seeding and is only available for kmeans++.

    +

    +
    +
    rel_initial_centroids
    +

    TEXT. Table or view containing the set of initial centroids.

    +

    +
    +
    expr_centroid
    +

    TEXT. The name of the column (or the array expression) in the rel_initial_centroids table or view that contains the centroid coordinates.

    +

    +
    +
    initial_centroids
    +
    DOUBLE PRECISION[][]. Array expression with the initial centroid coordinates.
    +
    +

    Output
    + The output of the k-means module is a composite type with the following columns:

    + + + + + + + + + + +
    centroids DOUBLE PRECISION[][]. The final centroid positions.
    cluster_variance DOUBLE PRECISION[]. The value of the objective function per cluster.
    objective_fn DOUBLE PRECISION. The value of the objective function.
    frac_reassigned DOUBLE PRECISION. The fraction of points reassigned in the last iteration.
    num_iterations INTEGER. The total number of iterations executed.
    +

    Auto Clustering Function
    +

    The optimal number of centroids can be determined automatically, from a set of candidate values that you provide, for random seeding or k-means++ seeding. The simplified silhouette method or the elbow method are used to pick the best k value.

    +
      +
    • Uniform random centroid seeding method. 
      +kmeans_random_auto( rel_source,
+                    output_table,
+                    expr_point,
+                    k,
+                    fn_dist,
+                    agg_centroid,
+                    max_num_iterations,
+                    min_frac_reassigned,
+                    k_selection_algorithm
+                  )
+
      • +
    • k-means++ centroid seeding method. 
      +kmeanspp_auto( rel_source,
+               output_table,
+               expr_point,
+               k,
+               fn_dist,
+               agg_centroid,
+               max_num_iterations,
+               min_frac_reassigned,
+               seeding_sample_ratio,
+               k_selection_algorithm
+              )
+
      • +
    +

    Arguments
    + The arguments for auto k selection are the same as described above, with the following additions:

    +
    output_table
    +

    TEXT. Name of the output table containing results for each k value. Details of the output table are shown below. A summary table called <output_table>_summary will also be created for the best k value as per the selection algorithm.

    +

    +
    +
    k
    +

    INTEGER[]. Array of k values to test. Does not need to be contiguous but all elements must be >1 and cannot repeat within the array. Parameter 'k_selection_algorithm' determines the evaluation method.

    +

    +
    +
    k_selection_algorithm (optional)
    +

    TEXT, default: 'silhouette'. Method to evaluate optimal number of centroids k. Current approaches supported: 'silhouette', 'elbow' or 'both'. The text can be any subset of the strings; for e.g., 'silh' will use the silhouette method. Note that for large data sets, the silhouette computation can be expensive.

    +
    Note
    Note that the auto k-means algorithms require the NumPy python package to be installed on the system since the elbow method uses the NumPy gradient function [2]. For Greenplum clusters, installing NumPy only on the host machine of the master segment will be sufficient. The suggested installation method is: pip install numpy –user
    +
    +
    +

    Output Tables
    + Two output tables are created for auto k-means. The first is called 'output_table' and contains one row per k value:

    + + + + + + + + + + + + + + + + + + + + +
    k INTEGER. Number of centroids.
    centroids DOUBLE PRECISION[][]. The final centroid positions.
    cluster_variance DOUBLE PRECISION[]. The value of the objective function per cluster.
    objective_fn DOUBLE PRECISION. The value of the objective function.
    frac_reassigned DOUBLE PRECISION. The fraction of points reassigned in the last iteration.
    num_iterations INTEGER. The total number of iterations executed.
    k INTEGER. Number of centroids as per the specified 'k_selection_algorithm'. If 'both' is specified, the best k value will correspond to the silhouette method.
    silhouette DOUBLE PRECISION. The value of the simplified silhouette score for the k value, if computed.
    elbow DOUBLE PRECISION. The value of the elbow score for the k value, if computed.
    selection_algorithm TEXT. Algorithm used to select the best k (either 'silhouette' or 'elbow')
    +

    A summary table named <output_table>_summary is also created, which has the same output as the 'output_table' above but only contains one row for best k value as per the selection algorithm. If 'both' is specified for 'k_selection_algorithm' the best k value returned will correspond to the silhouette method.

    +

    Cluster Assignment
    +

    After clustering, the cluster assignment for each data point can be computed with the help of the closest_column() utility function:

    +
    +closest_column( m,
+                x,
+                dist
+                )
+

    Arguments

    +
    m
    +

    DOUBLE PRECISION[][]. Learned centroids from the training function.

    +

    +
    +
    x
    +

    DOUBLE PRECISION[]. Data points.

    +

    +
    +
    dist (optional)
    +
    TEXT, default: 'squared_dist_norm2'. The name of the function to use to calculate the distance from a data point vector to a centroid vector. See the fn_dist argument of the k-means training function for more details on distance functions.
    +
    +

    Output
    + The output is a composite type with the following columns:

    + + + + +
    column_id INTEGER. Cluster assignment (zero-based, i.e., 0,1,2...).
    distance DOUBLE PRECISION. Distance to the cluster centroid.
    +

    Simple Silhouette
    +

    A common method to assess the quality of the clustering is the silhouette coefficient, a simplified version of which is implemented in MADlib [3]. There are two silhouette functions: average score across all data points, and a per-point score. The average silhouette function has the following syntax: 

    +simple_silhouette( rel_source,
+                   expr_point,
+                   centroids,
+                   fn_dist
+                 )
+

    The per-point silhouette function has two formats. The first takes an array of centroids: 

    +simple_silhouette_points(rel_source,
+                         output_table,
+                         pid,
+                         expr_point,
+                         centroids,
+                         fn_dist
+                        )
+

    The second takes a centroids column from a table: 

    +simple_silhouette_points(rel_source,
+                         output_table,
+                         pid,
+                         expr_point,
+                         centroids_table,
+                         centroids_col,
+                         fn_dist
+                        )
+

    Arguments

    +
    rel_source
    +

    TEXT. The name of the table containing the input data points.

    +

    +
    +
    expr_point
    +

    TEXT. The name of the column with point coordinates or an array expression.

    +

    +
    +
    centroids
    +

    DOUBLE PRECISION[][]. An expression evaluating to an array of centroids.

    +

    +
    +
    fn_dist (optional)
    +

    TEXT, default: 'squared_dist_norm2'. The name of the function to use to calculate the distance from a data point vector to a centroid vector. See the fn_dist argument of the k-means training function for more details on distance functions.

    +

    +
    +
    output_table
    +

    TEXT. Name of the output table to contain sihouette score for each point.

    +

    +
    +
    pid
    +

    TEXT. Column containing point ID in the table 'rel_source' containing the data points.

    +

    +
    +
    centroids_table
    +

    TEXT. Name of the table containing the centroids.

    +

    +
    +
    centroids_col
    +

    TEXT. Name of the column in the table 'centroids_table' containing the centroids.

    +

    +
    +
    +

    Output
    + For the average function, a single value for simple silhouette score is returned. For the per-point function, the output table contains the following columns:

    + + + + + + + + +
    pid

    INTEGER. Point ID.

    +

    +
    centroid_id

    INTEGER. The cluster that the point is assigned to.

    +

    +
    neighbor_centroid_id

    INTEGER. The next closest cluster to the one that the point is assigned to.

    +

    +
    simple_silhouette DOUBLE PRECISION. Simplified silhouette score for the point.
    +

    Examples
    +
    Note
    Your results may not be exactly the same as below due to the nature random nature of the k-means algorithm. Also, remember to be consistent in the distance functions that you use in the k-means, silhouette and helper functions.
    +

    Clustering for Single k Value

    +
      +
    1. Create input data: 
      +DROP TABLE IF EXISTS km_sample;
+CREATE TABLE km_sample(pid int, points double precision[]);
+INSERT INTO km_sample VALUES
+(1,  '{14.23, 1.71, 2.43, 15.6, 127, 2.8, 3.0600, 0.2800, 2.29, 5.64, 1.04, 3.92, 1065}'),
+(2,  '{13.2, 1.78, 2.14, 11.2, 1, 2.65, 2.76, 0.26, 1.28, 4.38, 1.05, 3.49, 1050}'),
+(3,  '{13.16, 2.36,  2.67, 18.6, 101, 2.8,  3.24, 0.3, 2.81, 5.6799, 1.03, 3.17, 1185}'),
+(4,  '{14.37, 1.95, 2.5, 16.8, 113, 3.85, 3.49, 0.24, 2.18, 7.8, 0.86, 3.45, 1480}'),
+(5,  '{13.24, 2.59, 2.87, 21, 118, 2.8, 2.69, 0.39, 1.82, 4.32, 1.04, 2.93, 735}'),
+(6,  '{14.2, 1.76, 2.45, 15.2, 112, 3.27, 3.39, 0.34, 1.97, 6.75, 1.05, 2.85, 1450}'),
+(7,  '{14.39, 1.87, 2.45, 14.6, 96, 2.5, 2.52, 0.3, 1.98, 5.25, 1.02, 3.58, 1290}'),
+(8,  '{14.06, 2.15, 2.61, 17.6, 121, 2.6, 2.51, 0.31, 1.25, 5.05, 1.06, 3.58, 1295}'),
+(9,  '{14.83, 1.64, 2.17, 14, 97, 2.8, 2.98, 0.29, 1.98, 5.2, 1.08, 2.85, 1045}'),
+(10, '{13.86, 1.35, 2.27, 16, 98, 2.98, 3.15, 0.22, 1.8500, 7.2199, 1.01, 3.55, 1045}');
+
      2. +
    2. Run k-means clustering using kmeans++ for centroid seeding. Use squared Euclidean distance which is a commonly used distance function. 
      +DROP TABLE IF EXISTS km_result;
+CREATE TABLE km_result AS
+SELECT * FROM madlib.kmeanspp( 'km_sample',   -- Table of source data
+                               'points',      -- Column containing point co-ordinates
+                               2,             -- Number of centroids to calculate
+                               'madlib.squared_dist_norm2',   -- Distance function
+                               'madlib.avg',  -- Aggregate function
+                               20,            -- Number of iterations
+                               0.001          -- Fraction of centroids reassigned to keep iterating
+                             );
+\x on;
+SELECT * FROM km_result;
+
      +-[ RECORD 1 ]----+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+centroids        | {{14.255,1.9325,2.5025,16.05,110.5,3.055,2.9775,0.2975,1.845,6.2125,0.9975,3.365,1378.75},{13.7533333333333,1.905,2.425,16.0666666666667,90.3333333333333,2.805,2.98,0.29,2.005,5.40663333333333,1.04166666666667,3.31833333333333,1020.83333333333}}
+cluster_variance | {30561.74805,122999.110416013}
+objective_fn     | 153560.858466013
+frac_reassigned  | 0
+num_iterations   | 2
+
      3. +
    3. Simplified silhouette coefficient. First find average for whole data set. Make sure to use the same distance function as k-means above. 
      +SELECT * FROM madlib.simple_silhouette( 'km_sample',          -- Input points table
+                                        'points',             -- Column containing points
+                                        (SELECT centroids FROM km_result),  -- Centroids
+                                        'madlib.squared_dist_norm2'   -- Distance function
+                                      );
+
      +-[ RECORD 1 ]-----+------------------
+simple_silhouette | 0.868174608939623
+
      Now calculate simplified silhouette coefficient for each point in the data set: 
      +DROP TABLE IF EXISTS km_points_silh;
+SELECT * FROM madlib.simple_silhouette_points( 'km_sample',          -- Input points table
+                                              'km_points_silh',      -- Output table
+                                              'pid',                 -- Point ID column in input table
+                                              'points',              -- Points column in input table
+                                              'km_result',           -- Centroids table
+                                              'centroids',           -- Column in centroids table containing centroids
+                                              'madlib.squared_dist_norm2'   -- Distance function
+                                      );
+\x off
+SELECT * FROM km_points_silh ORDER BY pid;
+
      + pid | centroid_id | neighbor_centroid_id |       silh
+-----+-------------+----------------------+-------------------
+   1 |           1 |                    0 | 0.966608819821713
+   2 |           1 |                    0 | 0.926251125077039
+   3 |           1 |                    0 |  0.28073008848306
+   4 |           0 |                    1 | 0.951447083910869
+   5 |           1 |                    0 |  0.80098239014753
+   6 |           0 |                    1 | 0.972487557020722
+   7 |           0 |                    1 |  0.88838568723116
+   8 |           0 |                    1 | 0.906334719972002
+   9 |           1 |                    0 | 0.994315140692314
+  10 |           1 |                    0 |  0.99420347703982
+(10 rows)
+
      4. +
    4. Find the cluster assignment for each point. Use the closest_column() function to map each point to the cluster that it belongs to. 
      +DROP TABLE IF EXISTS point_cluster_map;
+CREATE TABLE point_cluster_map AS
+SELECT data.*, (madlib.closest_column(centroids, points, 'madlib.squared_dist_norm2')).*
+FROM km_sample as data, km_result;
+ALTER TABLE point_cluster_map RENAME column_id to cluster_id; -- change column name
+SELECT * FROM point_cluster_map ORDER BY pid;
+
      + pid |                               points                               | cluster_id |     distance
+-----+--------------------------------------------------------------------+------------+------------------
+   1 | {14.23,1.71,2.43,15.6,127,2.8,3.06,0.28,2.29,5.64,1.04,3.92,1065}  |          1 | 3296.12614333444
+   2 | {13.2,1.78,2.14,11.2,1,2.65,2.76,0.26,1.28,4.38,1.05,3.49,1050}    |          1 | 8856.90882600111
+   3 | {13.16,2.36,2.67,18.6,101,2.8,3.24,0.3,2.81,5.6799,1.03,3.17,1185} |          1 | 27072.3216580044
+   4 | {14.37,1.95,2.5,16.8,113,3.85,3.49,0.24,2.18,7.8,0.86,3.45,1480}   |          0 |    10261.9450375
+   5 | {13.24,2.59,2.87,21,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735}     |          1 | 82492.8673553345
+   6 | {14.2,1.76,2.45,15.2,112,3.27,3.39,0.34,1.97,6.75,1.05,2.85,1450}  |          0 |     5080.3612375
+   7 | {14.39,1.87,2.45,14.6,96,2.5,2.52,0.3,1.98,5.25,1.02,3.58,1290}    |          0 |     8090.4485875
+   8 | {14.06,2.15,2.61,17.6,121,2.6,2.51,0.31,1.25,5.05,1.06,3.58,1295}  |          0 |     7128.9931875
+   9 | {14.83,1.64,2.17,14,97,2.8,2.98,0.29,1.98,5.2,1.08,2.85,1045}      |          1 | 634.301947334443
+  10 | {13.86,1.35,2.27,16,98,2.98,3.15,0.22,1.85,7.2199,1.01,3.55,1045}  |          1 | 646.584486004443
+(10 rows)
+
      5. +
    5. Display cluster ID. There are two steps to get the cluster id associated with the centroid coordinates, if you need it. First unnest the cluster centroids 2-D array to get a set of 1-D centroid arrays: 
      +DROP TABLE IF EXISTS km_centroids_unnest;
+-- Run unnest function
+CREATE TABLE km_centroids_unnest AS
+SELECT (madlib.array_unnest_2d_to_1d(centroids)).*
+FROM km_result;
+SELECT * FROM km_centroids_unnest ORDER BY 1;
+
      + unnest_row_id |                                                                       unnest_result
+---------------+------------------------------------------------------------------------------------------------------------------------------------------------------------
+             1 | {14.255,1.9325,2.5025,16.05,110.5,3.055,2.9775,0.2975,1.845,6.2125,0.9975,3.365,1378.75}
+             2 | {13.7533333333333,1.905,2.425,16.0666666666667,90.3333333333333,2.805,2.98,0.29,2.005,5.40663333333333,1.04166666666667,3.31833333333333,1020.83333333333}
+(2 rows)
+
      Note that the ID column returned by array_unnest_2d_to_1d() is just a row ID and not the cluster ID assigned by k-means. The second step to get the cluster_id is: 
      +SELECT cent.*,  (madlib.closest_column(centroids, unnest_result, 'madlib.squared_dist_norm2')).column_id as cluster_id
+FROM km_centroids_unnest as cent, km_result
+ORDER BY cent.unnest_row_id;
+
      + unnest_row_id |                                                                       unnest_result                                                                        | cluster_id
+---------------+------------------------------------------------------------------------------------------------------------------------------------------------------------+------------
+             1 | {14.255,1.9325,2.5025,16.05,110.5,3.055,2.9775,0.2975,1.845,6.2125,0.9975,3.365,1378.75}                                                                   |          0
+             2 | {13.7533333333333,1.905,2.425,16.0666666666667,90.3333333333333,2.805,2.98,0.29,2.005,5.40663333333333,1.04166666666667,3.31833333333333,1020.83333333333} |          1
+(2 rows)
+
      6. +
    6. Run the same example as above, but using array input. Create the input table: 
      +DROP TABLE IF EXISTS km_arrayin CASCADE;
+CREATE TABLE km_arrayin(pid int,
+                        p1 float,
+                        p2 float,
+                        p3 float,
+                        p4 float,
+                        p5 float,
+                        p6 float,
+                        p7 float,
+                        p8 float,
+                        p9 float,
+                        p10 float,
+                        p11 float,
+                        p12 float,
+                        p13 float);
+INSERT INTO km_arrayin VALUES
+(1,  14.23, 1.71, 2.43, 15.6, 127, 2.8, 3.0600, 0.2800, 2.29, 5.64, 1.04, 3.92, 1065),
+(2,  13.2, 1.78, 2.14, 11.2, 1, 2.65, 2.76, 0.26, 1.28, 4.38, 1.05, 3.49, 1050),
+(3,  13.16, 2.36,  2.67, 18.6, 101, 2.8,  3.24, 0.3, 2.81, 5.6799, 1.03, 3.17, 1185),
+(4,  14.37, 1.95, 2.5, 16.8, 113, 3.85, 3.49, 0.24, 2.18, 7.8, 0.86, 3.45, 1480),
+(5,  13.24, 2.59, 2.87, 21, 118, 2.8, 2.69, 0.39, 1.82, 4.32, 1.04, 2.93, 735),
+(6,  14.2, 1.76, 2.45, 15.2, 112, 3.27, 3.39, 0.34, 1.97, 6.75, 1.05, 2.85, 1450),
+(7,  14.39, 1.87, 2.45, 14.6, 96, 2.5, 2.52, 0.3, 1.98, 5.25, 1.02, 3.58, 1290),
+(8,  14.06, 2.15, 2.61, 17.6, 121, 2.6, 2.51, 0.31, 1.25, 5.05, 1.06, 3.58, 1295),
+(9,  14.83, 1.64, 2.17, 14, 97, 2.8, 2.98, 0.29, 1.98, 5.2, 1.08, 2.85, 1045),
+(10, 13.86, 1.35, 2.27, 16, 98, 2.98, 3.15, 0.22, 1.8500, 7.2199, 1.01, 3.55, 1045);
+
      Now find the cluster assignment for each point using random seeding: 
      +DROP TABLE IF EXISTS km_result_array;
+-- Run kmeans algorithm
+CREATE TABLE km_result_array AS
+SELECT * FROM madlib.kmeans_random('km_arrayin',                 -- Table of source data
+                                'ARRAY[p1, p2, p3, p4, p5, p6,   -- Points
+                                      p7, p8, p9, p10, p11, p12, p13]',
+                                2,                               -- Number of centroids to calculate
+                                'madlib.squared_dist_norm2',     -- Distance function
+                                'madlib.avg',                    -- Aggregate function
+                                20,                              -- Number of iterations
+                                0.001);                          -- Fraction of centroids reassigned to keep iterating
+-- Get point assignment
+SELECT data.*,  (madlib.closest_column(centroids,
+                                       ARRAY[p1, p2, p3, p4, p5, p6,
+                                      p7, p8, p9, p10, p11, p12, p13],
+                                       'madlib.squared_dist_norm2')).column_id as cluster_id
+FROM km_arrayin as data, km_result_array
+ORDER BY data.pid;
+
      This produces the result in column format: 
      + pid |  p1   |  p2  |  p3  |  p4  | p5  |  p6  |  p7  |  p8  |  p9  |  p10   | p11  | p12  | p13  | cluster_id
+-----+-------+------+------+------+-----+------+------+------+------+--------+------+------+------+------------
+   1 | 14.23 | 1.71 | 2.43 | 15.6 | 127 |  2.8 | 3.06 | 0.28 | 2.29 |   5.64 | 1.04 | 3.92 | 1065 |          0
+   2 |  13.2 | 1.78 | 2.14 | 11.2 |   1 | 2.65 | 2.76 | 0.26 | 1.28 |   4.38 | 1.05 | 3.49 | 1050 |          0
+   3 | 13.16 | 2.36 | 2.67 | 18.6 | 101 |  2.8 | 3.24 |  0.3 | 2.81 | 5.6799 | 1.03 | 3.17 | 1185 |          1
+   4 | 14.37 | 1.95 |  2.5 | 16.8 | 113 | 3.85 | 3.49 | 0.24 | 2.18 |    7.8 | 0.86 | 3.45 | 1480 |          1
+   5 | 13.24 | 2.59 | 2.87 |   21 | 118 |  2.8 | 2.69 | 0.39 | 1.82 |   4.32 | 1.04 | 2.93 |  735 |          0
+   6 |  14.2 | 1.76 | 2.45 | 15.2 | 112 | 3.27 | 3.39 | 0.34 | 1.97 |   6.75 | 1.05 | 2.85 | 1450 |          1
+   7 | 14.39 | 1.87 | 2.45 | 14.6 |  96 |  2.5 | 2.52 |  0.3 | 1.98 |   5.25 | 1.02 | 3.58 | 1290 |          1
+   8 | 14.06 | 2.15 | 2.61 | 17.6 | 121 |  2.6 | 2.51 | 0.31 | 1.25 |   5.05 | 1.06 | 3.58 | 1295 |          1
+   9 | 14.83 | 1.64 | 2.17 |   14 |  97 |  2.8 | 2.98 | 0.29 | 1.98 |    5.2 | 1.08 | 2.85 | 1045 |          0
+  10 | 13.86 | 1.35 | 2.27 |   16 |  98 | 2.98 | 3.15 | 0.22 | 1.85 | 7.2199 | 1.01 | 3.55 | 1045 |          0
+(10 rows)
+
      7. +
    +

    Auto Clustering for Range of k Values

    +
      +
    1. Auto k selection. Now let's run k-means random for a variety of k values and compare using simple silhouette and elbow methods. 
      +DROP TABLE IF EXISTS km_result_auto, km_result_auto_summary;
+SELECT madlib.kmeans_random_auto(
+    'km_sample',                   -- points table
+    'km_result_auto',              -- output table
+    'points',                      -- column name in point table
+    ARRAY[2,3,4,5,6],              -- k values to try
+    'madlib.squared_dist_norm2',   -- distance function
+    'madlib.avg',                  -- aggregate function
+    20,                            -- max iterations
+    0.001,                         -- minimum fraction of centroids reassigned to continue iterating
+    'both'                         -- k selection algorithm  (simple silhouette and elbow)
+);
+\x on
+SELECT * FROM km_result_auto_summary;
+
      -[ RECORD 1 ]-------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+k                   | 6
+centroids           | {{14.23,1.71,2.43,15.6,127,2.8,3.06,0.28,2.29,5.64,1.04,3.92,1065},{13.24,2.59,2.87,21,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735},{14.285,1.855,2.475,16,112.5,3.56,3.44,0.29,2.075,7.275,0.955,3.15,1465},{13.87,2.12666666666667,2.57666666666667,16.9333333333333,106,2.63333333333333,2.75666666666667,0.303333333333333,2.01333333333333,5.32663333333333,1.03666666666667,3.44333333333333,1256.66666666667},{14.345,1.495,2.22,15,97.5,2.89,3.065,0.255,1.915,6.20995,1.045,3.2,1045},{13.2,1.78,2.14,11.2,1,2.65,2.76,0.26,1.28,4.38,1.05,3.49,1050}}
+cluster_variance    | {0,0,452.7633,8078.22646267333,5.346498005,0}
+objective_fn        | 8536.33626067833
+frac_reassigned     | 0
+num_iterations      | 3
+silhouette          | 0.954496117675027
+elbow               | -50296.3677976633
+selection_algorithm | silhouette
+
      The best selection above is made by the silhouette algorithm by default. Note that the elbow method may select a different k value as the best. To see results for all k values: 
      +SELECT * FROM km_result_auto ORDER BY k;
+
      +-[ RECORD 1 ]----+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+k                | 2
+centroids        | {{14.036,2.018,2.536,16.56,108.6,3.004,3.03,0.298,2.038,6.10598,1.004,3.326,1340},{13.872,1.814,2.376,15.56,88.2,2.806,2.928,0.288,1.844,5.35198,1.044,3.348,988}}
+cluster_variance | {60672.638245208,90512.324426408}
+objective_fn     | 151184.962671616
+frac_reassigned  | 0
+num_iterations   | 3
+silhouette       | 0.872087020146542
+elbow            | -1056.25028126836
+-[ RECORD 2 ]----+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+k                | 3
+centroids        | {{13.87,2.12666666666667,2.57666666666667,16.9333333333333,106,2.63333333333333,2.75666666666667,0.303333333333333,2.01333333333333,5.32663333333333,1.03666666666667,3.44333333333333,1256.66666666667},{14.285,1.855,2.475,16,112.5,3.56,3.44,0.29,2.075,7.275,0.955,3.15,1465},{13.872,1.814,2.376,15.56,88.2,2.806,2.928,0.288,1.844,5.35198,1.044,3.348,988}}
+cluster_variance | {8078.22646267333,452.7633,90512.324426408}
+objective_fn     | 99043.3141890814
+frac_reassigned  | 0
+num_iterations   | 2
+silhouette       | 0.895849874221733
+elbow            | 20549.7753189989
+-[ RECORD 3 ]----+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+k                | 4
+centroids        | {{14.02,1.765,2.385,16.05,105.75,2.845,3.1075,0.2725,2.2325,5.93495,1.04,3.3725,1085},{13.24,2.59,2.87,21,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735},{14.255,1.9325,2.5025,16.05,110.5,3.055,2.9775,0.2975,1.845,6.2125,0.9975,3.365,1378.75},{13.2,1.78,2.14,11.2,1,2.65,2.76,0.26,1.28,4.38,1.05,3.49,1050}}
+cluster_variance | {14227.41709401,0,30561.74805,0}
+objective_fn     | 44789.16514401
+frac_reassigned  | 0
+num_iterations   | 3
+silhouette       | 0.877839150000438
+elbow            | 17535.7421610686
+-[ RECORD 4 ]----+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+k                | 5
+centroids        | {{14.285,1.855,2.475,16,112.5,3.56,3.44,0.29,2.075,7.275,0.955,3.15,1465},{14.225,2.01,2.53,16.1,108.5,2.55,2.515,0.305,1.615,5.15,1.04,3.58,1292.5},{13.2,1.78,2.14,11.2,1,2.65,2.76,0.26,1.28,4.38,1.05,3.49,1050},{14.04,1.8225,2.435,16.65,110,2.845,2.97,0.295,1.985,5.594975,1.0425,3.3125,972.5},{13.16,2.36,2.67,18.6,101,2.8,3.24,0.3,2.81,5.6799,1.03,3.17,1185}}
+cluster_variance | {452.7633,329.8988,0,76176.4564000075,0}
+objective_fn     | 76959.1185000075
+frac_reassigned  | 0
+num_iterations   | 2
+silhouette       | 0.771207558995578
+elbow            | -28690.3421973961
+-[ RECORD 5 ]----+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+k                | 6
+centroids        | {{14.23,1.71,2.43,15.6,127,2.8,3.06,0.28,2.29,5.64,1.04,3.92,1065},{13.24,2.59,2.87,21,118,2.8,2.69,0.39,1.82,4.32,1.04,2.93,735},{14.285,1.855,2.475,16,112.5,3.56,3.44,0.29,2.075,7.275,0.955,3.15,1465},{13.87,2.12666666666667,2.57666666666667,16.9333333333333,106,2.63333333333333,2.75666666666667,0.303333333333333,2.01333333333333,5.32663333333333,1.03666666666667,3.44333333333333,1256.66666666667},{14.345,1.495,2.22,15,97.5,2.89,3.065,0.255,1.915,6.20995,1.045,3.2,1045},{13.2,1.78,2.14,11.2,1,2.65,2.76,0.26,1.28,4.38,1.05,3.49,1050}}
+cluster_variance | {0,0,452.7633,8078.22646267333,5.346498005,0}
+objective_fn     | 8536.33626067833
+frac_reassigned  | 0
+num_iterations   | 3
+silhouette       | 0.954496117675027
+elbow            | -50296.3677976633
+
      2. +
    2. Simplified silhouette per point. Let's say we want the simplified silhouette coefficient for each point in the data set, for the case where k=3: 
      +DROP TABLE IF EXISTS km_points_silh;
+SELECT * FROM madlib.simple_silhouette_points( 'km_sample',          -- Input points table
+                                              'km_points_silh',     -- Output table
+                                              'pid',                -- Point ID column in input table
+                                              'points',             -- Points column in input table
+                                              (SELECT centroids FROM km_result_auto WHERE k=3), -- centroids array
+                                              'madlib.squared_dist_norm2'   -- Distance function
+                                      );
+\x off
+SELECT * FROM km_points_silh ORDER BY pid;
+
      + pid | centroid_id | neighbor_centroid_id |       silh
+-----+-------------+----------------------+-------------------
+   1 |           2 |                    0 | 0.800019825058391
+   2 |           2 |                    0 | 0.786712987562913
+   3 |           0 |                    2 | 0.867496080386644
+   4 |           1 |                    0 | 0.995466498952947
+   5 |           2 |                    0 | 0.761551610381542
+   6 |           1 |                    0 | 0.993950286967157
+   7 |           0 |                    1 | 0.960621637528528
+   8 |           0 |                    1 | 0.941493577405087
+   9 |           2 |                    0 | 0.925822020308802
+  10 |           2 |                    0 |  0.92536421766532
+(10 rows)
+
      3. +
    +

    Technical Background
    +

    k-means Algorithm
    + Formally, we wish to minimize the following objective function:

    +\[ (c_1, \dots, c_k) \mapsto \sum_{i=1}^n \min_{j=1}^k \operatorname{dist}(x_i, c_j) \] +

    +

    In the most common case, \( \operatorname{dist} \) is the square of the Euclidean distance, though other distance measures can be used.

    +

    This problem is computationally difficult (NP-hard), yet the local-search heuristic proposed by Lloyd [4] performs reasonably well in practice. In fact, it is so ubiquitous today that it is often referred to as the standard algorithm or even just the k-means algorithm. It works as follows:

    +
      +
    1. Seed the \( k \) centroids, meaning specify their initial positions (see below).
      2. +
    2. Repeat until convergence:
        +
      1. Assign each point to its closest centroid.
        2. +
      2. Move each centroid to a position that minimizes the sum of distances in this cluster.
        3. +
      +
      3. +
    3. Convergence is achieved when no points change their assignments during step 2a.
      4. +
    +

    Since the objective function decreases in every step, this algorithm is guaranteed to converge to a local optimum.

    +

    The quality of k-means is highly influenced by the choice of the seeding. In MADlib we support uniform-at-random sampling, kmeans++ as well as the ability for the user to enter manual seeding based on other methods.

    +

    k-means++ seeding [1] starts with a single centroid chosen randomly among the input points. It then iteratively chooses new centroids from the input points until there are a total of k centroids. The probability for picking a particular point is proportional to its minimum distance to any existing centroid. Intuitively, k-means++ favors seedings where centroids are spread out over the whole range of the input points, while at the same time not being too susceptible to outliers.

    +

    Silhouette
    +

    +

    To evaluate the validity of clustering with different k values, the objective function is not ideal because it decreases as k value increases, so it has a bias toward selecting the largest k as the best result [6]. Therefore we use other internal measures to evaluate cluster validity.

    +

    One such measure is silhouette score. The original formulation [7] computes the average distance of a data point to all the other data points in its own cluster, and to all the data points in the neighbouring cluster nearest to the data point. This is expensive for a large number of points since it requires the full pairwise distance matrix over all data.

    +

    In the simplified silhouette [3] which is used in MADlib, the distance of a data point to a cluster is represented with the distance to the cluster centroid instead of the average distance to all (other) data points in the cluster. This has the advantage of being much faster to compute, and can be shown to be comparable in performance to the full silhouette [8].

    +

    Elbow Method
    + The elbow method considers the percentage of variance explained as a function of number of clusters. The idea is not to add another cluster if it doesn't model the data better. Graphically it means identifying the "elbow" in the curve of sum of squared errors vs. number of clusters (k). This was possibly originally suggested in [9]. To locate the elbow, we use the 2nd derivative of the objective function using the NumPy gradient function [2].

    +

    Literature
    +

    [1] David Arthur, Sergei Vassilvitskii: k-means++: the advantages of careful seeding, Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'07), pp. 1027-1035.

    +

    [2] NumPy gradient function, https://docs.scipy.org/doc/numpy/reference/generated/numpy.gradient.html

    +

    [3] E. R. Hruschka, L. N. C. Silva, R. J. G. B. Campello: Clustering Gene-Expression Data: A Hybrid Approach that Iterates Between k-Means and Evolutionary Search. In: Studies in Computational Intelligence - Hybrid Evolutionary Algorithms. pp. 313-335. Springer. 2007.

    +

    [4] Lloyd, Stuart: Least squares quantization in PCM. Technical Note, Bell Laboratories. Published much later in: IEEE Transactions on Information Theory 28(2), pp. 128-137. 1982.

    +

    [5] Leisch, Friedrich: A Toolbox for K-Centroids Cluster Analysis. In: Computational Statistics and Data Analysis, 51(2). pp. 526-544. 2006.

    +

    [6] Jain, A.K.: Data clustering: 50 years beyond k-means. Pattern recognition letters 31(8), 651–666 (2010)

    +

    [7] Peter J. Rousseeuw (1987). “Silhouettes: a Graphical Aid to the Interpretation and Validation of Cluster Analysis”. Computational and Applied Mathematics 20: 53-65

    +

    [8] Wang F., Franco-Penya HH., Kelleher J.D., Pugh J., Ross R. (2017) An Analysis of the Application of Simplified Silhouette to the Evaluation of k-means Clustering Validity. In: Perner P. (eds) Machine Learning and Data Mining in Pattern Recognition. MLDM 2017. Lecture Notes in Computer Science, vol 10358. Springer, Cham

    +

    [9] Robert L. Thorndike (December 1953). "Who Belongs in the Family?". Psychometrika. 18 (4): 267–276. doi:10.1007/BF02289263.

    +

    Related Topics
    +

    File kmeans.sql_in documenting the k-Means SQL functions

    +

    Sparse Vectors

    +

    closest_column()

    +

    array_unnest_2d_to_1d()

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__knn.html b/docs/docs/v2.1.0/group__grp__knn.html new file mode 100644 index 00000000..59565b8d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__knn.html @@ -0,0 +1,546 @@ + + + + + + + + +MADlib: k-Nearest Neighbors + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    k-Nearest Neighbors
    Supervised Learning
    +
    +
    +
    Contents +

    K-nearest neighbors is a method for finding the \(k\) closest points to a given data point in terms of a given metric. Its input consists of data points as features from testing examples and it looks for \(k\) closest points in the training set for each of the data points in test set. The output of KNN depends on the type of task. For classification, the output is the majority vote of the classes of the \(k\) nearest data points. For regression, the output is the average of the values of \(k\) nearest neighbors of the given test point.

    +

    For unsupervised nearest neighbors, set the training set to match the test set so the nearest neighbor of each point is the point itself, with zero distance.

    +

    Both exact and approximate methods are supported. The approximate methods can be used in the case that run-time is too long using the exact method.

    +

    Usage
    +knn( point_source,
+     point_column_name,
+     point_id,
+     label_column_name,
+     test_source,
+     test_column_name,
+     test_id,
+     output_table,
+     k,
+     output_neighbors,
+     fn_dist,
+     weighted_avg,
+     algorithm,
+     algorithm_params
+   )
+
    +

    Arguments

    +
    point_source
    +

    TEXT. Name of the table containing the training data points. Training data points are expected to be stored row-wise in a column of type DOUBLE PRECISION[].

    +

    +
    +
    point_column_name
    +

    TEXT. Name of the column with training data points or expression that evaluates to a numeric array

    +

    +
    +
    point_id
    +

    TEXT. Name of the column in 'point_source’ containing source data ids. The ids are of type INTEGER with no duplicates. They do not need to be contiguous. This parameter must be used if the list of nearest neighbors are to be output, i.e., if the parameter 'output_neighbors' below is TRUE or if 'label_column_name' is NULL.

    +

    +
    +
    label_column_name
    +

    TEXT. Name of the column with labels/values of training data points. If this column is a Boolean, integer or text, it will run KNN classification, else if it is double precision values will run KNN regression. If you set this to NULL, it will only return the set of neighbors without actually doing classification or regression.

    +

    +
    +
    test_source
    +

    TEXT. Name of the table containing the test data points. Testing data points are expected to be stored row-wise in a column of type DOUBLE PRECISION[].

    +

    +
    +
    test_column_name
    +

    TEXT. Name of the column with testing data points or expression that evaluates to a numeric array

    +
    Note
    For unsupervised nearest neighbors, make the test dataset the same as the source dataset, so the nearest neighbor of each point is the point itself, with a zero distance.
    +
    +
    test_id
    +

    TEXT. Name of the column having ids of data points in test data table.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table to store final results.

    +

    +
    +
    k (optional)
    +

    INTEGER. default: 1. Number of nearest neighbors to consider. For classification, should be an odd number to break ties, otherwise the result may depend on ordering of the input data.

    +

    +
    +
    output_neighbors (optional)
    +

    BOOLEAN default: TRUE. Outputs the list of k-nearest neighbors (and their respective distances to the target point) that were used in the voting/averaging, sorted from closest to furthest.

    +

    +
    +
    fn_dist (optional)
    +

    TEXT, default: 'squared_dist_norm2'. The name of the function used to calculate the distance between data points.

    +

    The following distance functions can be used:

      +
    • +dist_norm1: 1-norm/Manhattan
      • +
    • +dist_norm2: 2-norm/Euclidean
      • +
    • +squared_dist_norm2: squared Euclidean distance
      • +
    • +dist_angle: angle
      • +
    • +dist_tanimoto: tanimoto
      • +
    • +user defined function with signature DOUBLE PRECISION[] x, DOUBLE PRECISION[] y -> DOUBLE PRECISION. Must return a value greater than or equal to zero.
      • +
    +
    Note
    Always qualify the distance function with the schema name. For example, if you install MADlib in a schema called 'madlib' then the 'fn_dist' parameter would be 'madlib.dist_norm2', etc.
    +
    +
    weighted_avg (optional)
    +

    BOOLEAN, default: FALSE. Calculates classification or regression values using a weighted average. The idea is to weigh the contribution of each of the k neighbors according to their distance to the test point, giving greater influence to closer neighbors. The distance function 'fn_dist' specified above is used. For classification, majority voting weighs a neighbor according to inverse distance. For regression, the inverse distance weighting approach is used from Shepard [4].

    +

    +
    +
    algorithm (optional)
    +

    TEXT, default: 'brute_force'. The name of the algorithm used to compute nearest neighbors. The following options are supported:

      +
    • +brute_force: Produces an exact result by searching all points in the search space. You can also use a short form "b" or "brute" etc. to select brute force.
      • +
    • +kd_tree: Produces an approximate result by searching a subset of the search space, that is, only certain leaf nodes in the kd-tree as specified by "algorithm_params" below. You can also use a short form "k" or "kd" etc. to select kd-tree.
      • +
    +

    +
    +
    algorithm_params (optional)
    +

    TEXT, default: 'depth=3, leaf_nodes=2'. These parameters apply to the kd-tree algorithm only.

      +
    • +depth: Depth of the kd-tree. Increasing this value will decrease run-time but reduce the accuracy.
      • +
    • +leaf_nodes: Number of leaf nodes (regions) to search for each test point. Inceasing this value will improve the accuracy but increase run-time.
      • +
    +
    Note
    Please note that the kd-tree accuracy will be lower for datasets with a high number of features. It is advised to use at least two leaf nodes. Refer to the Technical Background for more information on how the kd-tree is implemented.
    +
    +
    +

    Output Format
    +

    The output of the KNN module is a table with the following columns:

    + + + + + + + + + + +
    id INTEGER. The ids of test data points.
    test_column_name DOUBLE PRECISION[]. The test data points.
    prediction INTEGER. Label in case of classification, average value in case of regression.
    k_nearest_neighbours INTEGER[]. List of nearest neighbors, sorted closest to furthest from the corresponding test point.
    distance DOUBLE PRECISION[]. List of distance to nearest neighbors, sorted closest to furthest from the corresponding test point.
    +

    Examples
    +
      +
    1. Prepare some training data for classification: 
      +DROP TABLE IF EXISTS knn_train_data;
+CREATE TABLE knn_train_data (
+                    id integer,
+                    data integer[],
+                    label integer  -- Integer label means for classification
+                    );
+INSERT INTO knn_train_data VALUES
+(1, '{1,1}', 1),
+(2, '{2,2}', 1),
+(3, '{3,3}', 1),
+(4, '{4,4}', 1),
+(5, '{4,5}', 1),
+(6, '{20,50}', 0),
+(7, '{10,31}', 0),
+(8, '{81,13}', 0),
+(9, '{1,111}', 0);
+
      2. +
    2. Prepare some training data for regression: 
      +DROP TABLE IF EXISTS knn_train_data_reg;
+CREATE TABLE knn_train_data_reg (
+                    id integer,
+                    data integer[],
+                    label float  -- Float label means for regression
+                    );
+INSERT INTO knn_train_data_reg VALUES
+(1, '{1,1}', 1.0),
+(2, '{2,2}', 1.0),
+(3, '{3,3}', 1.0),
+(4, '{4,4}', 1.0),
+(5, '{4,5}', 1.0),
+(6, '{20,50}', 0.0),
+(7, '{10,31}', 0.0),
+(8, '{81,13}', 0.0),
+(9, '{1,111}', 0.0);
+
      3. +
    3. Prepare some testing data: 
      +DROP TABLE IF EXISTS knn_test_data CASCADE;
+CREATE TABLE knn_test_data (
+                    id integer,
+                    data integer[]
+                    );
+INSERT INTO knn_test_data VALUES
+(1, '{2,1}'),
+(2, '{2,6}'),
+(3, '{15,40}'),
+(4, '{12,1}'),
+(5, '{2,90}'),
+(6, '{50,45}');
+
      4. +
    4. Run KNN for classification. Prepend the distance function parameter with the schema where MADlib is installed (in this example 'madlib.squared_dist_norm2'): 
      +DROP TABLE IF EXISTS knn_result_classification;
+SELECT * FROM madlib.knn(
+                'knn_train_data',      -- Table of training data
+                'data',                -- Col name of training data
+                'id',                  -- Col name of id in train data
+                'label',               -- Training labels
+                'knn_test_data',       -- Table of test data
+                'data',                -- Col name of test data
+                'id',                  -- Col name of id in test data
+                'knn_result_classification',  -- Output table
+                 3,                    -- Number of nearest neighbors
+                 True,                 -- True to list nearest-neighbors by id
+                'madlib.squared_dist_norm2' -- Distance function
+                );
+SELECT * from knn_result_classification ORDER BY id;
+
      Result: 
      + id |  data   | prediction | k_nearest_neighbours | distance
+----+---------+------------+----------------------+---------------------
+  1 | {2,1}   |          1 | {1,2,3}              | {1,1,5}
+  2 | {2,6}   |          1 | {5,4,3}              | {5,8,10}
+  3 | {15,40} |          0 | {7,6,5}              | {106,125,1346}
+  4 | {12,1}  |          1 | {4,5,3}              | {73,80,85}
+  5 | {2,90}  |          0 | {9,6,7}              | {442,1924,3545}
+  6 | {50,45} |          0 | {6,7,8}              | {925,1796,1985}
+(6 rows)
+
      Note that the nearest neighbors are sorted from closest to furthest from the corresponding test point.
      5. +
    5. Run KNN for regression: 
      +DROP TABLE IF EXISTS knn_result_regression;
+SELECT * FROM madlib.knn(
+                'knn_train_data_reg',  -- Table of training data
+                'data',                -- Col name of training data
+                'id',                  -- Col Name of id in train data
+                'label',               -- Training labels
+                'knn_test_data',       -- Table of test data
+                'data',                -- Col name of test data
+                'id',                  -- Col name of id in test data
+                'knn_result_regression',  -- Output table
+                 3,                    -- Number of nearest neighbors
+                 True,                 -- True to list nearest-neighbors by id
+                'madlib.dist_norm2'    -- Distance function
+                );
+SELECT * FROM knn_result_regression ORDER BY id;
+
      Result: 
      + id |  data   |    prediction     | k_nearest_neighbours |                 distance
+----+---------+-------------------+----------------------+------------------------------------------------------
+  1 | {2,1}   |                 1 | {1,2,3}              | {1,1,2.23606797749979}
+  2 | {2,6}   |                 1 | {5,4,3}              | {2.23606797749979,2.82842712474619,3.16227766016838}
+  3 | {15,40} | 0.333333333333333 | {7,6,5}              | {10.295630140987,11.1803398874989,36.6878726556883}
+  4 | {12,1}  |                 1 | {4,5,3}              | {8.54400374531753,8.94427190999916,9.21954445729289}
+  5 | {2,90}  |                 0 | {9,6,7}              | {21.0237960416286,43.8634243989226,59.5399025864168}
+  6 | {50,45} |                 0 | {6,7,8}              | {30.4138126514911,42.3792402008342,44.5533388198909}
+(6 rows)
+
      6. +
    6. List nearest neighbors only, without doing classification or regression: 
      +DROP TABLE IF EXISTS knn_result_list_neighbors;
+SELECT * FROM madlib.knn(
+                'knn_train_data_reg',  -- Table of training data
+                'data',                -- Col name of training data
+                'id',                  -- Col Name of id in train data
+                 NULL,                 -- NULL training labels means just list neighbors
+                'knn_test_data',       -- Table of test data
+                'data',                -- Col name of test data
+                'id',                  -- Col name of id in test data
+                'knn_result_list_neighbors', -- Output table
+                 3                     -- Number of nearest neighbors
+                );
+SELECT * FROM knn_result_list_neighbors ORDER BY id;
+
      Result, with neighbors sorted from closest to furthest: 
      + id |  data   | k_nearest_neighbours | distance
+----+---------+----------------------+---------------------
+  1 | {2,1}   | {1,2,3}              | {1,1,5}
+  2 | {2,6}   | {5,4,3}              | {5,8,10}
+  3 | {15,40} | {7,6,5}              | {106,125,1346}
+  4 | {12,1}  | {4,5,3}              | {73,80,85}
+  5 | {2,90}  | {9,6,7}              | {442,1924,3545}
+  6 | {50,45} | {6,7,8}              | {925,1796,1985}
+(6 rows)
+
      7. +
    7. Run KNN for classification using the weighted average: 
      +DROP TABLE IF EXISTS knn_result_classification;
+SELECT * FROM madlib.knn(
+                'knn_train_data',      -- Table of training data
+                'data',                -- Col name of training data
+                'id',                  -- Col name of id in train data
+                'label',               -- Training labels
+                'knn_test_data',       -- Table of test data
+                'data',                -- Col name of test data
+                'id',                  -- Col name of id in test data
+                'knn_result_classification',  -- Output table
+                 3,                    -- Number of nearest neighbors
+                 True,                 -- True to list nearest-neighbors by id
+                'madlib.squared_dist_norm2', -- Distance function
+                 True                 -- For weighted average
+                );
+SELECT * FROM knn_result_classification ORDER BY id;
+
      + id |  data   | prediction | k_nearest_neighbours | distance
+----+---------+------------+----------------------+---------------------
+  1 | {2,1}   |          1 | {1,2,3}              | {1,1,5}
+  2 | {2,6}   |          1 | {5,4,3}              | {5,8,10}
+  3 | {15,40} |          0 | {7,6,5}              | {106,125,1346}
+  4 | {12,1}  |          1 | {4,5,3}              | {73,80,85}
+  5 | {2,90}  |          0 | {9,6,7}              | {442,1924,3545}
+  6 | {50,45} |          0 | {6,7,8}              | {925,1796,1985}
+(6 rows)
+
      8. +
    8. Use kd-tree option. First we build a kd-tree to depth 4 and search half (8) of the 16 leaf nodes (i.e., 2^4 total leaf nodes): 
      +DROP TABLE IF EXISTS knn_result_classification_kd;
+SELECT madlib.knn(
+                'knn_train_data',        -- Table of training data
+                'data',                  -- Col name of training data
+                'id',                    -- Col name of id in train data
+                 NULL,                   -- Training labels
+                'knn_test_data',         -- Table of test data
+                'data',                  -- Col name of test data
+                'id',                    -- Col name of id in test data
+                'knn_result_classification_kd',  -- Output table
+                 3,                      -- Number of nearest neighbors
+                 True,                   -- True to list nearest-neighbors by id
+                'madlib.squared_dist_norm2', -- Distance function
+                 False,                  -- For weighted average
+                'kd_tree',               -- Use kd-tree
+                'depth=4, leaf_nodes=8'  -- Kd-tree options
+                 );
+SELECT * FROM knn_result_classification_kd ORDER BY id;
+
      + id |  data   | k_nearest_neighbours | distance
+----+---------+----------------------+---------------------
+  1 | {2,1}   | {1,2,3}              | {1,1,5}
+  2 | {2,6}   | {5,4,3}              | {5,8,10}
+  3 | {15,40} | {7,6,5}              | {106,125,1346}
+  4 | {12,1}  | {4,5,3}              | {73,80,85}
+  5 | {2,90}  | {9,6,7}              | {442,1924,3545}
+  6 | {50,45} | {6,7,8}              | {925,1796,1985}
+(6 rows)
+
      The result above is the same as brute force. If we search just 1 leaf node, run-time will be faster but accuracy will be lower. This shows up in this very small data set by not being able to find 3 nearest neighbors for all test points: 
      +DROP TABLE IF EXISTS knn_result_classification_kd;
+SELECT madlib.knn(
+                'knn_train_data',        -- Table of training data
+                'data',                  -- Col name of training data
+                'id',                    -- Col name of id in train data
+                 NULL,                   -- Training labels
+                'knn_test_data',         -- Table of test data
+                'data',                  -- Col name of test data
+                'id',                    -- Col name of id in test data
+                'knn_result_classification_kd',  -- Output table
+                 3,                      -- Number of nearest neighbors
+                 True,                   -- True to list nearest-neighbors by id
+                'madlib.squared_dist_norm2', -- Distance function
+                 False,                  -- For weighted average
+                'kd_tree',               -- Use kd-tree
+                'depth=4, leaf_nodes=1'  -- Kd-tree options
+                 );
+SELECT * FROM knn_result_classification_kd ORDER BY id;
+
      + id |  data   | k_nearest_neighbours | distance
+----+---------+----------------------+---------------------
+  1 | {2,1}   | {1}                  | {1}
+  2 | {2,6}   | {3,2}                | {10,16}
+  3 | {15,40} | {7}                  | {106}
+  5 | {2,90}  | {3,2}                | {7570,7744}
+  6 | {50,45} | {6,8}                | {925,1985}
+(5 rows)
+
      9. +
    9. Unsupervised nearest neighbors. Here the training set matches the test set so the nearest neighbor of each point is the point itself, with a zero distance: 
      +DROP TABLE IF EXISTS knn_result_classification_unsup;
+SELECT * FROM madlib.knn(
+                'knn_train_data',      -- Table of training data
+                'data',                -- Col name of training data
+                'id',                  -- Col name of id in train data
+                 NULL,                 -- NULL training labels means just list neighbors
+                'knn_train_data',      -- Table of test data (same as training data)
+                'data',                -- Col name of test data
+                'id',                  -- Col name of id in test data
+                'knn_result_classification_unsup',  -- Output table
+                 3,                    -- Number of nearest neighbors
+                 True,                 -- True to list nearest-neighbors by id
+                'madlib.squared_dist_norm2' -- Distance function
+                );
+SELECT * from knn_result_classification_unsup ORDER BY id;
+
      Result, with point and neighbors sorted from closest to furthest: 
      + id |  data   | k_nearest_neighbours |   distance
+----+---------+----------------------+---------------
+  1 | {1,1}   | {1,2,3}              | {0,2,8}
+  2 | {2,2}   | {2,3,1}              | {0,2,2}
+  3 | {3,3}   | {3,2,4}              | {0,2,2}
+  4 | {4,4}   | {4,5,3}              | {0,1,2}
+  5 | {4,5}   | {5,4,3}              | {0,1,5}
+  6 | {20,50} | {6,7,5}              | {0,461,2281}
+  7 | {10,31} | {7,6,5}              | {0,461,712}
+  8 | {81,13} | {8,6,7}              | {0,5090,5365}
+  9 | {1,111} | {9,6,7}              | {0,4082,6481}
+(9 rows)
+
      10. +
    10. User defined distance function. There are several built-in distance functions, but you can create your own using a UDF if desired. For example, to create a Chebyshev distance function [6], first create the function: 
      +CREATE OR REPLACE FUNCTION chebychev_distance (x double precision[], y double precision[])
+  RETURNS double precision
+AS $$
+    from scipy.spatial import distance
+    return distance.chebyshev(x, y)
+$$ LANGUAGE plpython3u;
+
      Then pass the function as an argument: 
      +DROP TABLE IF EXISTS knn_result_classification_udf;
+SELECT * FROM madlib.knn(
+                'knn_train_data',      -- Table of training data
+                'data',                -- Col name of training data
+                'id',                  -- Col name of id in train data
+                'label',               -- Training labels
+                'knn_test_data',       -- Table of test data
+                'data',                -- Col name of test data
+                'id',                  -- Col name of id in test data
+                'knn_result_classification_udf',  -- Output table
+                 3,                    -- Number of nearest neighbors
+                 True,                 -- True to list nearest-neighbors by id
+                'chebychev_distance'   -- Distance function
+                );
+SELECT * from knn_result_classification_udf ORDER BY id;
+
      Result, with point and neighbors sorted from closest to furthest: 
      + id |  data   | prediction | k_nearest_neighbours |  distance
+----+---------+------------+----------------------+------------
+  1 | {2,1}   |          1 | {1,2,3}              | {1,1,2}
+  2 | {2,6}   |          1 | {5,4,3}              | {2,2,3}
+  3 | {15,40} |          0 | {7,6,5}              | {9,10,35}
+  4 | {12,1}  |          1 | {5,4,3}              | {8,8,9}
+  5 | {2,90}  |          0 | {9,6,7}              | {21,40,59}
+  6 | {50,45} |          0 | {6,8,7}              | {30,32,40}
+(6 rows)
+
      11. +
    +

    Technical Background
    +

    The training data points are vectors in a multidimensional feature space, each with a class label. The training phase of the algorithm consists only of storing the feature vectors and class labels of the training points.

    +

    In the prediction phase, \(k\) is a user-defined constant, and an unlabeled vector (a test point) is predicted by using the label from the the \(k\) training samples nearest to that test point.

    +

    Since distances between points are used to find the nearest neighbors, the data should be standardized across features. This ensures that all features are given equal weightage in the distance computation.

    +

    An approximation method can be used to speed the prediction phase by building appropriate data structures in the training phase. An example of such a data structure is kd-trees [5]. Using the kd-tree algorithm can improve the execution time of the \(k\)-NN operation, but at expense of sacrificing some accuracy. The kd-tree implementation divides the training dataset into multiple regions that correspond to the leaf nodes of a tree. For example, a tree of depth \(3\) will have a total of \(2^3 = 8\) regions. The algorithm will look for the nearest neighbors in a subset of all regions instead of searching the whole dataset. For a given test point, the first (home) region is found by traversing the tree and finding its associated node. If the user requests additional leaf nodes to be searched, we look at the distance between the point and the centroids of other regions and expand the search to the specified number of closest regions.

    +

    It's important to note that the nodes that each level of the kd-tree search over a single feature and the features are explored in the same order as that in the data.

    +

    The kd-tree accuracy might suffer on datasets with a high number of features (dimensions). For example, let's say we are using a dataset with 20 features and kd-tree depth of only 3. This means the kd-tree is constructed based on the first 3 features. Therefore, it is possible to miss nearest neighbors that are closer in those 17 dimensions because they got assigned to a further region (the distance computation would still uses all 20 features).

    +

    Literature
    +

    [1] Wikipedia, k-nearest neighbors algorithm, https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm

    +

    [2] N. S. Altman: An Introduction to Kernel and Nearest-Neighbor Nonparametric Regression http://www.stat.washington.edu/courses/stat527/s13/readings/Altman_AmStat_1992.pdf

    +

    [3] Gongde Guo1, Hui Wang, David Bell, Yaxin Bi, Kieran Greer: KNN Model-Based Approach in Classification, https://ai2-s2-pdfs.s3.amazonaws.com/a7e2/814ec5db800d2f8c4313fd436e9cf8273821.pdf

    +

    [4] Shepard, Donald (1968). "A two-dimensional interpolation function for +irregularly-spaced data". Proceedings of the 1968 ACM National Conference. pp. 517–524.

    +

    [5] Bentley, J. L. (1975). "Multidimensional binary search trees used for +associative searching". Communications of the ACM. 18 (9): 509. doi:10.1145/361002.361007.

    +

    [6] https://en.wikipedia.org/wiki/Chebyshev_distance

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__lda.html b/docs/docs/v2.1.0/group__grp__lda.html new file mode 100644 index 00000000..3f90e3df --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__lda.html @@ -0,0 +1,807 @@ + + + + + + + + +MADlib: Latent Dirichlet Allocation + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Latent Dirichlet Allocation
    Unsupervised Learning » Topic Modelling
    +
    +
    +
    Contents +

    Latent Dirichlet Allocation (LDA) is a generative probabilistic model for natural texts. It is used in problems such as automated topic discovery, collaborative filtering, and document classification.

    +

    In addition to an implementation of LDA, this MADlib module also provides a number of additional helper functions to interpret results of the LDA output.

    +
    Note
    Topic modeling is often used as part of a larger text processing pipeline, which may include operations such as term frequency, stemming and stop word removal. You can use the function Term Frequency to generate the required vocabulary format from raw documents for the LDA training function. See the examples later on this page for more details.
    +

    Background
    +

    The LDA model posits that each document is associated with a mixture of various topics (e.g., a document is related to Topic 1 with probability 0.7, and Topic 2 with probability 0.3), and that each word in the document is attributable to one of the document's topics. There is a (symmetric) Dirichlet prior with parameter \( \alpha \) on each document's topic mixture. In addition, there is another (symmetric) Dirichlet prior with parameter \( \beta \) on the distribution of words for each topic.

    +

    The following generative process then defines a distribution over a corpus of documents:

    +
      +
    • Sample for each topic \( i \), a per-topic word distribution \( \phi_i \) from the Dirichlet ( \(\beta\)) prior.
      • +
    • For each document:
        +
      • Sample a document length N from a suitable distribution, say, Poisson.
        • +
      • Sample a topic mixture \( \theta \) for the document from the Dirichlet ( \(\alpha\)) distribution.
        • +
      • For each of the N words:
          +
        • Sample a topic \( z_n \) from the multinomial topic distribution \( \theta \).
          • +
        • Sample a word \( w_n \) from the multinomial word distribution \( \phi_{z_n} \) associated with topic \( z_n \).
          • +
        +
        • +
      +
      • +
    +

    In practice, only the words in each document are observable. The topic mixture of each document and the topic for each word in each document are latent unobservable variables that need to be inferred from the observables, and this is referred to as the inference problem for LDA. Exact inference is intractable, but several approximate inference algorithms for LDA have been developed. The simple and effective Gibbs sampling algorithm described in Griffiths and Steyvers [2] appears to be the current algorithm of choice.

    +

    This implementation provides a parallel and scalable in-database solution for LDA based on Gibbs sampling. It takes advantage of the shared-nothing MPP architecture and is a different implementation than one would find for MPI or map/reduce.

    +

    Training Function
    The LDA training function has the following syntax: 
    +lda_train( data_table,
+           model_table,
+           output_data_table,
+           voc_size,
+           topic_num,
+           iter_num,
+           alpha,
+           beta,
+           evaluate_every,
+           perplexity_tol
+         )
+
    Arguments
    +
    data_table
    +

    TEXT. Name of the table storing the training dataset. Each row is in the form <docid, wordid, count> where docid, wordid, and count are non-negative integers. The docid column refers to the document ID, the wordid column is the word ID (the index of a word in the vocabulary), and count is the number of occurrences of the word in the document. Please note:

    +
      +
    • wordid must be contiguous integers going from from 0 to voc_size − 1.
      • +
    • column names for docid, wordid, and count are currently fixed, so you must use these exact names in the data_table.
      • +
    +

    The function Term Frequency can be used to generate vocabulary in the required format from raw documents.

    +

    +
    +
    model_table
    +
    TEXT. This is an output table generated by LDA which contains the learned model. It has one row with the following columns: + + + + + + + + + + + + + + + + +
    voc_size INTEGER. Size of the vocabulary. As mentioned above for the input table, wordid consists of contiguous integers going from 0 to voc_size − 1.
    topic_num INTEGER. Number of topics.
    alpha DOUBLE PRECISION. Dirichlet prior for the per-document topic multinomial.
    beta DOUBLE PRECISION. Dirichlet prior for the per-topic word multinomial.
    model BIGINT[]. The encoded model description (not human readable).
    num_iterations INTEGER. Number of iterations that training ran for, which may be less than the maximum value specified in the parameter 'iter_num' if the perplexity tolerance was reached.
    perplexity DOUBLE PRECISION[]. Array of perplexity values as per the 'evaluate_every' parameter. For example, if 'evaluate_every=5' this would be an array of perplexity values for every 5th iteration, plus the last iteration.
    perplexity_iters INTEGER[]. Array indicating the iterations for which perplexity is calculated, as derived from the parameters 'iter_num' and 'evaluate_every'. For example, if 'iter_num=5' and 'evaluate_every=2', then 'perplexity_iters' value would be {2,4,5} indicating that perplexity is computed at iterations 2, 4 and 5 (at the end), unless of course it terminated earlier due to 'perplexity_tol'. If 'iter_num=5' and 'evaluate_every=1', then 'perplexity_iters' value would be {1,2,3,4,5} indicating that perplexity is computed at every iteration, again assuming it ran the full number of iterations.
    +
    +
    output_data_table
    +
    TEXT. The name of the table generated by LDA that stores the output data. It has the following columns: + + + + + + + + + + + + +
    docid INTEGER. Document id from input 'data_table'.
    wordcount INTEGER. Count of number of words in the document, including repeats. For example, if a word appears 3 times in the document, it is counted 3 times.
    words INTEGER[]. Array of wordid in the document, not including repeats. For example, if a word appears 3 times in the document, it appears only once in the words array.
    counts INTEGER[]. Frequency of occurance of a word in the document, indexed the same as the words array above. For example, if the 2nd element of the counts array is 4, it means that the word in the 2nd element of the words array occurs 4 times in the document.
    topic_count INTEGER[]. Array of the count of words in the document that correspond to each topic. This array is of length topic_num. Topic ids are continuous integers going from 0 to topic_num − 1.
    topic_assignment INTEGER[]. Array indicating which topic each word in the document corresponds to. This array is of length wordcount. Words that are repeated n times in the document will show up consecutively n times in this array.
    +
    +
    voc_size
    +
    INTEGER. Size of the vocabulary. As mentioned above for the input 'data_table', wordid consists of continuous integers going from 0 to voc_size − 1.
    +
    topic_num
    +
    INTEGER. Desired number of topics.
    +
    iter_num
    +
    INTEGER. Maximum number of iterations. If a 'perplexity_tol' is set, LDA may train for less than the maximum number of iterations if the tolerance is reached.
    +
    alpha
    +
    DOUBLE PRECISION. Dirichlet prior for the per-document topic multinomial (e.g., 50/topic_num is a reasonable value to start with as per Griffiths and Steyvers [2]).
    +
    beta
    +
    DOUBLE PRECISION. Dirichlet prior for the per-topic word multinomial (e.g., 0.01 is a reasonable value to start with).
    +
    evaluate_every (optional)
    +
    INTEGER, default: 0. How often to evaluate perplexity. Set it to 0 or a negative number to not evaluate perplexity in training at all. Evaluating perplexity can help you check convergence during the training process, but it will also increase total training time. For example, evaluating perplexity in every iteration might increase training time up to two-fold.
    +
    perplexity_tol (optional)
    +
    DOUBLE PRECISION, default: 0.1. Perplexity tolerance to stop iteration. Only used when the parameter 'evaluate_every' is greater than 0.
    +
    +
    +

    Prediction Function
    +

    Prediction involves labelling test documents using a learned LDA model: 

    +lda_predict( data_table,
+             model_table,
+             output_predict_table
+           );
+

    Arguments

    +
    data_table
    +
    TEXT. Name of the table storing the test dataset (new document to be labeled).
    +
    model_table
    +
    TEXT. The model table generated by the training process.
    +
    output_predict_table
    +
    TEXT. The prediction output table. Each row in the table stores the topic distribution and the topic assignments for a document in the dataset. This table has the exact same columns and interpretation as the 'output_data_table' from the training function above.
    +
    +

    Perplexity
    Perplexity describes how well the model fits the data by computing word likelihoods averaged over the documents. This function returns a single perplexity value. 
    +lda_get_perplexity( model_table,
+                    output_data_table
+                  );
+
    Arguments
    +
    model_table
    +
    TEXT. The model table generated by the training process.
    +
    output_data_table
    +
    TEXT. Output table generated by the training or predict functions, containing the topic assignments by word.
    +
    +
    +

    Helper Functions
    +

    The helper functions can help to interpret the output from LDA training and LDA prediction.

    +

    Topic description by top-k words with highest probability

    +

    Applies to LDA training only.

    +
    +lda_get_topic_desc( model_table,
+                    vocab_table,
+                    output_table,
+                    top_k
+                  )
+

    Arguments

    +
    model_table
    +
    TEXT. The model table generated by the training process.
    +
    vocab_table
    +
    TEXT. The vocabulary table in the form <wordid, word>. Reminder that this table can be created using the term_frequency function (Term Frequency) with the parameter compute_vocab set to TRUE.
    +
    output_table
    +
    TEXT. The output table with per-topic description generated by this helper function. It has the following columns: + + + + + + + + +
    topicid INTEGER. Topic id.
    wordid INTEGER. Word id.
    prob DOUBLE PRECISION. Probability that this topic will generate the word.
    word TEXT. Word in text form.
    +
    +
    top_k
    +
    TEXT. The desired number of top words to show for each topic.
    +
    +

    Per-word topic counts

    +

    Applies to LDA training only.

    +
    +lda_get_word_topic_count( model_table,
+                          output_table
+                        )
+

    Arguments

    +
    model_table
    +
    TEXT. The model table generated by the training process.
    +
    output_table
    +
    TEXT. The output table with per-word topic counts generated by this helper function. It has the following columns: + + + + +
    wordid INTEGER. Word id.
    topic_count INTEGER[]. Count of word association with each topic, i.e., shows how many times a given word is assigned to a topic. Array is of length number of topics.
    +
    +
    +

    Per-topic word counts

    +

    Applies to LDA training only.

    +
    +lda_get_topic_word_count( model_table,
+                          output_table
+                        )
+

    Arguments

    +
    model_table
    +
    TEXT. The model table generated by the training process.
    +
    output_table
    +
    TEXT. The output table with per-topic word counts generated by this helper function. It has the following columns: + + + + +
    topicid INTEGER. Topic id.
    word_count INTEGER[]. Array showing which words are associated with the topic by frequency. Array is of length number of words.
    +
    +
    +

    Per-document word to topic mapping

    +

    Applies to both LDA training and LDA prediction.

    +
    +lda_get_word_topic_mapping( output_data_table,  -- From training or prediction
+                            output_table
+                          )
+

    Arguments

    +
    output_data_table
    +
    TEXT. The output data table generated by either LDA training or LDA prediction.
    +
    output_table
    +
    TEXT. The output table with word to topic mappings generated by this helper function. It has the following columns: + + + + + + +
    docid INTEGER. Document id.
    wordid INTEGER. Word id.
    topicid INTEGER. Topic id.
    +
    +
    +

    Examples
    +
      +
    1. Prepare a training dataset for LDA. The examples below are small strings extracted from various Wikipedia documents: 
      +DROP TABLE IF EXISTS documents;
+CREATE TABLE documents(docid INT4, contents TEXT);
+INSERT INTO documents VALUES
+(0, 'Statistical topic models are a class of Bayesian latent variable models, originally developed for analyzing the semantic content of large document corpora.'),
+(1, 'By the late 1960s, the balance between pitching and hitting had swung in favor of the pitchers. In 1968 Carl Yastrzemski won the American League batting title with an average of just .301, the lowest in history.'),
+(2, 'Machine learning is closely related to and often overlaps with computational statistics; a discipline that also specializes in prediction-making. It has strong ties to mathematical optimization, which deliver methods, theory and application domains to the field.'),
+(3, 'California''s diverse geography ranges from the Sierra Nevada in the east to the Pacific Coast in the west, from the Redwood–Douglas fir forests of the northwest, to the Mojave Desert areas in the southeast. The center of the state is dominated by the Central Valley, a major agricultural area.');
+
      You can apply stemming, stop word removal and tokenization at this point in order to prepare the documents for text processing. Depending upon your database version, various tools are available. Databases based on more recent versions of PostgreSQL may do something like: 
      +SELECT tsvector_to_array(to_tsvector('english',contents)) from documents;
+
      +                        tsvector_to_array
++-----------------------------------------------------------------------
+ {analyz,bayesian,class,content,corpora,develop,document,larg,...}
+ {1960s,1968,301,american,averag,balanc,bat,carl,favor,histori,...}
+ {also,applic,close,comput,deliv,disciplin,domain,field,learn,...}
+ {agricultur,area,california,center,central,coast,desert,divers,...}
+(4 rows)
+
      In this example, we assume a database based on an older version of PostgreSQL and just perform basic punctuation removal and tokenization. The array of words is added as a new column to the documents table: 
      +ALTER TABLE documents ADD COLUMN words TEXT[];
+UPDATE documents SET words =
+    regexp_split_to_array(lower(
+    regexp_replace(contents, E'[,.;\']','', 'g')
+    ), E'[\\s+]');
+\x on
+SELECT * FROM documents ORDER BY docid;
+
      +-[ RECORD 1 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+docid    | 0
+contents | Statistical topic models are a class of Bayesian latent variable models, originally developed for analyzing the semantic content of large document corpora.
+words    | {statistical,topic,models,are,a,class,of,bayesian,latent,variable,models,originally,developed,for,analyzing,the,semantic,content,of,large,document,corpora}
+-[ RECORD 2 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+docid    | 1
+contents | By the late 1960s, the balance between pitching and hitting had swung in favor of the pitchers. In 1968 Carl Yastrzemski won the American League batting title with an average of just .301, the lowest in history.
+words    | {by,the,late,1960s,the,balance,between,pitching,and,hitting,had,swung,in,favor,of,the,pitchers,in,1968,carl,yastrzemski,won,the,american,league,batting,title,with,an,average,of,just,301,the,lowest,in,history}
+-[ RECORD 3 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+docid    | 2
+contents | Machine learning is closely related to and often overlaps with computational statistics; a discipline that also specializes in prediction-making. It has strong ties to mathematical optimization, which deliver methods, theory and application domains to the field.
+words    | {machine,learning,is,closely,related,to,and,often,overlaps,with,computational,statistics,a,discipline,that,also,specializes,in,prediction-making,it,has,strong,ties,to,mathematical,optimization,which,deliver,methods,theory,and,application,domains,to,the,field}
+-[ RECORD 4 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+docid    | 3
+contents | California's diverse geography ranges from the Sierra Nevada in the east to the Pacific Coast in the west, from the Redwood–Douglas fir forests of the northwest, to the Mojave Desert areas in the southeast. The center of the state is dominated by the Central Valley, a major agricultural area.
+words    | {californias,diverse,geography,ranges,from,the,sierra,nevada,in,the,east,to,the,pacific,coast,in,the,west,from,the,redwood–douglas,fir,forests,of,the,northwest,to,the,mojave,desert,areas,in,the,southeast,the,center,of,the,state,is,dominated,by,the,central,valley,a,major,agricultural,area}
+
      2. +
    2. Build a word count table by extracting the words and building a histogram for each document using the term_frequency function (Term Frequency). 
      +DROP TABLE IF EXISTS documents_tf, documents_tf_vocabulary;
+SELECT madlib.term_frequency('documents',    -- input table
+                             'docid',        -- document id column
+                             'words',        -- vector of words in document
+                             'documents_tf', -- output documents table with term frequency
+                             TRUE);          -- TRUE to created vocabulary table
+\x off
+SELECT * FROM documents_tf ORDER BY docid LIMIT 20;
+
      + docid | wordid | count
+-------+--------+-------
+     0 |     71 |     1
+     0 |     90 |     1
+     0 |     56 |     1
+     0 |     68 |     2
+     0 |     85 |     1
+     0 |     28 |     1
+     0 |     35 |     1
+     0 |     54 |     1
+     0 |     64 |     2
+     0 |      8 |     1
+     0 |     29 |     1
+     0 |     80 |     1
+     0 |     24 |     1
+     0 |     11 |     1
+     0 |     17 |     1
+     0 |     32 |     1
+     0 |      3 |     1
+     0 |     42 |     1
+     0 |     97 |     1
+     0 |     95 |     1
+(20 rows)
+
      Here is the associated vocabulary table. Note that wordid starts at 0: 
      +SELECT * FROM documents_tf_vocabulary ORDER BY wordid LIMIT 20;
+
      + wordid |     word
+--------+--------------
+      0 | 1960s
+      1 | 1968
+      2 | 301
+      3 | a
+      4 | agricultural
+      5 | also
+      6 | american
+      7 | an
+      8 | analyzing
+      9 | and
+     10 | application
+     11 | are
+     12 | area
+     13 | areas
+     14 | average
+     15 | balance
+     16 | batting
+     17 | bayesian
+     18 | between
+     19 | by
+(20 rows)
+
      The total number of words in the vocabulary across all documents is: 
      +SELECT COUNT(*) FROM documents_tf_vocabulary;
+
      + count
++------
+   103
+(1 row)
+
      3. +
    3. Train LDA model. For Dirichlet priors we use initial rule-of-thumb values of 50/(number of topics) for alpha and 0.01 for beta. Reminder that column names for docid, wordid, and count are currently fixed, so you must use these exact names in the input table. After a successful run of the LDA training function two tables are generated, one for storing the learned model and the other for storing the output data table. 
      +DROP TABLE IF EXISTS lda_model, lda_output_data;
+SELECT madlib.lda_train( 'documents_tf',     -- documents table in the form of term frequency
+                         'lda_model',        -- model table created by LDA training (not human readable)
+                         'lda_output_data',  -- readable output data table
+                         103,                -- vocabulary size
+                         5,                  -- number of topics
+                         10,                 -- number of iterations
+                         5,                  -- Dirichlet prior for the per-doc topic multinomial (alpha)
+                         0.01                -- Dirichlet prior for the per-topic word multinomial (beta)
+                       );
+\x on
+SELECT * FROM lda_output_data ORDER BY docid;
+
      +-[ RECORD 1 ]----+------------------------------------------------------------------------------------------------------
+docid            | 0
+wordcount        | 22
+words            | {24,17,11,95,90,85,68,54,42,35,28,8,3,97,80,71,64,56,32,29}
+counts           | {1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1}
+topic_count      | {4,2,4,3,9}
+topic_assignment | {4,2,4,1,2,1,2,2,0,3,4,4,3,0,0,4,0,4,4,4,3,4}
+-[ RECORD 2 ]----+------------------------------------------------------------------------------------------------------
+docid            | 1
+wordcount        | 37
+words            | {1,50,49,46,19,16,14,9,7,0,90,68,57,102,101,100,93,88,75,74,59,55,53,48,39,21,18,15,6,2}
+counts           | {1,3,1,1,1,1,1,1,1,1,5,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
+topic_count      | {2,5,14,9,7}
+topic_assignment | {0,3,3,3,1,4,2,2,2,1,3,1,2,2,2,2,2,2,2,1,4,3,2,0,4,2,4,2,3,4,3,1,3,4,3,2,4}
+-[ RECORD 3 ]----+------------------------------------------------------------------------------------------------------
+docid            | 2
+wordcount        | 36
+words            | {10,27,33,40,47,51,58,62,63,69,72,83,100,99,94,92,91,90,89,87,86,79,76,70,60,52,50,36,30,25,9,5,3}
+counts           | {1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1}
+topic_count      | {15,10,1,7,3}
+topic_assignment | {0,3,1,3,0,0,3,3,1,0,1,0,0,0,0,1,1,0,4,2,0,4,1,0,1,0,0,4,3,3,3,0,1,1,1,0}
+-[ RECORD 4 ]----+------------------------------------------------------------------------------------------------------
+docid            | 3
+wordcount        | 49
+words            | {77,78,81,82,67,65,51,45,44,43,34,26,13,98,96,94,90,84,73,68,66,61,50,41,38,37,31,23,22,20,19,12,4,3}
+counts           | {1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2,11,1,1,2,1,1,3,1,1,1,1,1,1,1,1,1,1,1}
+topic_count      | {5,5,26,5,8}
+topic_assignment | {4,4,4,0,2,0,0,2,4,4,2,2,2,1,2,4,1,0,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,4,3,3,3,2,3,2,3,2,1,4,2,2,1,0}
+
      Review summary table: 
      +SELECT voc_size, topic_num, alpha, beta, num_iterations, perplexity, perplexity_iters from lda_model;
+
      +-[ RECORD 1 ]----+-----
+voc_size         | 103
+topic_num        | 5
+alpha            | 5
+beta             | 0.01
+num_iterations   | 10
+perplexity       |
+perplexity_iters |
+
      4. +
    4. Review learned model using helper functions. First, we get topic description by top-k words. These are the k words with the highest probability for the topic. Note that if there are ties in probability, more than k words may actually be reported for each topic. Also note that topicid starts at 0: 
      +DROP TABLE IF EXISTS helper_output_table;
+SELECT madlib.lda_get_topic_desc( 'lda_model',                -- LDA model generated in training
+                                  'documents_tf_vocabulary',  -- vocabulary table that maps wordid to word
+                                  'helper_output_table',      -- output table for per-topic descriptions
+                                  5);                         -- k: number of top words for each topic
+\x off
+SELECT * FROM helper_output_table ORDER BY topicid, prob DESC LIMIT 40;
+
      + topicid | wordid |        prob        |       word
+---------+--------+--------------------+-------------------
+       0 |      3 |  0.111357750647429 | a
+       0 |     51 |  0.074361820199778 | is
+       0 |     94 |  0.074361820199778 | to
+       0 |     70 | 0.0373658897521273 | optimization
+       0 |     82 | 0.0373658897521273 | southeast
+       0 |     60 | 0.0373658897521273 | machine
+       0 |     71 | 0.0373658897521273 | originally
+       0 |     69 | 0.0373658897521273 | often
+       0 |     99 | 0.0373658897521273 | which
+       0 |     83 | 0.0373658897521273 | specializes
+       0 |      1 | 0.0373658897521273 | 1968
+       0 |     97 | 0.0373658897521273 | variable
+       0 |     25 | 0.0373658897521273 | closely
+       0 |     93 | 0.0373658897521273 | title
+       0 |     47 | 0.0373658897521273 | has
+       0 |     65 | 0.0373658897521273 | mojave
+       0 |     79 | 0.0373658897521273 | related
+       0 |     89 | 0.0373658897521273 | that
+       0 |     10 | 0.0373658897521273 | application
+       0 |    100 | 0.0373658897521273 | with
+       0 |     92 | 0.0373658897521273 | ties
+       0 |     54 | 0.0373658897521273 | large
+       1 |     94 |  0.130699088145897 | to
+       1 |      9 |  0.130699088145897 | and
+       1 |      5 | 0.0438558402084238 | also
+       1 |     57 | 0.0438558402084238 | league
+       1 |     49 | 0.0438558402084238 | hitting
+       1 |     13 | 0.0438558402084238 | areas
+       1 |     39 | 0.0438558402084238 | favor
+       1 |     85 | 0.0438558402084238 | statistical
+       1 |     95 | 0.0438558402084238 | topic
+       1 |      0 | 0.0438558402084238 | 1960s
+       1 |     76 | 0.0438558402084238 | prediction-making
+       1 |     86 | 0.0438558402084238 | statistics
+       1 |     84 | 0.0438558402084238 | state
+       1 |     72 | 0.0438558402084238 | overlaps
+       1 |     22 | 0.0438558402084238 | center
+       1 |      4 | 0.0438558402084238 | agricultural
+       1 |     63 | 0.0438558402084238 | methods
+       1 |     33 | 0.0438558402084238 | discipline
+(40 rows)
+
      Get the per-word topic counts. This mapping shows how many times a given word is assigned to a topic. E.g., wordid 3 is assigned to topicid 0 three times: 
      +DROP TABLE IF EXISTS helper_output_table;
+SELECT madlib.lda_get_word_topic_count( 'lda_model',            -- LDA model generated in training
+                                        'helper_output_table'); -- output table for per-word topic counts
+SELECT * FROM helper_output_table ORDER BY wordid LIMIT 20;
+
      + wordid | topic_count
+--------+-------------
+      0 | {0,1,0,0,0}
+      1 | {1,0,0,0,0}
+      2 | {1,0,0,0,0}
+      3 | {3,0,0,0,0}
+      4 | {0,0,0,0,1}
+      5 | {0,1,0,0,0}
+      6 | {1,0,0,0,0}
+      7 | {0,0,0,1,0}
+      8 | {0,1,0,0,0}
+      9 | {0,0,0,3,0}
+     10 | {1,0,0,0,0}
+     11 | {1,0,0,0,0}
+     12 | {0,0,1,0,0}
+     13 | {0,0,0,0,1}
+     14 | {0,1,0,0,0}
+     15 | {0,0,0,0,1}
+     16 | {0,1,0,0,0}
+     17 | {0,0,1,0,0}
+     18 | {1,0,0,0,0}
+     19 | {2,0,0,0,0}
+(20 rows)
+
      Get the per-topic word counts. This mapping shows which words are associated with each topic by frequency: 
      +DROP TABLE IF EXISTS topic_word_count;
+SELECT madlib.lda_get_topic_word_count( 'lda_model',
+                                        'topic_word_count');
+\x on
+SELECT * FROM topic_word_count ORDER BY topicid;
+
      +-[ RECORD 1 ]----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+topicid    | 1
+word_count | {1,1,0,0,0,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1,0,0,1,1,0,0,0,0,0,0,0,1,0}
+-[ RECORD 2 ]----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+topicid    | 2
+word_count | {0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1,1,2,0,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,4,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,5,0,1,0,0,1,0,0,0}
+-[ RECORD 3 ]----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+topicid    | 3
+word_count | {0,0,0,0,0,0,0,0,0,3,0,1,0,1,1,0,0,0,0,2,0,0,0,0,1,0,0,1,0,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,1,0,0,2,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0}
+-[ RECORD 4 ]----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+topicid    | 4
+word_count | {0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0,7,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,1,0,0,0,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,1}
+-[ RECORD 5 ]----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+topicid    | 5
+word_count | {0,0,0,3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,1,0,0,1,0,0,0,0,0,0,0,0,18,0,0,0,0,0,0,0,1,0,2,0,0}
+
      Get the per-document word to topic mapping: 
      +DROP TABLE IF EXISTS helper_output_table;
+SELECT madlib.lda_get_word_topic_mapping('lda_output_data',  -- Output table from training
+                                         'helper_output_table');
+\x off
+SELECT * FROM helper_output_table ORDER BY docid LIMIT 40;
+
      + docid | wordid | topicid
+-------+--------+---------
+     0 |     56 |       1
+     0 |     54 |       1
+     0 |     42 |       2
+     0 |     35 |       1
+     0 |     32 |       1
+     0 |     29 |       3
+     0 |     28 |       4
+     0 |     24 |       3
+     0 |     17 |       2
+     0 |     11 |       0
+     0 |      8 |       1
+     0 |      3 |       0
+     0 |     97 |       0
+     0 |     95 |       3
+     0 |     90 |       0
+     0 |     85 |       0
+     0 |     80 |       2
+     0 |     71 |       2
+     0 |     68 |       0
+     0 |     64 |       1
+     1 |      2 |       0
+     1 |      1 |       0
+     1 |      0 |       1
+     1 |    102 |       4
+     1 |    101 |       2
+     1 |    100 |       1
+     1 |     93 |       3
+     1 |     90 |       2
+     1 |     90 |       0
+     1 |     88 |       1
+     1 |     75 |       1
+     1 |     74 |       3
+     1 |     68 |       0
+     1 |     59 |       2
+     1 |     57 |       4
+     1 |     55 |       3
+     1 |     53 |       3
+     1 |     50 |       0
+     1 |     49 |       1
+     1 |     48 |       0
+(40 rows)
+
      5. +
    5. Use a learned LDA model for prediction (that is, to label new documents). In this example, we use the same input table as we used to train, just for demonstration purpose. Normally, the test document is a new one that we want to predict on. 
      +DROP TABLE IF EXISTS outdata_predict;
+SELECT madlib.lda_predict( 'documents_tf',          -- Document to predict
+                           'lda_model',             -- LDA model from training
+                           'outdata_predict'        -- Output table for predict results
+                         );
+\x on
+SELECT * FROM outdata_predict;
+
      +-[ RECORD 1 ]----+------------------------------------------------------------------------------------------------------
+docid            | 0
+wordcount        | 22
+words            | {17,11,28,29,95,3,32,97,85,35,54,80,64,90,8,24,42,71,56,68}
+counts           | {1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,2}
+topic_count      | {1,3,16,1,1}
+topic_assignment | {2,2,1,0,2,2,2,3,2,2,2,2,2,2,4,2,2,2,2,2,1,1}
+-[ RECORD 2 ]----+------------------------------------------------------------------------------------------------------
+docid            | 1
+wordcount        | 37
+words            | {90,101,2,88,6,7,75,46,74,68,39,9,48,49,102,50,59,53,55,57,100,14,15,16,18,19,93,21,0,1}
+counts           | {5,1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
+topic_count      | {0,1,11,6,19}
+topic_assignment | {4,4,4,4,4,4,4,4,4,2,4,2,2,1,3,2,2,4,4,4,3,3,3,4,3,3,2,4,4,2,2,4,2,4,2,4,2}
+-[ RECORD 3 ]----+------------------------------------------------------------------------------------------------------
+docid            | 2
+wordcount        | 36
+words            | {90,3,5,9,10,25,27,30,33,36,40,47,50,51,52,58,60,62,63,69,70,72,76,79,83,86,87,89,91,92,94,99,100}
+counts           | {1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1}
+topic_count      | {26,3,5,1,1}
+topic_assignment | {4,0,0,2,2,0,0,0,0,2,0,0,0,3,0,0,0,0,0,0,0,0,0,2,0,2,0,0,0,0,0,1,1,1,0,0}
+-[ RECORD 4 ]----+------------------------------------------------------------------------------------------------------
+docid            | 3
+wordcount        | 49
+words            | {41,38,3,77,78,94,37,81,82,19,84,34,96,13,31,98,90,51,26,61,23,22,50,65,66,67,45,44,68,4,12,43,20,73}
+counts           | {1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,3,1,1,1,1,2,2,1,1,1,1,1}
+topic_count      | {0,28,0,4,17}
+topic_assignment | {1,1,4,1,1,1,1,1,1,4,1,1,1,3,1,1,1,4,4,4,4,4,4,4,4,4,4,4,4,1,1,1,4,3,3,3,1,1,4,4,1,1,1,1,1,1,1,1,1}
+
      The test table is expected to be in the same form as the training table and can be created with the same process. The LDA prediction results have the same format as the output table generated by the LDA training function.
      6. +
    6. Review prediction using helper function. (This is the same per-document word to topic mapping that we used on the learned model.) 
      +DROP TABLE IF EXISTS helper_output_table;
+SELECT madlib.lda_get_word_topic_mapping('outdata_predict',  -- Output table from prediction
+                                         'helper_output_table');
+\x off
+SELECT * FROM helper_output_table ORDER BY docid LIMIT 40;
+
      + docid | wordid | topicid
+-------+--------+---------
+     0 |     54 |       4
+     0 |     42 |       1
+     0 |     35 |       4
+     0 |     32 |       4
+     0 |     29 |       4
+     0 |     28 |       1
+     0 |     24 |       4
+     0 |     17 |       1
+     0 |     11 |       4
+     0 |      8 |       4
+     0 |      3 |       0
+     0 |     97 |       4
+     0 |     95 |       1
+     0 |     90 |       2
+     0 |     85 |       4
+     0 |     80 |       0
+     0 |     71 |       0
+     0 |     68 |       0
+     0 |     64 |       4
+     0 |     64 |       1
+     0 |     56 |       4
+     1 |      2 |       4
+     1 |      1 |       4
+     1 |      0 |       2
+     1 |    102 |       4
+     1 |    101 |       4
+     1 |    100 |       4
+     1 |     93 |       4
+     1 |     90 |       2
+     1 |     90 |       0
+     1 |     88 |       2
+     1 |     75 |       2
+     1 |     74 |       0
+     1 |     68 |       0
+     1 |     59 |       4
+     1 |     57 |       2
+     1 |     55 |       2
+     1 |     53 |       1
+     1 |     50 |       0
+     1 |     49 |       2
+(40 rows)
+
      7. +
    7. Call the perplexity function to see how well the model fits the data. Perplexity computes word likelihoods averaged over the test documents. 
      +SELECT madlib.lda_get_perplexity( 'lda_model',        -- LDA model from training
+                                  'outdata_predict'   -- Prediction output
+                                );
+
      + lda_get_perplexity
++--------------------
+    79.481894411824
+(1 row)
+
      8. +
    8. Perplexity by iteration. Now let's look at how perplexity changes from one iteration to the next: 
      +DROP TABLE IF EXISTS lda_model_perp, lda_output_data_perp;
+SELECT madlib.lda_train( 'documents_tf',          -- documents table in the form of term frequency
+                         'lda_model_perp',        -- model table created by LDA training (not human readable)
+                         'lda_output_data_perp',  -- readable output data table
+                         103,                     -- vocabulary size
+                         5,                       -- number of topics
+                         30,                      -- number of iterations
+                         5,                       -- Dirichlet prior for the per-doc topic multinomial (alpha)
+                         0.01,                    -- Dirichlet prior for the per-topic word multinomial (beta)
+                         2,                       -- Evaluate perplexity every n iterations
+                         0.3                      -- Tolerance to stop iteration
+                       );
+\x on
+SELECT voc_size, topic_num, alpha, beta, num_iterations, perplexity, perplexity_iters from lda_model_perp;
+
      +-[ RECORD 1 ]----+----------------------------------------------------------------------------------------------------
+voc_size         | 103
+topic_num        | 5
+alpha            | 5
+beta             | 0.01
+num_iterations   | 14
+perplexity       | {70.0297335165,65.6497887327,70.2040806534,68.2594871716,70.3816093812,67.9193935299,67.6325562682}
+perplexity_iters | {2,4,6,8,10,12,14}
+
      Iterating stops at 14 since the tolerance is reached. There are 7 perplexity values because we computed it only every 2nd iteration to save time. As expected, the perplexity on the training data is that same as the final iteration value: 
      +\x off
+SELECT madlib.lda_get_perplexity( 'lda_model_perp',
+                                  'lda_output_data_perp'
+                                );
+
      + lda_get_perplexity
+--------------------+
+    67.632556268157
+
      9. +
    +

    Literature
    +

    [1] D.M. Blei, A.Y. Ng, M.I. Jordan, Latent Dirichlet Allocation, Journal of Machine Learning Research, vol. 3, pp. 993-1022, 2003.

    +

    [2] T. Griffiths and M. Steyvers, Finding scientific topics, PNAS, vol. 101, pp. 5228-5235, 2004.

    +

    [3] Y. Wang, H. Bai, M. Stanton, W-Y. Chen, and E.Y. Chang, lda: Parallel Dirichlet Allocation for Large-scale Applications, AAIM, 2009.

    +

    [4] http://en.wikipedia.org/wiki/Latent_Dirichlet_allocation

    +

    [5] J. Chang, Collapsed Gibbs sampling methods for topic models, R manual, 2010.

    +

    Related Topics
    File lda.sql_in documenting the SQL functions.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__linalg.html b/docs/docs/v2.1.0/group__grp__linalg.html new file mode 100644 index 00000000..1ba0972b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__linalg.html @@ -0,0 +1,298 @@ + + + + + + + + +MADlib: Norms and Distance Functions + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    Norms and Distance Functions
    Data Types and Transformations » Arrays and Matrices
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    Contents +

    The linalg module consists of useful utility functions for basic linear algebra operations. Several of these functions can be used while implementing new algorithms. These functions operate on vectors (1-D FLOAT8 array) and matrices (2-D FLOAT8 array). Note that other array types may need to be casted into FLOAT8[] before calling the functions.

    +

    Refer to the linalg.sql_in file for documentation on each of the utility functions.

    +

    Linear Algebra Utility Functions
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    norm1()

    1-norm of a vector, \(\|\vec{a}\|_1\).

    +

    +
    norm2()

    2-norm of a vector, \(\|\vec{a}\|_2\).

    +

    +
    dist_norm1()

    1-norm of the difference between two vectors, \(\|\vec{a} - \vec{b}\|_1\).

    +

    +
    dist_norm2()

    2-norm of the difference between two vectors, \(\|\vec{a} - \vec{b}\|_2\).

    +

    +
    dist_pnorm()

    Generic p-norm of the difference between two vectors, \(\|\vec{a} - \vec{b}\|_p, p > 0\).

    +

    +
    dist_inf_norm()

    Infinity-norm of the difference between two vectors, \(\|\vec{a} - \vec{b}\|_\infty\).

    +

    +
    squared_dist_norm2()

    Squared 2-norm of the difference between two vectors, \(\|\vec{a} - \vec{b}\|_2^2\).

    +

    +
    cosine_similarity()

    Cosine score between two vectors, \(\frac{\vec{a} \cdot \vec{b}}{\|\vec{a}\|_2 \|\vec{b}\|_2}\).

    +

    +
    dist_angle()

    Angle between two vectors in an Euclidean space, \(\cos^{-1}(\frac{\vec{a} \cdot \vec{b}}{\|\vec{a}\|_2 \|\vec{b}\|_2})\).

    +

    +
    dist_tanimoto()

    Tanimoto distance between two vectors. [1]

    +

    +
    dist_jaccard()

    Jaccard distance between two varchar vectors treated as sets.

    +

    +
    get_row()

    Return the indexed row of a matrix (2-D array).

    +

    +
    get_col()

    Return the indexed col of a matrix (2-D array).

    +

    +
    avg()

    Compute the average of vectors.

    +

    +
    normalized_avg()

    Compute the normalized average of vectors (unit vector in an Euclidean space).

    +

    +
    matrix_agg()

    Combine vectors to a matrix.

    +

    +
    +
    +

    +

    Vector Norms and Distances

    +
      +
    1. Create a database table with two vector columns and add some data. 
      +CREATE TABLE two_vectors(
+    id  integer,
+    a   float8[],
+    b   float8[]);
+
      +INSERT INTO two_vectors VALUES
+(1, '{3,4}', '{4,5}'),
+(2, '{1,1,0,-4,5,3,4,106,14}', '{1,1,0,6,-3,1,2,92,2}');
+
      2. +
    2. Invoke norm functions. 
      +SELECT
+    id,
+    madlib.norm1(a),
+    madlib.norm2(a)
+FROM two_vectors;
+
      Result: 
      + id | norm1 |      norm2
+----+-------+------------------
+  1 |     7 |                5
+  2 |   138 | 107.238052947636
+(2 rows)
+
      3. +
    3. Invoke distance functions. 
      +SELECT
+    id,
+    madlib.dist_norm1(a, b),
+    madlib.dist_norm2(a, b),
+    madlib.dist_pnorm(a, b, 5) AS norm5,
+    madlib.dist_inf_norm(a, b),
+    madlib.squared_dist_norm2(a, b) AS sq_dist_norm2,
+    madlib.cosine_similarity(a, b),
+    madlib.dist_angle(a, b),
+    madlib.dist_tanimoto(a, b),
+    madlib.dist_jaccard(a::text[], b::text[])
+FROM two_vectors;
+
      Result: 
      + id | dist_norm1 |    dist_norm2    |      norm5       | dist_inf_norm | sq_dist_norm2 | cosine_similarity |     dist_angle     |   dist_tanimoto    |   dist_jaccard
+----+------------+------------------+------------------+---------------+---------------+-------------------+--------------------+--------------------+-------------------
+  1 |          2 |  1.4142135623731 | 1.14869835499704 |             1 |             2 | 0.999512076087079 | 0.0312398334302684 | 0.0588235294117647 | 0.666666666666667
+  2 |         48 | 22.6274169979695 |  15.585086360695 |            14 |           512 | 0.985403348449008 |   0.17106899659286 | 0.0498733684005455 | 0.833333333333333
+(2 rows)
+
      4. +
    +

    Matrix Functions

    +
      +
    1. Create a database table with a matrix column. 
      +CREATE TABLE matrix(
+    id  integer,
+    m   float8[]);
+
      +INSERT INTO matrix VALUES
+(1, '{{4,5},{3,5},{9,0}}');
+
      2. +
    2. Invoke matrix functions. 
      +SELECT
+    madlib.get_row(m, 1) AS row_1,
+    madlib.get_row(m, 2) AS row_2,
+    madlib.get_row(m, 3) AS row_3,
+    madlib.get_col(m, 1) AS col_1,
+    madlib.get_col(m, 2) AS col_2
+FROM matrix;
+
      Result: 
      + row_1 | row_2 | row_3 |  col_1  |  col_2
+-------+-------+-------+---------+---------
+ {4,5} | {3,5} | {9,0} | {4,3,9} | {5,5,0}
+(1 row)
+
      3. +
    +

    Aggregate Functions

    +
      +
    1. Create a database table with a vector column. 
      +CREATE TABLE vector(
+    id  integer,
+    v   float8[]);
+
      +INSERT INTO vector VALUES
+(1, '{4,3}'),
+(2, '{8,6}'),
+(3, '{12,9}');
+
      2. +
    2. Invoke aggregate functions. 
      +SELECT
+    madlib.avg(v),
+    madlib.normalized_avg(v),
+    madlib.matrix_agg(v)
+FROM vector;
+
      Result: 
      +  avg  | normalized_avg |      matrix_agg
+-------+----------------+----------------------
+ {8,6} | {0.8,0.6}      | {{4,3},{8,6},{12,9}}
+(1 row)
+
      3. +
    +

    Literature
    +

    [1] http://en.wikipedia.org/wiki/Jaccard_index#Tanimoto_similarity_and_distance

    +

    Related Topics
    File linalg.sql_in documenting the SQL functions.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__linear__solver.html b/docs/docs/v2.1.0/group__grp__linear__solver.html new file mode 100644 index 00000000..6a0665b3 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__linear__solver.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: Linear Solvers + + + + + + + + + + + + + + + + + + + +
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    +Modules
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    Linear Solvers
    Utilities
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    +

    Detailed Description

    +

    Methods that implement solutions for systems of consistent linear equations.

    + + + + + + + + +

    +Modules

     Dense Linear Systems
     Implements solution methods for large dense linear systems. Currently, restricted to problems that fit in memory.
     
     Sparse Linear Systems
     Implements solution methods for linear systems with sparse matrix input. Currently, restricted to problems that fit in memory.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__linear__solver.js b/docs/docs/v2.1.0/group__grp__linear__solver.js new file mode 100644 index 00000000..01508a75 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__linear__solver.js @@ -0,0 +1,5 @@ +var group__grp__linear__solver = +[ + [ "Dense Linear Systems", "group__grp__dense__linear__solver.html", null ], + [ "Sparse Linear Systems", "group__grp__sparse__linear__solver.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__linreg.html b/docs/docs/v2.1.0/group__grp__linreg.html new file mode 100644 index 00000000..5976d09c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__linreg.html @@ -0,0 +1,458 @@ + + + + + + + + +MADlib: Linear Regression + + + + + + + + + + + + + + + + + + + +
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    User Documentation for Apache MADlib
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    Linear Regression
    Supervised Learning » Regression Models
    +
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    Contents +

    Linear regression models a linear relationship of a scalar dependent variable \( y \) to one or more explanatory independent variables \( x \) and builds a model of coefficients.

    +

    Training Function
    +

    The linear regression training function has the following syntax. 

    +linregr_train( source_table,
+               out_table,
+               dependent_varname,
+               independent_varname,
+               grouping_cols,
+               heteroskedasticity_option
+             )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the training data.

    +

    +
    +
    out_table
    +

    TEXT. Name of the generated table containing the output model.

    +

    The output table contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + +
    <...> Any grouping columns provided during training. Present only if the grouping option is used.
    coef FLOAT8[]. Vector of the coefficients of the regression.
    r2 FLOAT8. R-squared coefficient of determination of the model.
    std_err FLOAT8[]. Vector of the standard error of the coefficients.
    t_stats FLOAT8[]. Vector of the t-statistics of the coefficients.
    p_values FLOAT8[]. Vector of the p-values of the coefficients.
    condition_no FLOAT8 array. The condition number of the \(X^{*}X\) matrix. A high condition number is usually an indication that there may be some numeric instability in the result yielding a less reliable model. A high condition number often results when there is a significant amount of colinearity in the underlying design matrix, in which case other regression techniques, such as elastic net regression, may be more appropriate.
    bp_stats FLOAT8. The Breush-Pagan statistic of heteroskedacity. Present only if the heteroskedacity argument was set to True when the model was trained.
    bp_p_value FLOAT8. The Breush-Pagan calculated p-value. Present only if the heteroskedacity parameter was set to True when the model was trained.
    num_rows_processed BIGINT. The number of rows that are actually used in each group.
    num_missing_rows_skipped INTEGER. The number of rows that have NULL values in the dependent and independent variables, and were skipped in the computation for each group.
    variance_covariance FLOAT[]. Variance/covariance matrix.
    +

    A summary table named <out_table>_summary is created together with the output table. It has the following columns:

    + + + + + + + + + + + + + + + + +
    method 'linregr' for linear regression.
    source_table The data source table name
    out_table The output table name
    dependent_varname The dependent variable
    independent_varname The independent variables
    num_rows_processed The total number of rows that were used in the computation.
    num_missing_rows_skipped The total number of rows that were skipped because of NULL values in them.
    grouping_cols Names of the grouping columns.
    +
    +
    +
    Note
    For p-values, we just return the computation result directly. Other statistical packages like 'R' produce the same result, but on printing the result to screen, another format function is used and any p-value that is smaller than the machine epsilon (the smallest positive floating-point number 'x' such that '1 + x != 1') will be printed on screen as "< xxx" (xxx is the value of the machine epsilon). Although the result may look different, they are in fact the same.
    +
    +
    dependent_varname
    +

    TEXT. Expression to evaluate for the dependent variable.

    +

    +
    +
    independent_varname
    +

    TEXT. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL GROUP BY clause. When this value is null, no grouping is used and a single result model is generated for the whole data set.

    +

    +
    +
    heteroskedasticity_option (optional)
    +
    BOOLEAN, default: FALSE. When TRUE, the heteroskedasticity of the model is also calculated and returned with the results.
    +
    +

    Warning
    The aggregate 'linregr' has been deprecated in favor of the function 'linregr_train'. If the aggregate 'linregr' is used to output the results of linear regression to a table, it is recommended to follow the general pattern shown below (replace text within '<...>' with the appropriate variable names). 
    +CREATE TABLE <output table> AS
+SELECT (r).*
+FROM (
+    SELECT linregr(<dependent variable>, <independent variable>) as r
+    FROM <source table>
+    ) q;
+
    +

    Prediction Function
    The prediction function is as follows: 
    +linregr_predict(coef, col_ind)
+
    Arguments
    +
    coef
    +
    FLOAT8[]. Vector of the coefficients of regression from training.
    +
    col_ind
    +

    FLOAT8[]. An array containing the independent variable column names, as was used for the training.

    +

    +
    +
    +
    +
    Examples
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS houses;
+CREATE TABLE houses (id INT, tax INT, bedroom INT, bath FLOAT, price INT,
+            size INT, lot INT);
+INSERT INTO houses VALUES
+  (1 ,  590 ,       2 ,    1 ,  50000 ,  770 , 22100),
+  (2 , 1050 ,       3 ,    2 ,  85000 , 1410 , 12000),
+  (3 ,   20 ,       3 ,    1 ,  22500 , 1060 ,  3500),
+  (4 ,  870 ,       2 ,    2 ,  90000 , 1300 , 17500),
+  (5 , 1320 ,       3 ,    2 , 133000 , 1500 , 30000),
+  (6 , 1350 ,       2 ,    1 ,  90500 ,  820 , 25700),
+  (7 , 2790 ,       3 ,  2.5 , 260000 , 2130 , 25000),
+  (8 ,  680 ,       2 ,    1 , 142500 , 1170 , 22000),
+  (9 , 1840 ,       3 ,    2 , 160000 , 1500 , 19000),
+ (10 , 3680 ,       4 ,    2 , 240000 , 2790 , 20000),
+ (11 , 1660 ,       3 ,    1 ,  87000 , 1030 , 17500),
+ (12 , 1620 ,       3 ,    2 , 118600 , 1250 , 20000),
+ (13 , 3100 ,       3 ,    2 , 140000 , 1760 , 38000),
+ (14 , 2070 ,       2 ,    3 , 148000 , 1550 , 14000),
+ (15 ,  650 ,       3 ,  1.5 ,  65000 , 1450 , 12000);
+
      2. +
    2. Train a regression model. First, we generate a single regression for all data. 
      +DROP TABLE IF EXISTS houses_linregr, houses_linregr_summary;
+SELECT madlib.linregr_train( 'houses',
+                             'houses_linregr',
+                             'price',
+                             'ARRAY[1, tax, bath, size]'
+                           );
+
      (Note that in this example we are dynamically creating the array of independent variables from column names. If you have large numbers of independent variables beyond the PostgreSQL limit of maximum columns per table, you would pre-build the arrays and store them in a single column.)
      3. +
    3. Next we generate three output models, one for each value of "bedroom". 
      +DROP TABLE IF EXISTS houses_linregr_bedroom, houses_linregr_bedroom_summary;
+SELECT madlib.linregr_train( 'houses',
+                             'houses_linregr_bedroom',
+                             'price',
+                             'ARRAY[1, tax, bath, size]',
+                             'bedroom'
+                           );
+
      4. +
    4. Examine the resulting models. 
      +-- Set extended display on for easier reading of output
+\x ON
+SELECT * FROM houses_linregr;
+
      Result: 
      +-[ RECORD 1 ]+---------------------------------------------------------------------------
+coef                     | {-12849.4168959872,28.9613922651765,10181.6290712648,50.516894915354}
+r2                       | 0.768577580597443
+std_err                  | {33453.0344331391,15.8992104963997,19437.7710925923,32.928023174087}
+t_stats                  | {-0.38410317968819,1.82156166004184,0.523806408809133,1.53416118083605}
+p_values                 | {0.708223134615422,0.0958005827189772,0.610804093526536,0.153235085548186}
+condition_no             | 9002.50457085737
+num_rows_processed       | 15
+num_missing_rows_skipped | 0
+variance_covariance      | {{1119105512.78479,217782.067878023,-283344228.394562,-616679.69319088}, ...
+
      Alternatively you can unnest the results for easier reading of output. 
      +\x OFF
+SELECT unnest(ARRAY['intercept','tax','bath','size']) as attribute,
+       unnest(coef) as coefficient,
+       unnest(std_err) as standard_error,
+       unnest(t_stats) as t_stat,
+       unnest(p_values) as pvalue
+FROM houses_linregr;
+
      Result: 
      + attribute |    coefficient    |  standard_error  |      t_stat       |       pvalue
+-----------+-------------------+------------------+-------------------+--------------------
+ intercept | -12849.4168959872 | 33453.0344331391 | -0.38410317968819 |  0.708223134615422
+ tax       |  28.9613922651765 | 15.8992104963997 |  1.82156166004184 | 0.0958005827189772
+ bath      |  10181.6290712648 | 19437.7710925923 | 0.523806408809133 |  0.610804093526536
+ size      |   50.516894915354 |  32.928023174087 |  1.53416118083605 |  0.153235085548186
+(4 rows)
+
      5. +
    5. View the results grouped by bedroom. 
      +\x ON
+SELECT * FROM houses_linregr_bedroom ORDER BY bedroom;
+
      Result: 
      +-[ RECORD 1 ]------------+----------------------------------------------------------------
+bedroom                  | 4
+coef                     | {0.0112536020318378,41.4132554771633,0.0225072040636757,31.3975496688276}
+r2                       | 1
+std_err                  | {0,0,0,0}
+t_stats                  | {Infinity,Infinity,Infinity,Infinity}
+p_values                 |
+condition_no             | Infinity
+num_rows_processed       | 1
+num_missing_rows_skipped | 0
+variance_covariance      | {{0,0,0,0},{0,0,0,0},{0,0,0,0},{0,0,0,0}}
+-[ RECORD 2 ]------------+----------------------------------------------------------------
+bedroom                  | 3
+coef                     | {-88155.8292501601,27.1966436294429,41404.0293363612,62.637521075324}
+r2                       | 0.841699901311252
+std_err                  | {57867.9999702625,17.8272309154689,43643.1321511114,70.8506824863954}
+t_stats                  | {-1.52339512849005,1.52556747362508,0.948695185143966,0.884077878676067}
+p_values                 | {0.188161432894871,0.187636685729869,0.386340032374927,0.417132778705789}
+condition_no             | 11722.6225642147
+num_rows_processed       | 9
+num_missing_rows_skipped | 0
+variance_covariance      | {{3348705420.5583,433697.545104226,-70253017.45773,-2593488.13800193}, ...
+-[ RECORD 3 ]------------+----------------------------------------------------------------
+bedroom                  | 2
+coef                     | {-84242.0345406597,55.4430144648696,-78966.9753675319,225.611910021192}
+r2                       | 0.968809546465313
+std_err                  | {35018.9991665742,19.5731125320686,23036.8071292552,49.0448678148784}
+t_stats                  | {-2.40560942761235,2.83261103077151,-3.42786111480046,4.60011251070697}
+p_values                 | {0.250804617665239,0.21605133377602,0.180704400437373,0.136272031474122}
+condition_no             | 10086.1048721726
+num_rows_processed       | 5
+num_missing_rows_skipped | 0
+variance_covariance      | {{1226330302.62852,-300921.595596804,551696673.397849,-1544160.63236119}, ...
+
      6. +
    6. Compare predicted price with actual. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) 
      +\x OFF
+SELECT houses.*,
+       madlib.linregr_predict( m.coef,
+                               ARRAY[1,tax,bath,size]
+                             ) as predict,
+        price -
+          madlib.linregr_predict( m.coef,
+                                  ARRAY[1,tax,bath,size]
+                                ) as residual
+FROM houses, houses_linregr m ORDER BY id;
+
      Result: 
      + id | tax  | bedroom | bath | price  | size |  lot  |     predict      |     residual
+----+------+---------+------+--------+------+-------+------------------+-------------------
+  1 |  590 |       2 |    1 |  50000 |  770 | 22100 | 53317.4426965542 | -3317.44269655424
+  2 | 1050 |       3 |    2 |  85000 | 1410 | 12000 | 109152.124955627 | -24152.1249556268
+  3 |   20 |       3 |    1 |  22500 | 1060 |  3500 | 51459.3486308563 | -28959.3486308563
+  4 |  870 |       2 |    2 |  90000 | 1300 | 17500 |  98382.215907206 | -8382.21590720605
+  5 | 1320 |       3 |    2 | 133000 | 1500 | 30000 | 121518.221409606 |  11481.7785903937
+  6 | 1350 |       2 |    1 |  90500 |  820 | 25700 | 77853.9455638561 |  12646.0544361439
+  7 | 2790 |       3 |  2.5 | 260000 | 2130 | 25000 | 201007.926371721 |  58992.0736282788
+  8 |  680 |       2 |    1 | 142500 | 1170 | 22000 | 76130.7259665617 |  66369.2740334383
+  9 | 1840 |       3 |    2 | 160000 | 1500 | 19000 | 136578.145387498 |  23421.8546125019
+ 10 | 3680 |       4 |    2 | 240000 | 2790 | 20000 |  255033.90159623 | -15033.9015962295
+ 11 | 1660 |       3 |    1 |  87000 | 1030 | 17500 | 97440.5250982852 | -10440.5250982852
+ 12 | 1620 |       3 |    2 | 118600 | 1250 | 20000 | 117577.415360321 |  1022.58463967926
+ 13 | 3100 |       3 |    2 | 140000 | 1760 | 38000 | 186203.892319613 | -46203.8923196126
+ 14 | 2070 |       2 |    3 | 148000 | 1550 | 14000 | 155946.739425521 | -7946.73942552117
+ 15 |  650 |       3 |  1.5 |  65000 | 1450 | 12000 | 94497.4293105379 | -29497.4293105379
+(15 rows)
+
      7. +
    7. Compare predicted price with actual with grouping. It means a different model is used depending on the number of bedrooms. 
      +\x OFF
+SELECT houses.*,
+       madlib.linregr_predict( m.coef,
+                              ARRAY[1,tax,bath,size]
+                             ) as predict,
+        price -
+          madlib.linregr_predict( m.coef,
+                                 ARRAY[1,tax,bath,size]
+                                ) as residual
+FROM houses, houses_linregr_bedroom m
+WHERE houses.bedroom = m.bedroom
+ORDER BY id;
+
      Result: 
      + id | tax  | bedroom | bath | price  | size |  lot  |     predict      |     residual
+----+------+---------+------+--------+------+-------+------------------+-------------------
+  1 |  590 |       2 |    1 |  50000 |  770 | 22100 | 43223.5393423978 |  6776.46065760222
+  2 | 1050 |       3 |    2 |  85000 | 1410 | 12000 | 111527.609949684 |  -26527.609949684
+  3 |   20 |       3 |    1 |  22500 | 1060 |  3500 | 20187.9052986341 |  2312.09470136587
+  4 |  870 |       2 |    2 |  90000 | 1300 | 17500 | 99354.9203362612 | -9354.92033626116
+  5 | 1320 |       3 |    2 | 133000 | 1500 | 30000 | 124508.080626412 |  8491.91937358756
+  6 | 1350 |       2 |    1 |  90500 |  820 | 25700 | 96640.8258367579 |  -6140.8258367579
+  7 | 2790 |       3 |  2.5 | 260000 | 2130 | 25000 | 224650.799707327 |  35349.2002926733
+  8 |  680 |       2 |    1 | 142500 | 1170 | 22000 | 138458.174652714 |  4041.82534728572
+  9 | 1840 |       3 |    2 | 160000 | 1500 | 19000 | 138650.335313722 |  21349.6646862777
+ 10 | 3680 |       4 |    2 | 240000 | 2790 | 20000 |           240000 |                 0
+ 11 | 1660 |       3 |    1 |  87000 | 1030 | 17500 | 62911.2752186594 |  24088.7247813406
+ 12 | 1620 |       3 |    2 | 118600 | 1250 | 20000 | 117007.693446414 |  1592.30655358579
+ 13 | 3100 |       3 |    2 | 140000 | 1760 | 38000 | 189203.861766403 | -49203.8617664034
+ 14 | 2070 |       2 |    3 | 148000 | 1550 | 14000 | 143322.539831869 |  4677.46016813093
+ 15 |  650 |       3 |  1.5 |  65000 | 1450 | 12000 | 82452.4386727394 | -17452.4386727394
+(15 rows)
+
      8. +
    +
    +

    Note
    All table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').
    +

    Technical Background
    +

    Ordinary least-squares (OLS) linear regression refers to a stochastic model in which the conditional mean of the dependent variable (usually denoted \( Y \)) is an affine function of the vector of independent variables (usually denoted \( \boldsymbol x \)). That is,

    +\[ E[Y \mid \boldsymbol x] = \boldsymbol c^T \boldsymbol x \] +

    +

    for some unknown vector of coefficients \( \boldsymbol c \). The assumption is that the residuals are i.i.d. distributed Gaussians. That is, the (conditional) probability density of \( Y \) is given by

    +\[ f(y \mid \boldsymbol x) = \frac{1}{\sqrt{2 \pi \sigma^2}} \cdot \exp\left(-\frac{1}{2 \sigma^2} \cdot (y - \boldsymbol x^T \boldsymbol c)^2 \right) \,. \] +

    +

    OLS linear regression finds the vector of coefficients \( \boldsymbol c \) that maximizes the likelihood of the observations.

    +

    Let

      +
    • \( \boldsymbol y \in \mathbf R^n \) denote the vector of observed dependent variables, with \( n \) rows, containing the observed values of the dependent variable,
      • +
    • \( X \in \mathbf R^{n \times k} \) denote the design matrix with \( k \) columns and \( n \) rows, containing all observed vectors of independent variables. \( \boldsymbol x_i \) as rows,
      • +
    • \( X^T \) denote the transpose of \( X \),
      • +
    • \( X^+ \) denote the pseudo-inverse of \( X \).
      • +
    +

    Maximizing the likelihood is equivalent to maximizing the log-likelihood \( \sum_{i=1}^n \log f(y_i \mid \boldsymbol x_i) \), which simplifies to minimizing the residual sum of squares \( RSS \) (also called sum of squared residuals or sum of squared errors of prediction),

    +\[ RSS = \sum_{i=1}^n ( y_i - \boldsymbol c^T \boldsymbol x_i )^2 = (\boldsymbol y - X \boldsymbol c)^T (\boldsymbol y - X \boldsymbol c) \,. \] +

    +

    The first-order conditions yield that the \( RSS \) is minimized at

    +\[ \boldsymbol c = (X^T X)^+ X^T \boldsymbol y \,. \] +

    +

    Computing the total sum of squares \( TSS \), the explained sum of squares \( ESS \) (also called the regression sum of squares), and the coefficient of determination \( R^2 \) is done according to the following formulas:

    +\begin{align*} ESS & = \boldsymbol y^T X \boldsymbol c - \frac{ \| y \|_1^2 }{n} \\ TSS & = \sum_{i=1}^n y_i^2 - \frac{ \| y \|_1^2 }{n} \\ R^2 & = \frac{ESS}{TSS} \end{align*} +

    +

    Note: The last equality follows from the definition \( R^2 = 1 - \frac{RSS}{TSS} \) and the fact that for linear regression \( TSS = RSS + ESS \). A proof of the latter can be found, e.g., at: http://en.wikipedia.org/wiki/Sum_of_squares

    +

    We estimate the variance \( Var[Y - \boldsymbol c^T \boldsymbol x \mid \boldsymbol x] \) as

    +\[ \sigma^2 = \frac{RSS}{n - k} \] +

    +

    and compute the t-statistic for coefficient \( i \) as

    +\[ t_i = \frac{c_i}{\sqrt{\sigma^2 \cdot \left( (X^T X)^{-1} \right)_{ii} }} \,. \] +

    +

    The \( p \)-value for coefficient \( i \) gives the probability of seeing a value at least as extreme as the one observed, provided that the null hypothesis ( \( c_i = 0 \)) is true. Letting \( F_\nu \) denote the cumulative density function of student-t with \( \nu \) degrees of freedom, the \( p \)-value for coefficient \( i \) is therefore

    +\[ p_i = \Pr(|T| \geq |t_i|) = 2 \cdot (1 - F_{n - k}( |t_i| )) \] +

    +

    where \( T \) is a student-t distributed random variable with mean 0.

    +

    The condition number [2] \( \kappa(X) = \|X\|_2\cdot\|X^{-1}\|_2\) is computed as the product of two spectral norms [3]. The spectral norm of a matrix \(X\) is the largest singular value of \(X\) i.e. the square root of the largest eigenvalue of the positive-semidefinite matrix \(X^{*}X\):

    +

    +\[ \|X\|_2 = \sqrt{\lambda_{\max}\left(X^{*}X\right)}\ , \] +

    +

    where \(X^{*}\) is the conjugate transpose of \(X\). The condition number of a linear regression problem is a worst-case measure of how sensitive the result is to small perturbations of the input. A large condition number (say, more than 1000) indicates the presence of significant multicollinearity.

    +

    Literature
    +

    [1] Cosma Shalizi: Statistics 36-350: Data Mining, Lecture Notes, 21 October 2009, http://www.stat.cmu.edu/~cshalizi/350/lectures/17/lecture-17.pdf

    +

    [2] Wikipedia: Condition Number, http://en.wikipedia.org/wiki/Condition_number.

    +

    [3] Wikipedia: Spectral Norm, http://en.wikipedia.org/wiki/Spectral_norm#Spectral_norm

    +

    [4] Wikipedia: Breusch–Pagan test, http://en.wikipedia.org/wiki/Breusch%E2%80%93Pagan_test

    +

    [5] Wikipedia: Heteroscedasticity-consistent standard errors, http://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors

    +

    Related Topics
    +

    Robust Variance

    +

    Clustered Variance

    +

    Cross Validation

    +

    File linear.sql_in, source file for the SQL functions

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__lmf.html b/docs/docs/v2.1.0/group__grp__lmf.html new file mode 100644 index 00000000..9eb55f9a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__lmf.html @@ -0,0 +1,268 @@ + + + + + + + + +MADlib: Low-Rank Matrix Factorization + + + + + + + + + + + + + + + + + + + +
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    + + + + + + + + +
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    + 2.1.0 +
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    User Documentation for Apache MADlib
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    Low-Rank Matrix Factorization
    Data Types and Transformations » Arrays and Matrices » Matrix Factorization
    +
    +
    +
    Contents +

    This module implements "factor model" for representing an incomplete matrix using a low-rank approximation [1]. Mathematically, this model seeks to find matrices U and V (also referred as factors) that, for any given incomplete matrix A, minimizes:

    +

    +\[ \|\boldsymbol A - \boldsymbol UV^{T} \|_2 \] +

    +

    subject to \(rank(\boldsymbol UV^{T}) \leq r\), where \(\|\cdot\|_2\) denotes the Frobenius norm. Let \(A\) be a \(m \times n\) matrix, then \(U\) will be \(m \times r\) and \(V\) will be \(n \times r\), in dimension, and \(1 \leq r \ll \min(m, n)\). This model is not intended to do the full decomposition, or to be used as part of inverse procedure. This model has been widely used in recommendation systems (e.g., Netflix [2]) and feature selection (e.g., image processing [3]).

    +

    Function Syntax
    +

    Low-rank matrix factorization of an incomplete matrix into two factors.

    +
    +lmf_igd_run( rel_output,
+             rel_source,
+             col_row,
+             col_column,
+             col_value,
+             row_dim,
+             column_dim,
+             max_rank,
+             stepsize,
+             scale_factor,
+             num_iterations,
+             tolerance
+           )
+

    Arguments

    +
    rel_output
    +

    TEXT. The name of the table to receive the output.

    +

    Output factors matrix U and V are in a flattened format. 

    RESULT AS (
+        matrix_u    DOUBLE PRECISION[],
+        matrix_v    DOUBLE PRECISION[],
+        rmse        DOUBLE PRECISION
+);

    Features correspond to row i is matrix_u[i:i][1:r]. Features correspond to column j is matrix_v[j:j][1:r].

    +
    +
    rel_source
    +

    TEXT. The name of the table containing the input data.

    +

    The input matrix> is expected to be of the following form: 

    {TABLE|VIEW} input_table (
+    row    INTEGER,
+    col    INTEGER,
+    value  DOUBLE PRECISION
+)

    Input is contained in a table that describes an incomplete matrix, with available entries specified as (row, column, value). The input matrix should be 1-based, which means row >= 1, and col >= 1. NULL values are not expected.

    +
    +
    col_row
    +
    TEXT. The name of the column containing the row number.
    +
    col_column
    +
    TEXT. The name of the column containing the column number.
    +
    col_value
    +
    DOUBLE PRECISION. The value at (row, col).
    +
    row_dim (optional)
    +
    INTEGER, default: "SELECT max(col_row) FROM rel_source". The number of columns in the matrix.
    +
    column_dim (optional)
    +
    INTEGER, default: "SELECT max(col_col) FROM rel_source". The number of rows in the matrix.
    +
    max_rank
    +
    INTEGER, default: 20. The rank of desired approximation.
    +
    stepsize (optional)
    +
    DOUBLE PRECISION, default: 0.01. Hyper-parameter that decides how aggressive the gradient steps are.
    +
    scale_factor (optional)
    +
    DOUBLE PRECISION, default: 0.1. Hyper-parameter that decides scale of initial factors.
    +
    num_iterations (optional)
    +
    INTEGER, default: 10. Maximum number if iterations to perform regardless of convergence.
    +
    tolerance (optional)
    +
    DOUBLE PRECISION, default: 0.0001. Acceptable level of error in convergence.
    +
    +

    Examples
    +
      +
    1. Prepare an input table/view: 
      +DROP TABLE IF EXISTS lmf_data;
+CREATE TABLE lmf_data (
+ row INT,
+ col INT,
+ val FLOAT8
+);
+
      2. +
    2. Populate the input table with some data. 
      +INSERT INTO lmf_data VALUES (1, 1, 5.0);
+INSERT INTO lmf_data VALUES (3, 100, 1.0);
+INSERT INTO lmf_data VALUES (999, 10000, 2.0);
+
      3. +
    3. Call the lmf_igd_run() stored procedure. 
      +DROP TABLE IF EXISTS lmf_model;
+SELECT madlib.lmf_igd_run( 'lmf_model',
+                           'lmf_data',
+                           'row',
+                           'col',
+                           'val',
+                           999,
+                           10000,
+                           3,
+                           0.1,
+                           2,
+                           10,
+                           1e-9
+                         );
+
      Example result (the exact result may not be the same). 
      +NOTICE:
+Finished low-rank matrix factorization using incremental gradient
+DETAIL:
+   table : lmf_data (row, col, val)
+Results:
+   RMSE = 0.0145966345300041
+Output:
+   view : SELECT * FROM lmf_model WHERE id = 1
+ lmf_igd_run
+ -----------
+           1
+ (1 row)
+
      4. +
    4. Sanity check of the result. You may need a model id returned and also indicated by the function lmf_igd_run(), assuming 1 here: 
      +SELECT array_dims(matrix_u) AS u_dims, array_dims(matrix_v) AS v_dims
+FROM lmf_model
+WHERE id = 1;
+
      Result: 
      +     u_dims    |     v_dims
+ --------------+----------------
+  [1:999][1:3] | [1:10000][1:3]
+ (1 row)
+
      5. +
    5. Query the result value. 
      +SELECT matrix_u[2:2][1:3] AS row_2_features
+FROM lmf_model
+WHERE id = 1;
+
      Example output (the exact result may not be the same): 
      +                       row_2_features
+ ---------------------------------------------------------
+  {{1.12030523084104,0.522217971272767,0.0264869043603539}}
+ (1 row)
+
      6. +
    6. Make prediction of a missing entry (row=2, col=7654). 
      +SELECT madlib.array_dot(
+    matrix_u[2:2][1:3],
+    matrix_v[7654:7654][1:3]
+    ) AS row_2_col_7654
+FROM lmf_model
+WHERE id = 1;
+
      Example output (the exact result may not be the same due the randomness of the algorithm): 
      +   row_2_col_7654
+ ------------------
+  1.3201582940851
+ (1 row)
+
      7. +
    +

    Literature
    +

    [1] N. Srebro and T. Jaakkola. “Weighted Low-Rank Approximations.” In: ICML. Ed. by T. Fawcett and N. Mishra. AAAI Press, 2003, pp. 720–727. isbn: 1-57735-189-4.

    +

    [2] Simon Funk, Netflix Update: Try This at Home, December 11 2006, http://sifter.org/~simon/journal/20061211.html

    +

    [3] J. Wright, A. Ganesh, S. Rao, Y. Peng, and Y. Ma. “Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization.” In: NIPS. Ed. by Y. Bengio, D. Schuurmans, J. D. Lafferty, C. K. I. Williams, and A. Culotta. Curran Associates, Inc., 2009, pp. 2080–2088. isbn: 9781615679119.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__logreg.html b/docs/docs/v2.1.0/group__grp__logreg.html new file mode 100644 index 00000000..d2344372 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__logreg.html @@ -0,0 +1,491 @@ + + + + + + + + +MADlib: Logistic Regression + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    Logistic Regression
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    Binomial logistic regression models the relationship between a dichotomous dependent variable and one or more predictor variables. The dependent variable may be a Boolean value or a categorial variable that can be represented with a Boolean expression. The probabilities describing the possible outcomes of a single trial are modeled, as a function of the predictor variables, using a logistic function.

    +

    Training Function
    The logistic regression training function has the following format: 
    +logregr_train( source_table,
+               out_table,
+               dependent_varname,
+               independent_varname,
+               grouping_cols,
+               max_iter,
+               optimizer,
+               tolerance,
+               verbose
+             )
+
    Arguments
    +
    source_table
    +

    TEXT. Name of the table containing the training data.

    +

    +
    +
    out_table
    +

    TEXT. Name of the generated table containing the output model.

    +

    The output table produced by the logistic regression training function contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + +
    <...>

    TEXT. Grouping columns, if provided in input. This could be multiple columns depending on the grouping_cols input.

    +

    +
    coef

    FLOAT8. Vector of the coefficients of the regression.

    +

    +
    log_likelihood

    FLOAT8. The log-likelihood \( l(\boldsymbol c) \).

    +

    +
    std_err

    FLOAT8[]. Vector of the standard error of the coefficients.

    +

    +
    z_stats

    FLOAT8[]. Vector of the z-statistics of the coefficients.

    +

    +
    p_values

    FLOAT8[]. Vector of the p-values of the coefficients.

    +

    +
    odds_ratios

    FLOAT8[]. The odds ratio, \( \exp(c_i) \).

    +

    +
    condition_no

    FLOAT8[]. The condition number of the \(X^{*}X\) matrix. A high condition number is usually an indication that there may be some numeric instability in the result yielding a less reliable model. A high condition number often results when there is a significant amount of colinearity in the underlying design matrix, in which case other regression techniques may be more appropriate.

    +

    +
    num_rows_processed

    INTEGER. The number of rows actually processed, which is equal to the total number of rows in the source table minus the number of skipped rows.

    +

    +
    num_missing_rows_skipped

    INTEGER. The number of rows skipped during the training. A row will be skipped if the independent_varname is NULL or contains NULL values.

    +

    +
    num_iterations

    INTEGER. The number of iterations actually completed. This would be different from the nIterations argument if a tolerance parameter is provided and the algorithm converges before all iterations are completed.

    +

    +
    variance_covariance FLOAT[]. Variance/covariance matrix.
    +

    A summary table named <out_table>_summary is also created at the same time, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + +
    method

    'logregr' for logistic regression.

    +

    +
    source_table

    The data source table name.

    +

    +
    out_table

    The output table name.

    +

    +
    dependent_varname

    The dependent variable name.

    +

    +
    independent_varname

    The independent variable names.

    +

    +
    optimizer_params

    A string that contains all the optimizer parameters, and has the form of 'optimizer=..., max_iter=..., tolerance=...'

    +

    +
    num_all_groups

    How many groups of data were fit by the logistic model.

    +

    +
    num_failed_groups

    How many groups failed in training.

    +

    +
    num_rows_processed

    The total number of rows used in the computation.

    +

    +
    num_missing_rows_skipped

    The total number of rows skipped.

    +

    +
    grouping_cols Names of the grouping columns.
    +

    +
    +
    dependent_varname
    +

    TEXT. Name of the dependent variable column (of type BOOLEAN) in the training data, or an expression evaluating to a BOOLEAN.

    +

    +
    +
    independent_varname
    +

    TEXT. Expression list to evaluate for the independent variables. An intercept variable is not assumed so it is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated for the whole data set.

    +

    +
    +
    max_iter (optional)
    +

    INTEGER, default: 20. The maximum number of iterations allowed.

    +

    +
    +
    optimizer (optional)
    +

    TEXT, default: 'irls'. The name of the optimizer to use:

    + + + + + + +
    'newton' or 'irls' Iteratively reweighted least squares
    'cg' conjugate gradient
    'igd' incremental gradient descent.
    +

    +
    +
    tolerance (optional)
    +

    FLOAT8, default: 0.0001. The difference between log-likelihood values in successive iterations that indicate convergence. A zero disables the convergence criterion, so that execution stops after the maximum iterations have completed, as set in the 'max_iter' parameter above.

    +

    +
    +
    verbose (optional)
    +
    BOOLEAN, default: FALSE. Provides verbose output of the results of training.
    +
    +
    +
    Note
    For p-values, we just return the computation result directly. Other statistical packages like 'R' produce the same result, but on printing the result to screen, another format function is used and any p-value that is smaller than the machine epsilon (the smallest positive floating-point number 'x' such that '1 + x != 1') will be printed on screen as "< xxx" (xxx is the value of the machine epsilon). Although the result may look different, they are in fact the same.
    +

    Prediction Function
    Two prediction functions are provided. One predicts the boolean value of the dependent variable, and the other predicts the probability of the value of the dependent variable being 'True'. Syntax is the same for both functions.
    +

    The function to predict the boolean value (True/False) of the dependent variable has the following syntax: 

    +logregr_predict(coefficients,
+                ind_var
+               )
+

    The function to predict the probability of the dependent variable being 'True' has the following syntax: 

    +logregr_predict_prob(coefficients,
+                     ind_var
+                    )
+

    Arguments

    +
    coefficients
    +

    DOUBLE PRECISION[]. Model coefficients obtained from training logregr_train().

    +

    +
    +
    ind_var
    +
    Independent variables expressed as a DOUBLE array. This should be the same length as the array obtained by evaluation of the 'independent_varname' argument in logregr_train().
    +
    +

    Examples
      +
    1. Create the training data table. This data set is related to predicting a second heart attack given treatment and health factors. 
      +DROP TABLE IF EXISTS patients;
+CREATE TABLE patients( id INTEGER NOT NULL,
+                       second_attack INTEGER,
+                       treatment INTEGER,
+                       trait_anxiety INTEGER);
+INSERT INTO patients VALUES
+(1,  1, 1, 70),
+(2,  1, 1, 80),
+(3,  1, 1, 50),
+(4,  1, 0, 60),
+(5,  1, 0, 40),
+(6,  1, 0, 65),
+(7,  1, 0, 75),
+(8,  1, 0, 80),
+(9,  1, 0, 70),
+(10, 1, 0, 60),
+(11, 0, 1, 65),
+(12, 0, 1, 50),
+(13, 0, 1, 45),
+(14, 0, 1, 35),
+(15, 0, 1, 40),
+(16, 0, 1, 50),
+(17, 0, 0, 55),
+(18, 0, 0, 45),
+(19, 0, 0, 50),
+(20, 0, 0, 60);
+
      2. +
    2. Train a regression model. 
      +DROP TABLE IF EXISTS patients_logregr, patients_logregr_summary;
+SELECT madlib.logregr_train( 'patients',                             -- Source table
+                             'patients_logregr',                     -- Output table
+                             'second_attack',                        -- Dependent variable
+                             'ARRAY[1, treatment, trait_anxiety]',   -- Feature vector
+                             NULL,                                   -- Grouping
+                             20,                                     -- Max iterations
+                             'irls'                                  -- Optimizer to use
+                           );
+
      Note that in the example above we are dynamically creating the array of independent variables from column names. If you have large numbers of independent variables beyond the PostgreSQL limit of maximum columns per table, you would typically pre-build the arrays and store them in a single column.
      3. +
    3. View the regression results. 
      +-- Set extended display on for easier reading of output
+\x on
+SELECT * from patients_logregr;
+
      Result: 
      +coef                     | {-6.36346994178192,-1.02410605239327,0.119044916668607}
+log_likelihood           | -9.41018298388876
+std_err                  | {3.21389766375099,1.17107844860319,0.0549790458269317}
+z_stats                  | {-1.97998524145757,-0.874498248699539,2.16527796868916}
+p_values                 | {0.0477051870698145,0.381846973530455,0.0303664045046183}
+odds_ratios              | {0.00172337630923221,0.359117354054956,1.12642051220895}
+condition_no             | 326.081922791575
+num_rows_processed       | 20
+num_missing_rows_skipped | 0
+num_iterations           | 5
+variance_covariance      | {{10.329138193064,-0.474304665195738,-0.171995901260057}, ...
+
      4. +
    4. Alternatively, unnest the arrays in the results for easier reading of output: 
      +\x off
+SELECT unnest(array['intercept', 'treatment', 'trait_anxiety']) as attribute,
+       unnest(coef) as coefficient,
+       unnest(std_err) as standard_error,
+       unnest(z_stats) as z_stat,
+       unnest(p_values) as pvalue,
+       unnest(odds_ratios) as odds_ratio
+    FROM patients_logregr;
+
      Result: 
      +   attribute   |    coefficient    |   standard_error   |       z_stat       |       pvalue       |     odds_ratio
+---------------+-------------------+--------------------+--------------------+--------------------+---------------------
+ intercept     | -6.36346994178192 |   3.21389766375099 |  -1.97998524145757 | 0.0477051870698145 | 0.00172337630923221
+ treatment     | -1.02410605239327 |   1.17107844860319 | -0.874498248699539 |  0.381846973530455 |   0.359117354054956
+ trait_anxiety | 0.119044916668607 | 0.0549790458269317 |   2.16527796868916 | 0.0303664045046183 |    1.12642051220895
+(3 rows)
+
      5. +
    5. Predict the dependent variable using the logistic regression model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) 
      +\x off
+-- Display prediction value along with the original value
+SELECT p.id, madlib.logregr_predict(coef, ARRAY[1, treatment, trait_anxiety]),
+       p.second_attack::BOOLEAN
+FROM patients p, patients_logregr m
+ORDER BY p.id;
+
      Result: 
      +  id | logregr_predict | second_attack
+----+-----------------+---------------
+  1 | t               | t
+  2 | t               | t
+  3 | f               | t
+  4 | t               | t
+  5 | f               | t
+  6 | t               | t
+  7 | t               | t
+  8 | t               | t
+  9 | t               | t
+ 10 | t               | t
+ 11 | t               | f
+ 12 | f               | f
+ 13 | f               | f
+ 14 | f               | f
+ 15 | f               | f
+ 16 | f               | f
+ 17 | t               | f
+ 18 | f               | f
+ 19 | f               | f
+ 20 | t               | f
+(20 rows)
+
      6. +
    6. Predict the probability of the dependent variable being TRUE. 
      +\x off
+-- Display prediction value along with the original value
+SELECT p.id, madlib.logregr_predict_prob(coef, ARRAY[1, treatment, trait_anxiety]),
+       p.second_attack::BOOLEAN
+FROM patients p, patients_logregr m
+ORDER BY p.id;
+
      Result: 
      + id | logregr_predict_prob | second_attack
+----+----------------------+---------------
+  1 |    0.720223028941527 | t
+  2 |    0.894354902502048 | t
+  3 |    0.192269541755171 | t
+  4 |    0.685513072239347 | t
+  5 |    0.167747881508857 | t
+  6 |     0.79809810891514 | t
+  7 |    0.928568075752503 | t
+  8 |    0.959305763693571 | t
+  9 |    0.877576117431452 | t
+ 10 |    0.685513072239347 | t
+ 11 |    0.586700895943317 | f
+ 12 |    0.192269541755171 | f
+ 13 |    0.116032010632994 | f
+ 14 |   0.0383829143134982 | f
+ 15 |   0.0674976224147597 | f
+ 16 |    0.192269541755171 | f
+ 17 |    0.545870774302621 | f
+ 18 |    0.267675422387132 | f
+ 19 |    0.398618639285111 | f
+ 20 |    0.685513072239347 | f
+(20 rows)
+
      7. +
    +
    +

    Notes
    All table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').
    +

    Technical Background
    +

    (Binomial) logistic regression refers to a stochastic model in which the conditional mean of the dependent dichotomous variable (usually denoted \( Y \in \{ 0,1 \} \)) is the logistic function of an affine function of the vector of independent variables (usually denoted \( \boldsymbol x \)). That is,

    +\[ E[Y \mid \boldsymbol x] = \sigma(\boldsymbol c^T \boldsymbol x) \] +

    +

    for some unknown vector of coefficients \( \boldsymbol c \) and where \( \sigma(x) = \frac{1}{1 + \exp(-x)} \) is the logistic function. Logistic regression finds the vector of coefficients \( \boldsymbol c \) that maximizes the likelihood of the observations.

    +

    Let

      +
    • \( \boldsymbol y \in \{ 0,1 \}^n \) denote the vector of observed dependent variables, with \( n \) rows, containing the observed values of the dependent variable,
      • +
    • \( X \in \mathbf R^{n \times k} \) denote the design matrix with \( k \) columns and \( n \) rows, containing all observed vectors of independent variables \( \boldsymbol x_i \) as rows.
      • +
    +

    By definition,

    +\[ P[Y = y_i | \boldsymbol x_i] = \sigma((-1)^{(1 - y_i)} \cdot \boldsymbol c^T \boldsymbol x_i) \,. \] +

    +

    Maximizing the likelihood \( \prod_{i=1}^n \Pr(Y = y_i \mid \boldsymbol x_i) \) is equivalent to maximizing the log-likelihood \( \sum_{i=1}^n \log \Pr(Y = y_i \mid \boldsymbol x_i) \), which simplifies to

    +\[ l(\boldsymbol c) = -\sum_{i=1}^n \log(1 + \exp((-1)^{(1 - y_i)} \cdot \boldsymbol c^T \boldsymbol x_i)) \,. \] +

    +

    The Hessian of this objective is \( H = -X^T A X \) where \( A = \text{diag}(a_1, \dots, a_n) \) is the diagonal matrix with \( a_i = \sigma(\boldsymbol c^T \boldsymbol x) \cdot \sigma(-\boldsymbol c^T \boldsymbol x) \,. \) Since \( H \) is non-positive definite, \( l(\boldsymbol c) \) is convex. There are many techniques for solving convex optimization problems. Currently, logistic regression in MADlib can use one of three algorithms:

      +
    • Iteratively Reweighted Least Squares
      • +
    • A conjugate-gradient approach, also known as Fletcher-Reeves method in the literature, where we use the Hestenes-Stiefel rule for calculating the step size.
      • +
    • Incremental gradient descent, also known as incremental gradient methods or stochastic gradient descent in the literature.
      • +
    +

    We estimate the standard error for coefficient \( i \) as

    +\[ \mathit{se}(c_i) = \left( (X^T A X)^{-1} \right)_{ii} \,. \] +

    +

    The Wald z-statistic is

    +\[ z_i = \frac{c_i}{\mathit{se}(c_i)} \,. \] +

    +

    The Wald \( p \)-value for coefficient \( i \) gives the probability (under the assumptions inherent in the Wald test) of seeing a value at least as extreme as the one observed, provided that the null hypothesis ( \( c_i = 0 \)) is true. Letting \( F \) denote the cumulative density function of a standard normal distribution, the Wald \( p \)-value for coefficient \( i \) is therefore

    +\[ p_i = \Pr(|Z| \geq |z_i|) = 2 \cdot (1 - F( |z_i| )) \] +

    +

    where \( Z \) is a standard normally distributed random variable.

    +

    The odds ratio for coefficient \( i \) is estimated as \( \exp(c_i) \).

    +

    The condition number is computed as \( \kappa(X^T A X) \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration). A large condition number (say, more than 1000) indicates the presence of significant multicollinearity.

    +

    Literature
    +

    A selection of references pertaining to logistic regression, with some good pointers to other literature.

    +

    [1] Cosma Shalizi: Statistics 36-350: Data Mining, Lecture Notes, 18 November 2009, http://www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf

    +

    [2] Thomas P. Minka: A comparison of numerical optimizers for logistic regression, 2003 (revised Mar 26, 2007), http://research.microsoft.com/en-us/um/people/minka/papers/logreg/minka-logreg.pdf

    +

    [3] Paul Komarek, Andrew W. Moore: Making Logistic Regression A Core Data Mining Tool With TR-IRLS, IEEE International Conference on Data Mining 2005, pp. 685-688, http://komarix.org/ac/papers/tr-irls.short.pdf

    +

    [4] D. P. Bertsekas: Incremental gradient, subgradient, and proximal methods for convex optimization: a survey, Technical report, Laboratory for Information and Decision Systems, 2010, http://web.mit.edu/dimitrib/www/Incremental_Survey_LIDS.pdf

    +

    [5] A. Nemirovski, A. Juditsky, G. Lan, and A. Shapiro: Robust stochastic approximation approach to stochastic programming, SIAM Journal on Optimization, 19(4), 2009, http://www2.isye.gatech.edu/~nemirovs/SIOPT_RSA_2009.pdf

    +

    Related Topics
    +

    File logistic.sql_in documenting the training function

    +

    logregr_train()

    +

    elastic_net_train()

    +

    Linear Regression

    +

    Multinomial Regression

    +

    Ordinal Regression

    +

    Robust Variance

    +

    Clustered Variance

    +

    Cross Validation

    +

    Marginal Effects

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__marginal.html b/docs/docs/v2.1.0/group__grp__marginal.html new file mode 100644 index 00000000..3082cacf --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__marginal.html @@ -0,0 +1,466 @@ + + + + + + + + +MADlib: Marginal Effects + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Marginal Effects
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    A marginal effect (ME) or partial effect measures the effect on the conditional mean of \( y \) for a change in one of the regressors, say \(X_k\). In the linear regression model, the ME equals the relevant slope coefficient, greatly simplifying analysis. For nonlinear models, specialized algorithms are required for calculating ME. The marginal effect computed is the average of the marginal effect at every data point present in the source table.

    +

    MADlib provides marginal effects regression functions for linear, logistic and multinomial logistic regressions. The implementation is similar to reference [1].

    +

    Marginal Effects with Interaction Terms
    +margins( model_table,
+         output_table,
+         x_design,
+         source_table,
+         marginal_vars
+       )
+
    Arguments
    +
    model_table
    +
    VARCHAR. The name of the model table, which is the output of logregr_train() or mlogregr_train().
    +
    output_table
    +
    VARCHAR. The name of the result table. The output table has the following columns. + + + + + + + + + + +
    variables INTEGER[]. The indices of the basis variables.
    margins DOUBLE PRECISION[]. The marginal effects.
    std_err DOUBLE PRECISION[]. An array of the standard errors, computed using the delta method.
    z_stats DOUBLE PRECISION[]. An array of the z-stats of the marginal effects.
    p_values DOUBLE PRECISION[]. An array of the Wald p-values of the marginal effects.
    +
    +
    x_design (optional)
    +

    VARCHAR, default: NULL. The design of independent variables, necessary only if interaction term or indicator (categorical) terms are present. This parameter is necessary since the independent variables in the underlying regression is not parsed to extract the relationship between variables.

    +

    Example: The independent_varname in the regression method can be specified in either of the following ways:

      +
    • ‘array[1, color_blue, color_green, gender_female, gpa, gpa^2, gender_female*gpa, gender_female*gpa^2, weight]’
      • +
    • ‘x’
      • +
    +

    In the second version, the column x is an array containing data identical to that expressed in the first version, computed in a prior data preparation step. Supply an x_design argument to the margins() function in the following way:

      +
    • ‘1, i.color_blue.color, i.color_green.color, i.gender_female, gpa, gpa^2, gender_female*gpa, gender_female*gpa^2, weight’
      • +
    +

    The variable names ('gpa', 'weight', ...), referred to here as identifiers, should be unique for each basis variable and need not be the same as the original variable name in independent_varname. They should, however, be in the same order as the corresponding variables in independent_varname. The length of x_design is expected to be the same as the length of independent_varname. Each identifier name can contain only alphanumeric characters and the underscore.

    +

    Indicator (dummy) variables are prefixed with an 'i.' (This is only necessary for the basis term; it is not needed in the interaction terms.) Indicator variables that are obtained from the same categorical variable (for example, 'color_blue' and 'color_green') need to have a common and unique suffix (for example, '.color'). The '.' is used to add the prefix and suffix. If a reference indicator variable is present, it should contain the prefix 'ir.'.

    +

    An identifier may contain alphanumeric characters and underscores. To include other characters, the string must be double-quoted. Escape-characters are not currently supported.

    +

    +
    +
    source_table (optional)
    +

    VARCHAR, default: NULL. Name of the data table to apply marginal effects on. If not provided or NULL then the marginal effects are computed on the training table.

    +

    +
    +
    marginal_vars (optional)
    +
    VARCHAR, default: NULL. Comma-separated string containing specific variable identifiers to calculate marginal effects on. When NULL, marginal effects for all variables are returned.
    +
    +
    +
    Note
    No output will be provided for the reference indicator variable, since the marginal effect for that variable is undefined. If a reference variable is included in the independent variables and marginal_vars, the margins() function will ignore that variable for the output. The variable can still be included in the regression and margins, since it will affect the values for other related indicator variables.
    +

    Marginal Effects for Logistic Regression
    +
    Warning
    This function has been deprecated in favor of the margins() function.
    +
    +margins_logregr( source_table,
+                 output_table,
+                 dependent_variable,
+                 independent_variable,
+                 grouping_cols,
+                 marginal_vars,
+                 max_iter,
+                 optimizer,
+                 tolerance,
+                 verbose_mode
+               )
+

    Arguments

    +
    source_table
    +
    VARCHAR. The name of the data table.
    +
    output_table
    +

    VARCHAR. The name of the result table. The output table has the following columns.

    + + + + + + + + +
    margins DOUBLE PRECISION[]. The marginal effects.
    std_err DOUBLE PRECISION[]. An array of the standard errors, using the delta method.
    z_stats DOUBLE PRECISION[]. An array of the z-stats of the marginal effects.
    p_values DOUBLE PRECISION[]. An array of the Wald p-values of the marginal effects.
    +

    A summary table named <output_table>_summary is also created, which is the same as the summary table created by logregr_train() function. Refer to the documentation for logistic regression for details.

    +

    +
    +
    dependent_variable
    +
    VARCHAR. The name of the column for dependent variables.
    +
    independent_variable
    +
    VARCHAR. The name of the column for independent variables. Can be any SQL expression that evaluates to an array.
    +
    grouping_cols (optional)
    +
    VARCHAR, default: NULL. Not currently implemented. Any non-NULL value is ignored. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single result model is generated.
    +
    marginal_vars (optional)
    +
    INTEGER[], default: NULL. An index list (base 1) representing the independent variables to compute marginal effects on. When NULL, computes marginal effects on all variables.
    +
    max_iter (optional)
    +
    INTEGER, default: 20. The maximum number of iterations for the logistic regression.
    +
    optimizer (optional)
    +
    VARCHAR, default: 'irls'. The optimizer to use for the logistic regression: newton/irls, cg, or igd.
    +
    tolerance (optional)
    +
    DOUBLE PRECISION, default: 1e-4. Termination criterion for logistic regression (relative).
    +
    verbose_mode (optional)
    +
    BOOLEAN, default FALSE. When TRUE, provides verbose output of the results of training.
    +
    +

    Marginal Effects for Multinomial Logistic Regression
    +
    Warning
    This function has been deprecated in favor of the margins() function.
    +
    +margins_mlogregr( source_table,
+                  out_table,
+                  dependent_varname,
+                  independent_varname,
+                  ref_category,
+                  grouping_cols,
+                  marginal_vars,
+                  optimizer_params,
+                  verbose_mode
+                )
+

    Arguments

    +
    source_table
    +
    VARCHAR. The name of data table.
    +
    out_table
    +

    VARCHAR. The name of result table. The output table has the following columns.

    + + + + + + + + + + + + +
    category The category.
    ref_category The refererence category used for modeling.
    margins DOUBLE PRECISION[]. The marginal effects.
    std_err DOUBLE PRECISION[]. An array of the standard errors, using the delta method.
    z_stats DOUBLE PRECISION[]. An array of the z-stats of the marginal effects.
    p_values DOUBLE PRECISION[]. An array of the Wald p-values of the marginal effects.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by mlogregr_train() function. Refer to the documentation for multinomial logistic regression for details.

    +

    +
    +
    dependent_varname
    +
    VARCHAR. The name of the column for dependent variables.
    +
    independent_varname
    +
    VARCHAR. The name of the column for independent variables. Can be any SQL expression that evaluates to an array.
    +
    ref_category (optional)
    +
    INTEGER, default: 0. Reference category for the multinomial logistic regression.
    +
    grouping_cols (optional)
    +
    VARCHAR, default: NULL. Not currently implemented. Any non-NULL value is ignored. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single result model is generated.
    +
    marginal_vars(optional)
    +
    INTEGER[], default: NULL. An index list (base 1) representing the independent variables to compute marginal effects on. When NULL, computes marginal effects on all variables.
    +
    optimizer_params (optional)
    +
    TEXT, default: NULL, which uses the default values of optimizer parameters: max_iter=20, optimizer='newton', tolerance=1e-4. It should be a string that contains 'key=value' pairs separated by commas.
    +
    verbose_mode (optional)
    +
    BOOLEAN, default FALSE. When TRUE, provides verbose output of the results of training.
    +
    +

    Examples
    +
      +
    1. Create the sample data set. Use the patients dataset from the Logistic Regression examples. 
      +DROP TABLE IF EXISTS patients;
+CREATE TABLE patients( id INTEGER NOT NULL,
+                       second_attack INTEGER,
+                       treatment INTEGER,
+                       trait_anxiety INTEGER);
+INSERT INTO patients VALUES
+(1,  1, 1, 70),
+(2,  1, 1, 80),
+(3,  1, 1, 50),
+(4,  1, 0, 60),
+(5,  1, 0, 40),
+(6,  1, 0, 65),
+(7,  1, 0, 75),
+(8,  1, 0, 80),
+(9,  1, 0, 70),
+(10, 1, 0, 60),
+(11, 0, 1, 65),
+(12, 0, 1, 50),
+(13, 0, 1, 45),
+(14, 0, 1, 35),
+(15, 0, 1, 40),
+(16, 0, 1, 50),
+(17, 0, 0, 55),
+(18, 0, 0, 45),
+(19, 0, 0, 50),
+(20, 0, 0, 60);
+
      2. +
    2. Run logistic regression to get the model, compute the marginal effects of all variables, and view the results. 
      +DROP TABLE IF EXISTS model_table;
+DROP TABLE IF EXISTS model_table_summary;
+DROP TABLE IF EXISTS margins_table;
+SELECT madlib.logregr_train( 'patients',
+                             'model_table',
+                             'second_attack',
+                             'ARRAY[1, treatment, trait_anxiety, treatment * trait_anxiety]'
+                           );
+SELECT madlib.margins( 'model_table',
+                       'margins_table',
+                       'intercept, treatment, trait_anxiety, treatment*trait_anxiety',
+                       NULL,
+                       NULL
+                     );
+\x ON
+SELECT * FROM margins_table;
+
      Result: 
      +variables | {intercept, treatment, trait_anxiety}
+margins   | {-0.876046514609573,-0.0648833521465306,0.0177196513589633}
+std_err   | {0.551714275062467,0.373592457067442,0.00458001207971933}
+z_stats   | {-1.58786269307674,-0.173674149247659,3.86890930646828}
+p_values  | {0.112317391159946,0.862121554662231,0.000109323294026272}
+
      3. +
    3. Compute the marginal effects of the first variable using the previous model and view the results (using different names in 'x_design'). 
      +DROP TABLE IF EXISTS result_table;
+SELECT madlib.margins( 'model_table',
+                       'result_table',
+                       'i, tre, tra, tre*tra',
+                       NULL,
+                       'tre'
+                     );
+SELECT * FROM result_table;
+
      Result: 
      +-[ RECORD 1 ]-------------------
+variables | {tre}
+margins   | {-0.110453283517281}
+std_err   | {0.228981529064089}
+z_stats   | {-0.482367656329023}
+p_values  | {0.629544793219806}
+
      4. +
    4. Create a sample data set for multinomial logistic regression. (The full dataset has three categories.) Use the dataset from the Multinomial Regression example. 
      +\x OFF
+DROP TABLE IF EXISTS test3;
+CREATE TABLE test3 (
+    feat1 INTEGER,
+    feat2 INTEGER,
+    cat INTEGER
+);
+INSERT INTO test3(feat1, feat2, cat) VALUES
+(1,35,1),
+(2,33,0),
+(3,39,1),
+(1,37,1),
+(2,31,1),
+(3,36,0),
+(2,36,1),
+(2,31,1),
+(2,41,1),
+(2,37,1),
+(1,44,1),
+(3,33,2),
+(1,31,1),
+(2,44,1),
+(1,35,1),
+(1,44,0),
+(1,46,0),
+(2,46,1),
+(2,46,2),
+(3,49,1),
+(2,39,0),
+(2,44,1),
+(1,47,1),
+(1,44,1),
+(1,37,2),
+(3,38,2),
+(1,49,0),
+(2,44,0),
+(3,61,2),
+(1,65,2),
+(3,67,1),
+(3,65,2),
+(1,65,2),
+(2,67,2),
+(1,65,2),
+(1,62,2),
+(3,52,2),
+(3,63,2),
+(2,59,2),
+(3,65,2),
+(2,59,0),
+(3,67,2),
+(3,67,2),
+(3,60,2),
+(3,67,2),
+(3,62,2),
+(2,54,2),
+(3,65,2),
+(3,62,2),
+(2,59,2),
+(3,60,2),
+(3,63,2),
+(3,65,2),
+(2,63,1),
+(2,67,2),
+(2,65,2),
+(2,62,2);
+
      5. +
    5. Run the regression function and then compute the marginal effects of all variables in the regression. 
      +DROP TABLE IF EXISTS model_table;
+DROP TABLE IF EXISTS model_table_summary;
+DROP TABLE IF EXISTS result_table;
+SELECT madlib.mlogregr_train('test3', 'model_table', 'cat',
+                             'ARRAY[1, feat1, feat2, feat1*feat2]',
+                             0);
+SELECT madlib.margins('model_table',
+                      'result_table',
+                      'intercept, feat1, feat2, feat1*feat2');
+\x ON
+SELECT * FROM result_table;
+
      Result: 
      +-[ RECORD 1 ]+-------------------------------------------------------------
+category     | 1
+ref_category | 0
+variables    | {intercept,feat1,feat2}
+margins      | {2.38176571752675,-0.0545733108729351,-0.0147264917310351}
+std_err      | {0.851299967007829,0.0697049196489632,0.00374946341567828}
+z_stats      | {2.79779843748643,-0.782919070099622,-3.92762646235104}
+p_values     | {0.00514522099923651,0.43367463815468,8.57883141882439e-05}
+-[ RECORD 2 ]+-------------------------------------------------------------
+category     | 2
+ref_category | 0
+variables    | {intercept,feat1,feat2}
+margins      | {-1.99279068434949,0.0922540608068343,0.0168049205501686}
+std_err      | {0.742790306495022,0.0690712705200096,0.00202015384479213}
+z_stats      | {-2.68284422524683,1.33563578767686,8.31863404536785}
+p_values     | {0.00729989838349161,0.181668346802398,8.89828265128986e-17}
+
      6. +
    +

    Note
    The marginal_vars argument is a list with the names matching those in 'x_design'. If no 'x_design' is present (i.e. no interaction and no indicator variables), then marginal_vars must be the indices (base 1) of variables in 'independent_varname'. Use NULL to use all independent variables. It is important to note that the independent_varname array in the underlying regression is assumed to start with a lower bound index of 1. Arrays that don't follow this would result in an incorrect solution.
    +

    Technical Background
    +

    The standard approach to modeling dichotomous/binary variables (so \(y \in \{0, 1\} \)) is to estimate a generalized linear model under the assumption that \( y \) follows some form of Bernoulli distribution. Thus the expected value of \( y \) becomes,

    +\[ y = G(X' \beta), \] +

    +

    where G is the specified binomial distribution. For logistic regression, the function \( G \) represents the inverse logit function.

    +

    In logistic regression:

    +\[ P = \frac{1}{1 + e^{-(\beta_0 + \beta_1 x_1 + \dots \beta_j x_j)}} = \frac{1}{1 + e^{-z}} \implies \frac{\partial P}{\partial X_k} = \beta_k \cdot \frac{1}{1 + e^{-z}} \cdot \frac{e^{-z}}{1 + e^{-z}} \\ = \beta_k \cdot P \cdot (1-P) \] +

    +

    There are several methods for calculating the marginal effects for dichotomous dependent variables. This package uses the average of the marginal effects at every sample observation.

    +

    This is calculated as follows:

    +\[ \frac{\partial y}{\partial x_k} = \beta_k \frac{\sum_{i=1}^n P(y_i = 1)(1-P(y_i = 1))}{n}, \\ \text{where}, P(y_i=1) = g(X^{(i)}\beta) \] +

    +

    We use the delta method for calculating standard errors on the marginal effects.

    +

    Literature
    +

    [1] Marginal effects in Stata: https://www.stata.com/

    +

    Related Topics
    +

    File marginal.sql_in documenting the SQL functions.

    +
    +
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    User Documentation for Apache MADlib
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    Matrix Operations
    Data Types and Transformations » Arrays and Matrices
    +
    +
    +
    Contents +

    This module provides a set of basic matrix operations for matrices that are too big to fit in memory. We provide two storage formats for a matrix:

    +
      +
    • Dense: The matrix is represented as a distributed collection of 1-D arrays. An example 3x10 matrix would be the table below: 
      + row_id |         row_vec
+--------+-------------------------
+   1    | {9,6,5,8,5,6,6,3,10,8}
+   2    | {8,2,2,6,6,10,2,1,9,9}
+   3    | {3,9,9,9,8,6,3,9,5,6}
+
      • +
    +

    A 'row' column (called row_id above) provides the row number of each row and a 'val' column (called row_vec above) provides each row as an array. The row column should contain a series of integers from 1 to N with no duplicates, where N is the row dimensionality.

    +
      +
    • Sparse: The matrix is represented using the row and column indices for each non-zero entry of the matrix. This representation is useful for sparse matrices, containing multiple zero elements. Given below is an example of a sparse 4x7 matrix with just 6 out of 28 entries being non-zero. The dimensionality of the matrix is inferred using the max value in row and col columns. Note the last entry is included (even though it is 0) to provide the dimensionality of the matrix, indicating that the 4th row and 7th column contain all zeros. 
      + row_id | col_id | value
+--------+--------+-------
+      1 |      1 |     9
+      1 |      5 |     6
+      1 |      6 |     6
+      2 |      1 |     8
+      3 |      1 |     3
+      3 |      2 |     9
+      4 |      7 |     0
+(6 rows)
+
      • +
    +

    For sparse matrices, the row and col columns together should not contain a duplicate entry and the val column should be of scalar (non-array) data type.
    + For comparison, the dense representation of this matrix is shown below. Note the dimensionality of the dense matrix is 4 x 7 since the max value of row and col is 4 and 7 respectively, leading to all zeros in the last row and last column.   

    + row_id |         row_vec
+--------+-------------------------
+   1    | {9,0,0,0,6,6,0}
+   2    | {8,0,0,0,0,0,0}
+   3    | {3,9,0,0,0,0,0}
+   4    | {0,0,0,0,0,0,0}
+
    Note
    The functions below support several numeric types (unless otherwise noted) including SMALLINT, INTEGER, BIGINT, DOUBLE PRECISION (FLOAT8), NUMERIC (internally casted into FLOAT8, so loss of precision can happen).
    +

    Matrix Operations
    +

    Below are the supported matrix operations. The meaning of the arguments and other terms are common to all functions and are provided at the end of the list in the glossary of arguments.

    +
      +
    • Representation 
      +-- Convert to sparse representation
+  matrix_sparsify( matrix_in, in_args, matrix_out, out_args)
+ 
+-- Convert to dense representation
+  matrix_densify( matrix_in, in_args, matrix_out, out_args)
+ 
+-- Get dimensions of matrix
+  matrix_ndims( matrix_in, in_args )
+
      • +
    • Mathematical operations 
      +-- Matrix transposition
+  matrix_trans( matrix_in, in_args, matrix_out, out_args)
+ 
+-- Matrix addition
+  matrix_add( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args)
+ 
+-- Matrix subtraction
+  matrix_sub( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args)
+ 
+-- Matrix multiplication
+  matrix_mult( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args)
+ 
+-- Element-wise matrix multiplication
+  matrix_elem_mult( matrix_a, a_args, matrix_b, b_args, matrix_out, out_args)
+ 
+-- Multiply matrix with scalar
+  matrix_scalar_mult( matrix_in, in_args, scalar, matrix_out, out_args)
+ 
+-- Multiply matrix with vector
+  matrix_vec_mult( matrix_in, in_args, vector)
+
      • +
    • Extraction/visitor methods 
      +-- Extract row from matrix given row index
+  matrix_extract_row( matrix_in, in_args, index)
+ 
+-- Extract column from matrix given column index
+  matrix_extract_col( matrix_in, in_args, index)
+ 
+-- Extract main (principal) diagonal elements
+  matrix_extract_diag( matrix_in, in_args)
+
      • +
    • Reduction operations (aggregate across specific dimension) 
      +-- Get max value along dim. Returns corresponding index if fetch_index = True
+  matrix_max( matrix_in, in_args, dim, matrix_out, fetch_index)
+ 
+-- Get min value along dim. Returns corresponding index if fetch_index = True
+  matrix_min( matrix_in, in_args, dim, matrix_out, fetch_index)
+ 
+-- Get sum value along dimension
+  matrix_sum( matrix_in, in_args, dim)
+ 
+-- Get mean value along dimension
+  matrix_mean( matrix_in, in_args, dim)
+ 
+-- Get matrix norm
+  matrix_norm( matrix_in, in_args, norm_type)
+
      • +
    • Creation methods 
      +-- Create a matrix initialized with ones of given row and column dimension
+  matrix_ones( row_dim, col_dim, matrix_out, out_args)
+ 
+-- Create a matrix initialized with zeros of given row and column dimension
+  matrix_zeros( row_dim, col_dim, matrix_out, out_args)
+ 
+-- Create an square identity matrix of size dim x dim
+  matrix_identity( dim, matrix_out, out_args)
+ 
+-- Create a diag matrix initialized with given diagonal elements
+  matrix_diag( diag_elements, matrix_out, out_args)
+-- Create a matrix initialized with values sampled from a distribution
+-- Supported distributions: normal, uniform, bernoulli
+  matrix_random( distribution, row_dim, col_dim, in_args, matrix_out, out_args )
+
      • +
    • Decomposition operations
      Note
      Please note that the decomposition operations below are only implemented for in-memory operations. The matrix data is collected on a single node and the decomposition is computed. This makes the operations applicable to smaller matrices since the calculation is not distributed across multiple nodes.
      +
      +-- Matrix inverse
+  matrix_inverse( matrix_in, in_args, matrix_out, out_args)
+ 
+-- Matrix generic inverse
+  matrix_pinv( matrix_in, in_args, matrix_out, out_args)
+ 
+-- Matrix eigenvalue extraction
+  matrix_eigen( matrix_in, in_args, matrix_out, out_args)
+ 
+-- Matrix Cholesky decomposition
+  matrix_cholesky( matrix_in, in_args, matrix_out_prefix, out_args)
+ 
+-- Matrix QR decomposition
+  matrix_qr( matrix_in, in_args, matrix_out_prefix, out_args)
+ 
+-- Matrix LU decomposition
+  matrix_lu( matrix_in, in_args, matrix_out_prefix, out_args)
+ 
+-- Matrix nuclear norm computing
+  matrix_nuclear_norm( matrix_in, in_args)
+ 
+-- Matrix rank computing
+  matrix_rank( matrix_in, in_args)
+
      • +
    +

    Arguments

    +

    The table below provides a glossary of the arguments used in the matrix operations.

    +
    +
    matrix_in, matrix_a, matrix_b
    +

    TEXT. Name of the table containing the input matrix.

      +
    • For functions accepting one matrix, matrix_in denotes the input matrix.
      • +
    • For functions accepting two matrices, matrix_a denotes the first matrix and matrix_b denotes the second matrix. These two matrices can independently be in either dense or sparse format.
      • +
    +

    +
    +
    in_args, a_args, b_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". This argument is used as a container for multiple parameters related to a single matrix.

    +

    The following parameters are supported for this string argument:

    + + + + + + + + +
    row (Default: 'row_num') Name of the column containing row index of the matrix.
    col (Default: 'col_num') Name of the column containing column index of the matrix.
    val (Default: 'val') Name of the column containing the entries of the matrix.
    trans (Default: False) Boolean flag to indicate if the matrix should be transposed before the operation. This is currently functional only for matrix_mult.
    +

    For example, the string argument with default values will be 'row=row_num, col=col_num, val=val, trans=False'. Alternatively, the string argument can be set to NULL or be blank ('') if default values are to be used.

    +

    +
    +
    matrix_out
    +

    TEXT. Name of the table to store the result matrix.

    +

    For Cholesky, QR and LU decompositions, a prefix (matrix_out_prefix) is used as a basis to build the names of the various output tables.

    +

    For Cholesky decomposition ( \( PA = LDL* \)), the following suffixes are added to matrix_out_prefix:

      +
    • _p for row permutation matrix P
      • +
    • _l for lower triangular factor L
      • +
    • _d for diagonal matrix D
      • +
    +

    For QR decomposition ( \( A = QR \)) the following suffixes are added to matrix_out_prefix:

      +
    • _q for orthogonal matrix Q
      • +
    • _r for upper triangular factor R
      • +
    +

    For LU decomposition with full pivoting ( \( PAQ = LU \)), the following suffixes are added to matrix_out_prefix:

      +
    • _p for row permutation matrix P
      • +
    • _q for column permutation matrix Q
      • +
    • _l for lower triangular factor L
      • +
    • _u for upper triangular factor U
      • +
    +

    +
    +
    out_args
    +

    TEXT. A comma-delimited string containing named arguments of the form "name=value". This is an optional parameter and the default value is set as follows:

      +
    • For functions with one input matrix, default out_args will the be same as specified in in_args.
      • +
    • For functions with two input matrices, default out_args will be the same as specified in a_args.
      • +
    +

    The following parameters are supported for this string argument:

    + + + + + + + + +
    row Name of the column containing row index of the matrix.
    col Name of the column containing column index of the matrix.
    val Name of the column containing the entries of the matrix.
    fmt Format of the output matrix. It could be either 'dense' or 'sparse'. When 'fmt' is not provided, the output fmt is inferred from the input matrices.
    +
    Note
    One exception is for matrix_eigen: the default output column name is ’eigen_values’ in the format (real, imaginary).
    +
    +
    index
    +

    INTEGER. An integer representing a row or column index of the matrix. Should be a number from 1 to N, where N is the maximum size of the dimension.

    +

    +
    +
    dim
    +

    INTEGER. Should either be 1 or 2. This value indicates the dimension to operate along for the reduction/aggregation operations. The value of dim should be interpreted as the dimension to be flattened i.e. whose length reduces to 1 in the result.

    +

    For any reduction function applied on an N x M matrix:

    +
      +
    • if dim=1, operation is applied on successive elements in each column; return value is a single vector with M elements (i.e. matrix with 1 row and M columns).
      +
      • +
    • if dim=2, operation is applied on successive elements in each row; return value is a single vector with N elements (i.e. matrix with N rows and 1 column).
      • +
    +

    +
    +
    row_dim
    +

    INTEGER. Should be greater than 0. This value indicates the row dimension of result matrix.

    +

    +
    +
    col_dim
    +

    INTEGER. Should be greater than 0. This value indicates the column dimension of result matrix.

    +

    +
    +
    diag_elements
    +

    ARRAY OF FLOAT. Should not be empty. This value indicates the float array which is used to generate diag elements of result output matrix.

    +

    +
    +
    norm_type
    +

    TEXT. Optional parameter. Defaults to Frobenius norm. Other supported norms for this string argument:

    + + + + + + + + + + + +
    'one' or 'o' 1 norm
    float > 0 Element-wise norm
    'inf' or 'i' Infinite norm
    'max' or 'm' Max absolute value norm
    'fro' or 'f' Frobenius norm (default)
    +

    +
    +
    +

    Examples (Dense Format)
    +

    Here are some examples of matrix operations in dense format. Later on this page we will show examples of matrix operations in sparse format.

    +
      +
    1. First let’s create example data tables in dense format: 
      +CREATE TABLE "mat_A" (
+        row_id integer,
+        row_vec integer[]
+);
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (1, '{9,6,5,8,5,6,6,3,10,8}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (2, '{8,2,2,6,6,10,2,1,9,9}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (3, '{3,9,9,9,8,6,3,9,5,6}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (4, '{6,4,2,2,2,7,8,8,0,7}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (5, '{6,8,9,9,4,6,9,5,7,7}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (6, '{4,10,7,3,9,5,9,2,3,4}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (7, '{8,10,7,10,1,9,7,9,8,7}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (8, '{7,4,5,6,2,8,1,1,4,8}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (9, '{8,8,8,5,2,6,9,1,8,3}');
+INSERT INTO "mat_A" (row_id, row_vec) VALUES (10, '{4,6,3,2,6,4,1,2,3,8}');
+
+CREATE TABLE "mat_B" (
+    row_id integer,
+    vector integer[]
+);
+INSERT INTO "mat_B" (row_id, vector) VALUES (1, '{9,10,2,4,6,5,3,7,5,6}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (2, '{5,3,5,2,8,6,9,7,7,6}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (3, '{0,1,2,3,2,7,7,3,10,1}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (4, '{2,9,0,4,3,6,8,6,3,4}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (5, '{3,8,7,7,0,5,3,9,2,10}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (6, '{5,3,1,7,6,3,5,3,6,4}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (7, '{4,8,4,4,2,7,10,0,3,3}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (8, '{4,6,0,1,3,1,6,6,9,8}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (9, '{6,5,1,7,2,7,10,6,0,6}');
+INSERT INTO "mat_B" (row_id, vector) VALUES (10, '{1,4,4,4,8,5,2,8,5,5}');
+
      2. +
    2. Transpose a matrix 
      +SELECT madlib.matrix_trans('"mat_B"', 'row=row_id, val=vector',
+                           'mat_r');
+SELECT * FROM mat_r ORDER BY row_id;
+
      +-- Note that the result matrix has inherited 'vector' as the name of the value column by default
+ row_id |         vector
+--------+-------------------------
+      1 | {9,5,0,2,3,5,4,4,6,1}
+      2 | {10,3,1,9,8,3,8,6,5,4}
+      3 | {2,5,2,0,7,1,4,0,1,4}
+      4 | {4,2,3,4,7,7,4,1,7,4}
+      5 | {6,8,2,3,0,6,2,3,2,8}
+      6 | {5,6,7,6,5,3,7,1,7,5}
+      7 | {3,9,7,8,3,5,10,6,10,2}
+      8 | {7,7,3,6,9,3,0,6,6,8}
+      9 | {5,7,10,3,2,6,3,9,0,5}
+      10 | {6,6,1,4,10,4,3,8,6,5}
+(10 rows)
+
      3. +
    3. Extract main diagonal of a matrix 
      +SELECT madlib.matrix_extract_diag('"mat_B"', 'row=row_id, val=vector');
+
      +-- Note the result is an array
+         matrix_extract_diag
+---------------------------------
+{9,3,2,4,0,3,10,6,0,5}
+(1 row)
+
      4. +
    4. Add two matrices 
      +SELECT madlib.matrix_add('"mat_A"', 'row=row_id, val=row_vec',
+                         '"mat_B"', 'row=row_id, val=vector',
+                         'mat_r', 'val=vector, fmt=dense');
+SELECT * FROM mat_r ORDER BY row_id;
+
      + row_id |            vector
+--------+-------------------------------
+      1 | {18,16,7,12,11,11,9,10,15,14}
+      2 | {13,5,7,8,14,16,11,8,16,15}
+      3 | {3,10,11,12,10,13,10,12,15,7}
+      4 | {8,13,2,6,5,13,16,14,3,11}
+      5 | {9,16,16,16,4,11,12,14,9,17}
+      6 | {9,13,8,10,15,8,14,5,9,8}
+      7 | {12,18,11,14,3,16,17,9,11,10}
+      8 | {11,10,5,7,5,9,7,7,13,16}
+      9 | {14,13,9,12,4,13,19,7,8,9}
+      10 | {5,10,7,6,14,9,3,10,8,13}
+(10 rows)
+
      5. +
    5. Multiply two matrices 
      +SELECT madlib.matrix_mult('"mat_A"', 'row=row_id, val=row_vec',
+                          '"mat_B"', 'row=row_id, val=vector, trans=true',
+                          'mat_r');
+SELECT * FROM mat_r ORDER BY row_id;
+
      + row_id |                  row_vec
+--------+-------------------------------------------
+     1  | {380,373,251,283,341,303,302,309,323,281}
+     2  | {318,318,222,221,269,259,236,249,264,248}
+     3  | {382,366,216,300,397,276,277,270,313,338}
+     4  | {275,284,154,244,279,183,226,215,295,204}
+     5  | {381,392,258,319,394,298,342,302,360,300}
+     6  | {321,333,189,276,278,232,300,236,281,250}
+     7  | {443,411,282,365,456,318,360,338,406,330}
+     8  | {267,240,150,186,270,194,210,184,233,193}
+     9  | {322,328,234,264,291,245,317,253,291,219}
+     10 | {246,221,109,173,222,164,167,185,181,189}
+(10 rows)
+
      6. +
    6. Create a diagonal matrix 
      +SELECT madlib.matrix_diag(array[9,6,3,10],
+                          'mat_r', 'row=row_id, col=col_id, val=val');
+SELECT * FROM mat_r ORDER BY row_id::bigint;
+
      + row_id | col_id  |  val
+--------+---------+--------
+      1 |       1 |      9
+      2 |       2 |      6
+      3 |       3 |      3
+      4 |       4 |     10
+(11 rows)
+
      7. +
    7. Create an identity matrix 
      +SELECT madlib.matrix_identity(4, 'mat_r', 'row=row_id,col=col_id,val=val');
+SELECT * FROM mat_r ORDER BY row_id;
+
      + row_id | col_id  |  val
+--------+---------+--------
+      1 |       1 |      1
+      2 |       2 |      1
+      3 |       3 |      1
+      4 |       4 |      1
+(5 rows)
+
      8. +
    8. Extract row and column from a matrix by specifying index 
      +SELECT madlib.matrix_extract_row('"mat_A"', 'row=row_id, val=row_vec', 2) as row,
+       madlib.matrix_extract_col('"mat_A"', 'row=row_id, val=row_vec', 3) as col;
+
      +          row           |          col
+------------------------+-----------------------
+ {8,2,2,6,6,10,2,1,9,9} | {5,2,9,2,9,7,7,5,8,3}
+(1 rows)
+
      9. +
    9. Get min and max values along a specific dimension, as well as the corresponding indices. Note that in this example dim=2 implies that the min and max is computed on each row, returning a column vector i.e. the column (dim=2) is flattened. 
      +SELECT madlib.matrix_max('"mat_A"', 'row=row_id, val=row_vec', 2, 'mat_max_r', true),
+       madlib.matrix_min('"mat_A"', 'row=row_id, val=row_vec', 2, 'mat_min_r', true);
+SELECT * from mat_max_r;
+SELECT * from mat_min_r;
+
      +         index         |            max
+-----------------------+---------------------------
+ {9,6,2,7,3,2,2,6,7,10} | {10,10,9,8,9,10,10,8,9,8}
+(1 rows)
+ 
+         index         |          min
+-----------------------+-----------------------
+ {8,8,1,9,5,8,5,7,8,7} | {3,1,3,0,4,2,1,1,1,1}
+(1 rows)
+
      10. +
    10. Initialize matrix with zeros in sparse format 
      +SELECT madlib.matrix_zeros(5, 4, 'mat_r', 'row=row_id, col=col_id, val=entry');
+SELECT * FROM mat_r;
+
      + row_id |  col_id | entry
+--------+---------+--------
+      5 |       4 |    0
+(1 rows)
+
      11. +
    11. Initialize matrix with zeros in dense format 
      +SELECT madlib.matrix_zeros(5, 4, 'mat_r', 'fmt=dense');
+SELECT * FROM mat_r ORDER BY row;
+
      +  row |    val
+-----+-----------
+   1 | {0,0,0,0}
+   2 | {0,0,0,0}
+   3 | {0,0,0,0}
+   4 | {0,0,0,0}
+   5 | {0,0,0,0}
+(5 rows)
+
      12. +
    12. Initialize matrix with ones 
      +SELECT madlib.matrix_ones(5, 4, 'mat_r', 'row=row,col=col, val=val');
+SELECT * FROM mat_r;
+
      + row | col | val
+-----+-----+-----
+   1 |   1 |   1
+   1 |   2 |   1
+   1 |   3 |   1
+   1 |   4 |   1
+   2 |   1 |   1
+   2 |   2 |   1
+   2 |   3 |   1
+   2 |   4 |   1
+   3 |   1 |   1
+   3 |   2 |   1
+   3 |   3 |   1
+   3 |   4 |   1
+   4 |   1 |   1
+   4 |   2 |   1
+   4 |   3 |   1
+   4 |   4 |   1
+   5 |   1 |   1
+   5 |   2 |   1
+   5 |   3 |   1
+   5 |   4 |   1
+(20 rows)
+
      13. +
    13. Initialize matrix with ones in dense format 
      +SELECT madlib.matrix_ones(5, 4, 'mat_r', 'fmt=dense');
+SELECT * FROM mat_r ORDER BY row;
+
      +  row |    val
+-----+-----------
+   1 | {1,1,1,1}
+   2 | {1,1,1,1}
+   3 | {1,1,1,1}
+   4 | {1,1,1,1}
+   5 | {1,1,1,1}
+(5 rows)
+
      14. +
    14. Element-wise multiplication between two matrices 
      +SELECT madlib.matrix_elem_mult('"mat_A"', 'row=row_id, val=row_vec',
+                               '"mat_B"', 'row=row_id, val=vector',
+                               'mat_r', 'val=vector');
+SELECT * FROM mat_r ORDER BY row_id;
+
      + row_id |             vector
+--------+---------------------------------
+     1  | {81,60,10,32,30,30,18,21,50,48}
+     2  | {40,6,10,12,48,60,18,7,63,54}
+     3  | {0,9,18,27,16,42,21,27,50,6}
+     4  | {12,36,0,8,6,42,64,48,0,28}
+     5  | {18,64,63,63,0,30,27,45,14,70}
+     6  | {20,30,7,21,54,15,45,6,18,16}
+     7  | {32,80,28,40,2,63,70,0,24,21}
+     8  | {28,24,0,6,6,8,6,6,36,64}
+     9  | {48,40,8,35,4,42,90,6,0,18}
+     10 | {4,24,12,8,48,20,2,16,15,40}
+
      15. +
    15. Get sum values along a dimension. In this example, the sum is computed for each row (i.e. column is flattened since dim=2). 
      +SELECT madlib.matrix_sum('"mat_A"', 'row=row_id, val=row_vec', 2);
+
      +           matrix_sum
+---------------------------------
+ {66,55,67,46,70,56,76,46,58,39}
+(1 rows)
+
      16. +
    16. Get mean values along dimension 
      +SELECT madlib.matrix_mean('"mat_A"', 'row=row_id, val=row_vec', 2);
+
      +               matrix_mean
+-----------------------------------------
+ {6.6,5.5,6.7,4.6,7,5.6,7.6,4.6,5.8,3.9}
+(1 rows)
+
      17. +
    17. Compute matrix norm. In this example, we ask for the Euclidean norm: 
      +SELECT madlib.matrix_norm('"mat_A"', 'row=row_id, val=row_vec', '2');
+
      +  matrix_norm
+---------------
+ 64.1014820421
+(1 row)
+
      18. +
    18. Multiply matrix with scalar 
      +SELECT madlib.matrix_scalar_mult('"mat_A"', 'row=row_id, val=row_vec', 3, 'mat_r');
+SELECT * FROM mat_r ORDER BY row_id;
+
      + row_id |             row_vec
+--------+---------------------------------
+      1 | {27,18,15,24,15,18,18,9,30,24}
+      2 | {24,6,6,18,18,30,6,3,27,27}
+      3 | {9,27,27,27,24,18,9,27,15,18}
+      4 | {18,12,6,6,6,21,24,24,0,21}
+      5 | {18,24,27,27,12,18,27,15,21,21}
+      6 | {12,30,21,9,27,15,27,6,9,12}
+      7 | {24,30,21,30,3,27,21,27,24,21}
+      8 | {21,12,15,18,6,24,3,3,12,24}
+      9 | {24,24,24,15,6,18,27,3,24,9}
+     10 | {12,18,9,6,18,12,3,6,9,24}
+(10 rows)
+
      19. +
    19. Get the row dimension and column dimension of matrix 
      +SELECT madlib.matrix_ndims('"mat_A"', 'row=row_id, val=row_vec');
+
      + matrix_ndims
+--------------
+ {10,10}
+(1 row)
+
      20. +
    20. Multiply matrix with vector 
      +SELECT madlib.matrix_vec_mult('"mat_A"', 'row=row_id, val=row_vec',
+                              array[1,2,3,4,5,6,7,8,9,10]);
+
      +              matrix_vec_mult
+-------------------------------------------
+ {365,325,358,270,377,278,411,243,287,217}
+(10 rows)
+
      21. +
    21. Inverse of matrix 
      +SELECT madlib.matrix_inverse('"mat_A"', 'row=row_id, val=row_vec', 'mat_r');
+SELECT row_vec FROM mat_r ORDER BY row_id;
+
      22. +
    22. Generic inverse of matrix 
      +SELECT madlib.matrix_pinv('"mat_A"', 'row=row_id, val=row_vec', 'mat_r');
+SELECT row_vec FROM mat_r ORDER BY row_id;
+
      23. +
    23. Eigenvalues of matrix (note default column name of eigenvalues) 
      +SELECT madlib.matrix_eigen('"mat_A"', 'row=row_id, val=row_vec', 'mat_r');
+SELECT eigen_values FROM mat_r ORDER BY row_id;
+
      24. +
    24. Cholesky decomposition of matrix 
      +SELECT madlib.matrix_cholesky('"mat_A"', 'row=row_id, val=row_vec', 'matrix_out_prefix');
+SELECT row_vec FROM matrix_out_prefix_p ORDER BY row_id;
+SELECT row_vec FROM matrix_out_prefix_l ORDER BY row_id;
+SELECT row_vec FROM matrix_out_prefix_d ORDER BY row_id;
+
      25. +
    25. QR decomposition of matrix 
      +SELECT madlib.matrix_qr('"mat_A"', 'row=row_id, val=row_vec', 'matrix_out_prefix');
+SELECT row_vec FROM matrix_out_prefix_q ORDER BY row_id;
+SELECT row_vec FROM matrix_out_prefix_r ORDER BY row_id;
+
      26. +
    26. LU decomposition of matrix 
      +SELECT madlib.matrix_lu('"mat_A"', 'row=row_id, val=row_vec', 'matrix_out_prefix');
+SELECT row_vec FROM matrix_out_prefix_l ORDER BY row_id;
+SELECT row_vec FROM matrix_out_prefix_u ORDER BY row_id;
+SELECT row_vec FROM matrix_out_prefix_p ORDER BY row_id;
+SELECT row_vec FROM matrix_out_prefix_q ORDER BY row_id;
+
      27. +
    27. Nuclear norm of matrix 
      +SELECT madlib.matrix_nuclear_norm('"mat_A"', 'row=row_id, val=row_vec');
+
      + matrix_nuclear_norm
+---------------------
+       118.852685995
+(1 row)
+
      28. +
    28. Rank of matrix 
      +SELECT madlib.matrix_rank('"mat_A"', 'row=row_id, val=row_vec');
+
      + matrix_rank
+-------------
+          10
+(1 row)
+
      29. +
    +
    Examples (Sparse Format)
    +

    Below are some examples of matrix operations in sparse format.

    +
      +
    1. Convert a matrix from dense to sparse format 
      +SELECT madlib.matrix_sparsify('"mat_B"', 'row=row_id, val=vector',
+                              '"mat_B_sparse"', 'col=col_id, val=val');
+SELECT * FROM "mat_B_sparse" ORDER BY row_id, col_id;
+
      2. +
    2. Create a matrix in sparse format. 
      +CREATE TABLE "mat_A_sparse" (
+    "rowNum" integer,
+    col_num integer,
+    entry integer
+);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 1, 9);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 2, 6);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 7, 3);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 8, 10);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (1, 9, 8);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (2, 1, 8);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (2, 2, 2);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (2, 3, 6);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (3, 5, 6);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (3, 6, 3);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (7, 1, 7);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (8, 2, 8);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (8, 3, 5);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (9, 1, 6);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (9, 2, 3);
+INSERT INTO "mat_A_sparse" ("rowNum", col_num, entry) VALUES (10, 10, 0);
+
      3. +
    3. Get the row_dims and col_dims of a matrix in sparse format 
      +SELECT madlib.matrix_ndims('"mat_A_sparse"', 'row="rowNum", val=entry')
+
      + matrix_ndims
+--------------
+ {10,10}
+(1 row)
+
      4. +
    4. Transpose a matrix in sparse format 
      +-- Note the double quotes for "rowNum" are required as per PostgreSQL rules since “N” is capitalized
+SELECT madlib.matrix_trans('"mat_A_sparse"', 'row="rowNum", val=entry',
+                           'matrix_r_sparse');
+SELECT "rowNum", col_num, entry FROM matrix_r_sparse ORDER BY col_num;
+
      + rowNum | col_num | entry
+--------+---------+-------
+      1 |       1 |     9
+      2 |       1 |     6
+      7 |       1 |     3
+      8 |       1 |    10
+      9 |       1 |     8
+      1 |       2 |     8
+      2 |       2 |     2
+      3 |       2 |     6
+      5 |       3 |     6
+      6 |       3 |     3
+      1 |       7 |     7
+      2 |       8 |     8
+      3 |       8 |     5
+      1 |       9 |     6
+      2 |       9 |     3
+     10 |      10 |     0
+(16 rows)
+
      5. +
    5. Main diagonal of a matrix in sparse format 
      +SELECT madlib.matrix_extract_diag('"mat_A_sparse"', 'row="rowNum", val=entry');
+
      + matrix_extract_diag
+-----------------
+{9,2,0,0,0,0,0,0,0,0}
+(1 row)
+
      6. +
    6. Add two sparse matrices then convert to dense format 
      +SELECT madlib.matrix_add('"mat_A_sparse"', 'row="rowNum", val=entry',
+                         '"mat_B_sparse"', 'row=row_id, col=col_id, val=val',
+                         'matrix_r_sparse', 'col=col_out');
+SELECT madlib.matrix_densify('matrix_r_sparse', 'row="rowNum", col=col_out, val=entry',
+                             'matrix_r');
+SELECT * FROM matrix_r ORDER BY "rowNum";
+
      + rowNum |           entry
+--------+---------------------------
+      1 | {18,16,2,4,6,5,6,17,13,6}
+      2 | {13,5,11,2,8,6,9,7,7,6}
+      3 | {0,1,2,3,8,10,7,3,10,1}
+      4 | {2,9,0,4,3,6,8,6,3,4}
+      5 | {3,8,7,7,0,5,3,9,2,10}
+      6 | {5,3,1,7,6,3,5,3,6,4}
+      7 | {11,8,4,4,2,7,10,0,3,3}
+      8 | {4,14,5,1,3,1,6,6,9,8}
+      9 | {12,8,1,7,2,7,10,6,0,6}
+     10 | {1,4,4,4,8,5,2,8,5,5}
+(10 rows)
+
      7. +
    7. Multiply two sparse matrices 
      +SELECT madlib.matrix_mult('"mat_A_sparse"', 'row="rowNum", col=col_num, val=entry',
+                          '"mat_B_sparse"', 'row=row_id, col=col_id, val=val, trans=true',
+                          'matrix_r');
+SELECT * FROM matrix_r ORDER BY "rowNum";
+
      + rowNum |                   entry
+--------+-------------------------------------------
+      1 | {260,216,137,180,190,156,138,222,174,159}
+      2 | {104,76,14,34,82,52,72,44,64,40}
+      3 | {51,66,33,36,15,45,33,21,33,63}
+      4 | {0,0,0,0,0,0,0,0,0,0}
+      5 | {0,0,0,0,0,0,0,0,0,0}
+      6 | {0,0,0,0,0,0,0,0,0,0}
+      7 | {63,35,0,14,21,35,28,28,42,7}
+      8 | {90,49,18,72,99,29,84,48,45,52}
+      9 | {84,39,3,39,42,39,48,42,51,18}
+     10 | {0,0,0,0,0,0,0,0,0,0}
+(10 rows)
+
      8. +
    8. Initialize matrix with ones 
      +SELECT madlib.matrix_ones(5, 4, 'mat_r', 'row=row,col=col, val=val');
+SELECT * FROM mat_r ORDER BY row, col;
+
      + row | col | val
+-----+-----+-----
+   1 |   1 |   1
+   1 |   2 |   1
+   1 |   3 |   1
+   1 |   4 |   1
+   2 |   1 |   1
+   2 |   2 |   1
+   2 |   3 |   1
+   2 |   4 |   1
+   3 |   1 |   1
+   3 |   2 |   1
+   3 |   3 |   1
+   3 |   4 |   1
+   4 |   1 |   1
+   4 |   2 |   1
+   4 |   3 |   1
+   4 |   4 |   1
+   5 |   1 |   1
+   5 |   2 |   1
+   5 |   3 |   1
+   5 |   4 |   1
+(20 rows)
+
      9. +
    9. Initialize matrix with zeros in sparse format 
      +SELECT madlib.matrix_zeros(5, 4, 'mat_r', 'row=row_id, col=col_id, val=entry');
+SELECT * FROM mat_r;
+
      + row_id |  col_id | entry
+--------+---------+--------
+      5 |       4 |    0
+(1 rows)
+
      10. +
    10. Compute matrix norm on sparse matrix. In this example, we ask for the Euclidean norm: 
      +SELECT madlib.matrix_norm('"mat_A_sparse"', 'row="rowNum", col=col_num, val=entry', '2');
+
      +  matrix_norm
+---------------
+ 24.9399278267
+(1 row)
+
      11. +
    +

    Related Topics
    +

    File array_ops.sql_in documents the array operations Array Operations

    +

    File matrix_ops.sql_in for list of functions and usage.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__matrix__factorization.html b/docs/docs/v2.1.0/group__grp__matrix__factorization.html new file mode 100644 index 00000000..5e86f577 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__matrix__factorization.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: Matrix Factorization + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
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    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Matrix Factorization
    Data Types and Transformations » Arrays and Matrices
    +
    +
    +

    Detailed Description

    +

    Linear algebra methods that factorize a matrix into a product of matrices.

    + + + + + + + + +

    +Modules

     Low-Rank Matrix Factorization
     Performs low-rank matrix factorization for an incomplete matrix.
     
     Singular Value Decomposition
     Performs factorization of dense and sparse matrices.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__matrix__factorization.js b/docs/docs/v2.1.0/group__grp__matrix__factorization.js new file mode 100644 index 00000000..5d3e1c90 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__matrix__factorization.js @@ -0,0 +1,5 @@ +var group__grp__matrix__factorization = +[ + [ "Low-Rank Matrix Factorization", "group__grp__lmf.html", null ], + [ "Singular Value Decomposition", "group__grp__svd.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__mdl.html b/docs/docs/v2.1.0/group__grp__mdl.html new file mode 100644 index 00000000..602364d3 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__mdl.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: Model Selection + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Model Selection
    +
    +
    +

    Detailed Description

    +

    Functions for model selection and model evaluation.

    + + + + + + + + + + + +

    +Modules

     Cross Validation
     Estimates the fit of a predictive model given a data set and specifications for the training, prediction, and error estimation functions.
     
     Prediction Metrics
     Provides various prediction accuracy metrics.
     
     Train-Test Split
     A method for splitting a data set into separate training and testing sets.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__mdl.js b/docs/docs/v2.1.0/group__grp__mdl.js new file mode 100644 index 00000000..4dc5e5dd --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__mdl.js @@ -0,0 +1,6 @@ +var group__grp__mdl = +[ + [ "Cross Validation", "group__grp__validation.html", null ], + [ "Prediction Metrics", "group__grp__pred.html", null ], + [ "Train-Test Split", "group__grp__train__test__split.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__mfvsketch.html b/docs/docs/v2.1.0/group__grp__mfvsketch.html new file mode 100644 index 00000000..885562e7 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__mfvsketch.html @@ -0,0 +1,167 @@ + + + + + + + + +MADlib: MFV (Most Frequent Values) + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
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    +
    + +
    +
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    + +
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    + +
    + +
    +
    +
    MFV (Most Frequent Values)
    Statistics » Descriptive Statistics » Cardinality Estimators
    +
    +
    +
    Contents +

    MFVSketch: Most Frequent Values variant of CountMin sketch, implemented as a UDA.

    +

    Produces an n-bucket histogram for a column where each bucket counts one of the most frequent values in the column. The output is an array of doubles {value, count} in descending order of frequency; counts are approximated via CountMin sketches. Ties are handled arbitrarily.

    +

    The MFV frequent-value UDA comes in two different versions:

      +
    • a faithful implementation that preserves the approximation guarantees of Cormode/Muthukrishnan, 
      +mfvsketch_top_histogram( col_name,
+                         n )
+
      • +
    • and a "quick and dirty" version that can do parallel aggregation in Greenplum at the expense of missing some of the most frequent values. 
      +mfvsketch_quick_histogram( col_name,
+                           n )
+
      • +
    +

    In PostgreSQL the two UDAs are identical. In Greenplum, the quick version should produce good results unless the number of values requested is small, or the distribution is flat.

    +
    Note
    This is a User Defined Aggregate which returns the results when used in a query. Use "CREATE TABLE AS ", with the UDA as subquery if the results are to be stored. This is unlike the usual MADlib stored procedure interface which places the results in a table instead of returning it.
    +

    Examples
    +
      +
    1. Generate some data. 
      +CREATE TABLE data(class INT, a1 INT);
+INSERT INTO data SELECT 1,1 FROM generate_series(1,10000);
+INSERT INTO data SELECT 1,2 FROM generate_series(1,15000);
+INSERT INTO data SELECT 1,3 FROM generate_series(1,10000);
+INSERT INTO data SELECT 2,5 FROM generate_series(1,1000);
+INSERT INTO data SELECT 2,6 FROM generate_series(1,1000);
+
      2. +
    2. Produce a histogram of 5 bins and return the most frequent value and associated count in each bin. 
      +SELECT mfvsketch_top_histogram( a1, 5 )
+FROM data;
+
      Result: 
      +                mfvsketch_top_histogram
+ -------------------------------------------------------------
+[0:4][0:1]={{2,15000},{1,10000},{3,10000},{5,1000},{6,1000}}
+(1 row)
+
      3. +
    +

    Literature
    This method is not usually called an MFV sketch in the literature; it is a natural extension of the CountMin sketch.
    +

    Related Topics
    +

    File sketch.sql_in documenting the SQL functions.

    +

    Module CountMin (Cormode-Muthukrishnan).

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__minibatch__preprocessing.html b/docs/docs/v2.1.0/group__grp__minibatch__preprocessing.html new file mode 100644 index 00000000..a6ffcf51 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__minibatch__preprocessing.html @@ -0,0 +1,447 @@ + + + + + + + + +MADlib: Mini-Batch Preprocessor + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Mini-Batch Preprocessor
    Utilities
    +
    +
    +
    Contents +

    The mini-batch preprocessor is a utility that prepares input data for use by models that support mini-batch as an optimization option. (This is currently only the case for Neural Networks.) It is effectively a packing operation that builds arrays of dependent and independent variables from the source data table.

    +

    The advantage of using mini-batching is that it can perform better than stochastic gradient descent (default MADlib optimizer) because it uses more than one training example at a time, typically resulting in faster and smoother convergence [1].

    +
    Note
    This preprocessor should not be used for deep learning methods. Please refer to the section on Deep Learning for more information.
    +

    Mini-Batch Preprocessor
    The mini-batch preprocessor has the following format:
    +
    +minibatch_preprocessor( source_table,
+                        output_table,
+                        dependent_varname,
+                        independent_varname,
+                        grouping_col,
+                        buffer_size,
+                        one_hot_encode_int_dep_var
+                        )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing input data. Can also be a view.

    +

    +
    +
    output_table
    +

    TEXT. Name of the output table from the preprocessor which will be used as input to algorithms that support mini-batching. Note that the arrays packed into the output table are randomized and normalized, so they will not match up in an obvious way with the rows in the source table.

    +

    +
    +
    dependent_varname
    +

    TEXT. Name of the dependent variable column.

    +

    +
    +
    independent_varname
    +
    TEXT. Column name or expression list to evaluate for the independent variable. Please note that independent variables are cast to double precision by the preprocessor, so categorical variables should be one-hot or dummy encoded as appropriate. See Encoding Categorical Variables for more details on this.
    Note
    Supported expressions for independent variables include:
      +
    • ‘ARRAY[x1,x2,x3]’, where x1, x2, and x3 are columns in the source table containing scalar values.
      • +
    • Single column in the source table containing an array like ARRAY[1,2,3] or {1,2,3}.
      • +
    +
    +
    +The following forms are not currently supported:
      +
    • ‘x1,x2,x3’, where x1,x2,x3 are columns in source table with scalar values
      • +
    • ARRAY[x1,x2] where x1 is scalar and x2 is array
      • +
    • ARRAY[x1,x2] where both x1 and x2 are arrays
      • +
    • ARRAY[x1] where x1 is array
      • +
    +
    +
    +
    grouping_col (optional)
    +
    TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, which runs the preprocessing separately for each group. When this value is NULL, no grouping is used and a single preprocessor step is run for the whole data set.
    Note
    If you plan to use grouping in model training, then you must set up the groups in the preprocessor exactly as you want to use them in training.
    +
    +
    buffer_size (optional)
    +

    INTEGER, default: computed. Buffer size is the number of rows from the source table that are packed into one row of the preprocessor output table. The default value is computed considering size of the source table, number of independent variables, number of groups, and number of segments in the database cluster. For larger data sets, the computed buffer size will typically be a value in the millions.

    +

    +
    +
    one_hot_encode_int_dep_var (optional)
    +

    BOOLEAN. default: FALSE. Flag to one-hot encode dependent variables that are scalar integers. This parameter is ignored if the dependent variable is not a scalar integer.

    +
    Note
    The mini-batch preprocessor automatically encodes dependent variables that are boolean and character types such as text, char and varchar. However, scalar integers are a special case because they can be used in both classification and regression problems, so you must tell the mini-batch preprocessor whether you want to encode them or not. In the case that you have already encoded the dependent variable yourself, you can ignore this parameter. Also, if you want to encode float values for some reason, cast them to text first.
    +
    +
    +

    Output tables
    + The output table produced by the mini-batch preprocessor contains the following columns:

    + + + + + + + + +
    __id__ INTEGER. Unique id for packed table.
    dependent_varname FLOAT8[]. Packed array of dependent variables. If the dependent variable in the source table is categorical, the preprocessor will one-hot encode it.
    independent_varname FLOAT8[]. Packed array of independent variables.
    grouping_cols TEXT. Name of grouping columns.
    +

    A summary table named <output_table>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + + + + + +
    source_table Name of the source table.
    output_table Name of output table generated by preprocessor.
    dependent_varname Dependent variable from the source table.
    independent_varname Independent variable from the source table.
    buffer_size Buffer size used in preprocessing step.
    class_values Class values (i.e., levels) of the dependent variable if categorical. If the dependent variable is not categorical, this will be NULL./td>
    num_rows_processed The total number of rows that were used in the preprocessing operation.
    num_missing_rows_skipped The total number of rows that were skipped because of NULL values in either the dependent or independent variables.
    grouping_col Comma separated list of grouping column names if grouping is used. If no grouping, will be NULL.
    +

    A standardization table named <output_table>_standardization is also created. This is needed by the models that will use the preprocessed data so is likely not of much interest to users. It has the following columns:

    + + + + + + +
    grouping columns If 'grouping_col' is specified, a column for each grouping column is created.
    mean Mean of independent variables.
    std Population standard deviation of independent variables.
    +

    Examples
      +
    1. Create an input data set based on the well known iris data set: 
      +DROP TABLE IF EXISTS iris_data;
+CREATE TABLE iris_data(
+    id serial,
+    attributes numeric[],
+    class_text varchar,
+    class integer,
+    state varchar
+);
+INSERT INTO iris_data(id, attributes, class_text, class, state) VALUES
+(1,ARRAY[5.0,3.2,1.2,0.2],'Iris_setosa',1,'Alaska'),
+(2,ARRAY[5.5,3.5,1.3,0.2],'Iris_setosa',1,'Alaska'),
+(3,ARRAY[4.9,3.1,1.5,0.1],'Iris_setosa',1,'Alaska'),
+(4,ARRAY[4.4,3.0,1.3,0.2],'Iris_setosa',1,'Alaska'),
+(5,ARRAY[5.1,3.4,1.5,0.2],'Iris_setosa',1,'Alaska'),
+(6,ARRAY[5.0,3.5,1.3,0.3],'Iris_setosa',1,'Alaska'),
+(7,ARRAY[4.5,2.3,1.3,0.3],'Iris_setosa',1,'Alaska'),
+(8,ARRAY[4.4,3.2,1.3,0.2],'Iris_setosa',1,'Alaska'),
+(9,ARRAY[5.0,3.5,1.6,0.6],'Iris_setosa',1,'Alaska'),
+(10,ARRAY[5.1,3.8,1.9,0.4],'Iris_setosa',1,'Alaska'),
+(11,ARRAY[4.8,3.0,1.4,0.3],'Iris_setosa',1,'Alaska'),
+(12,ARRAY[5.1,3.8,1.6,0.2],'Iris_setosa',1,'Alaska'),
+(13,ARRAY[5.7,2.8,4.5,1.3],'Iris_versicolor',2,'Alaska'),
+(14,ARRAY[6.3,3.3,4.7,1.6],'Iris_versicolor',2,'Alaska'),
+(15,ARRAY[4.9,2.4,3.3,1.0],'Iris_versicolor',2,'Alaska'),
+(16,ARRAY[6.6,2.9,4.6,1.3],'Iris_versicolor',2,'Alaska'),
+(17,ARRAY[5.2,2.7,3.9,1.4],'Iris_versicolor',2,'Alaska'),
+(18,ARRAY[5.0,2.0,3.5,1.0],'Iris_versicolor',2,'Alaska'),
+(19,ARRAY[5.9,3.0,4.2,1.5],'Iris_versicolor',2,'Alaska'),
+(20,ARRAY[6.0,2.2,4.0,1.0],'Iris_versicolor',2,'Alaska'),
+(21,ARRAY[6.1,2.9,4.7,1.4],'Iris_versicolor',2,'Alaska'),
+(22,ARRAY[5.6,2.9,3.6,1.3],'Iris_versicolor',2,'Alaska'),
+(23,ARRAY[6.7,3.1,4.4,1.4],'Iris_versicolor',2,'Alaska'),
+(24,ARRAY[5.6,3.0,4.5,1.5],'Iris_versicolor',2,'Alaska'),
+(25,ARRAY[5.8,2.7,4.1,1.0],'Iris_versicolor',2,'Alaska'),
+(26,ARRAY[6.2,2.2,4.5,1.5],'Iris_versicolor',2,'Alaska'),
+(27,ARRAY[5.6,2.5,3.9,1.1],'Iris_versicolor',2,'Alaska'),
+(28,ARRAY[5.0,3.4,1.5,0.2],'Iris_setosa',1,'Tennessee'),
+(29,ARRAY[4.4,2.9,1.4,0.2],'Iris_setosa',1,'Tennessee'),
+(30,ARRAY[4.9,3.1,1.5,0.1],'Iris_setosa',1,'Tennessee'),
+(31,ARRAY[5.4,3.7,1.5,0.2],'Iris_setosa',1,'Tennessee'),
+(32,ARRAY[4.8,3.4,1.6,0.2],'Iris_setosa',1,'Tennessee'),
+(33,ARRAY[4.8,3.0,1.4,0.1],'Iris_setosa',1,'Tennessee'),
+(34,ARRAY[4.3,3.0,1.1,0.1],'Iris_setosa',1,'Tennessee'),
+(35,ARRAY[5.8,4.0,1.2,0.2],'Iris_setosa',1,'Tennessee'),
+(36,ARRAY[5.7,4.4,1.5,0.4],'Iris_setosa',1,'Tennessee'),
+(37,ARRAY[5.4,3.9,1.3,0.4],'Iris_setosa',1,'Tennessee'),
+(38,ARRAY[6.0,2.9,4.5,1.5],'Iris_versicolor',2,'Tennessee'),
+(39,ARRAY[5.7,2.6,3.5,1.0],'Iris_versicolor',2,'Tennessee'),
+(40,ARRAY[5.5,2.4,3.8,1.1],'Iris_versicolor',2,'Tennessee'),
+(41,ARRAY[5.5,2.4,3.7,1.0],'Iris_versicolor',2,'Tennessee'),
+(42,ARRAY[5.8,2.7,3.9,1.2],'Iris_versicolor',2,'Tennessee'),
+(43,ARRAY[6.0,2.7,5.1,1.6],'Iris_versicolor',2,'Tennessee'),
+(44,ARRAY[5.4,3.0,4.5,1.5],'Iris_versicolor',2,'Tennessee'),
+(45,ARRAY[6.0,3.4,4.5,1.6],'Iris_versicolor',2,'Tennessee'),
+(46,ARRAY[6.7,3.1,4.7,1.5],'Iris_versicolor',2,'Tennessee'),
+(47,ARRAY[6.3,2.3,4.4,1.3],'Iris_versicolor',2,'Tennessee'),
+(48,ARRAY[5.6,3.0,4.1,1.3],'Iris_versicolor',2,'Tennessee'),
+(49,ARRAY[5.5,2.5,4.0,1.3],'Iris_versicolor',2,'Tennessee'),
+(50,ARRAY[5.5,2.6,4.4,1.2],'Iris_versicolor',2,'Tennessee'),
+(51,ARRAY[6.1,3.0,4.6,1.4],'Iris_versicolor',2,'Tennessee'),
+(52,ARRAY[5.8,2.6,4.0,1.2],'Iris_versicolor',2,'Tennessee');
+
      2. +
    2. Run the preprocessor: 
      +DROP TABLE IF EXISTS iris_data_packed, iris_data_packed_summary, iris_data_packed_standardization;
+SELECT madlib.minibatch_preprocessor('iris_data',         -- Source table
+                                     'iris_data_packed',  -- Output table
+                                     'class_text',        -- Dependent variable
+                                     'attributes'         -- Independent variables
+                                     );
+
      For small datasets like in this example, buffer size is mainly determined by the number of segments in the database. This example is run on a Greenplum database with 2 segments, so there are 2 rows with a buffer size of 26. For PostgresSQL, there would be only one row with a buffer size of 52 since it is a single node database. For larger data sets, other factors go into computing buffers size besides number of segments. Also, note that the dependent variable has been one-hot encoded since it is categorical. Here is a sample of the packed output table: 
      +\x on
+SELECT * FROM iris_data_packed;
+
      +-[ RECORD 1 ]-------+-------------------------------------
+__id__              | 0
+dependent_varname   | {{1,0},{0,1},{1,0},{0,1},{1,0},{0,1},{0,1},{1,0},{1,0},{1,0},{1,0},{0,1},{0,1},{0,1},{1,0},{0,1},{0,1},{0,1},{1,0},{0,1},{1,0},{0,1},{1,0},{1,0},{1,0},{0,1}}
+independent_varname | {{-0.767560815504508,0.806649237861967,-1.07515071152907,-1.18456909732025},{-0.0995580974152422,0.00385956572525086,1.03989986852812,1.17758048907675},...
+...
+-[ RECORD 2 ]-------+-------------------------------------
+__id__              | 1
+dependent_varname   | {{1,0},{1,0},{1,0},{0,1},{0,1},{1,0},{0,1},{0,1},{0,1},{0,1},{0,1},{0,1},{0,1},{1,0},{0,1},{0,1},{0,1},{0,1},{0,1},{1,0},{0,1},{1,0},{0,1},{1,0},{1,0},{0,1}}
+independent_varname | {{0.568444620674023,2.01083374606704,-1.28665576953479,-1.18456909732025},{-1.76956489263841,0.405254401793609,-1.21615408353289,-1.18456909732025},...
+...
+
      Review the output summary table: 
      +SELECT * FROM iris_data_packed_summary;
+
      +-[ RECORD 1 ]------------+------------------------------
+source_table             | iris_data
+output_table             | iris_data_packed
+dependent_varname        | class_text
+independent_varname      | attributes
+buffer_size              | 26
+class_values             | {Iris_setosa,Iris_versicolor}
+num_rows_processed       | 52
+num_missing_rows_skipped | 0
+grouping_cols            |
+
      Review the output standardization table: 
      +SELECT * FROM iris_data_packed_standardization;
+
      +-[ RECORD 1 ]------------------------------------------------------
+mean | {5.45961538462,2.99807692308,3.025,0.851923076923}
+std  | {0.598799958695,0.498262513686,1.41840579525,0.550346179381}
+
      3. +
    3. Generally the default buffer size will work well, but if you have occasion to change it: 
      +DROP TABLE IF EXISTS iris_data_packed, iris_data_packed_summary, iris_data_packed_standardization;
+SELECT madlib.minibatch_preprocessor('iris_data',         -- Source table
+                                     'iris_data_packed',  -- Output table
+                                     'class_text',        -- Dependent variable
+                                     'attributes',        -- Independent variables
+                                     NULL,                -- Grouping
+                                     10                   -- Buffer size
+                                     );
+
      Review the output summary table: 
      +SELECT * FROM iris_data_packed_summary;
+
      +-[ RECORD 1 ]------------+------------------------------
+source_table             | iris_data
+output_table             | iris_data_packed
+dependent_varname        | class_text
+independent_varname      | attributes
+buffer_size              | 10
+class_values             | {Iris_setosa,Iris_versicolor}
+num_rows_processed       | 52
+num_missing_rows_skipped | 0
+grouping_cols            |
+
      4. +
    4. Run the preprocessor with grouping by state: 
      +DROP TABLE IF EXISTS iris_data_packed, iris_data_packed_summary, iris_data_packed_standardization;
+SELECT madlib.minibatch_preprocessor('iris_data',         -- Source table
+                                     'iris_data_packed',  -- Output table
+                                     'class_text',        -- Dependent variable
+                                     'attributes',        -- Independent variables
+                                     'state'              -- Grouping
+                                     );
+
      Review the output table: 
      +SELECT * FROM iris_data_packed ORDER BY state, __id__;
+
      +-[ RECORD 1 ]-------+-------------------------------------
+__id__              | 0
+state               | Alaska
+dependent_varname   | {{0,1},{0,1},{1,0},{0,1},{0,1},{0,1},{1,0},{0,1},{0,1},{1,0},{1,0},{0,1},{0,1}}
+independent_varname | {{0.306242850830503,-0.977074857057813,0.680489757142278 ...
+...
+-[ RECORD 2 ]-------+-------------------------------------
+__id__              | 1
+state               | Alaska
+dependent_varname   | {{0,1},{1,0},{0,1},{0,1},{1,0},{1,0},{1,0},{0,1},{1,0},{0,1},{0,1},{1,0},{1,0}}
+independent_varname | {{1.10129640587123,-0.126074175104234,1.2524188915498 ...
+...
+-[ RECORD 3 ]-------+-------------------------------------
+__id__              | 2
+state               | Alaska
+dependent_varname   | {{1,0}}
+independent_varname | {{-0.647821415218373,1.15042684782613,-1.17827992968215 ...
+...
+-[ RECORD 4 ]-------+-------------------------------------
+__id__              | 0
+state               | Tennessee
+dependent_varname   | {{1,0},{0,1},{1,0},{1,0},{1,0},{0,1},{1,0},{0,1},{0,1},{0,1},{1,0},{1,0},{0,1}}
+independent_varname | {{0.32912603663053,2.59625206429212,-1.12079945083087 ...
+...
+-[ RECORD 5 ]-------+-------------------------------------
+__id__              | 1
+state               | Tennessee
+dependent_varname   | {{0,1},{0,1},{0,1},{1,0},{1,0},{0,1},{0,1},{1,0},{0,1},{0,1},{0,1},{0,1}}
+independent_varname | {{0.865744574615085,-0.267261241912424,0.970244300719264 ...
+...
+
      Review the output summary table: 
      +SELECT * FROM iris_data_packed_summary;
+
      +-[ RECORD 1 ]------------+------------------------------
+source_table             | iris_data
+output_table             | iris_data_packed
+dependent_varname        | class_text
+independent_varname      | attributes
+buffer_size              | 13
+class_values             | {Iris_setosa,Iris_versicolor}
+num_rows_processed       | 52
+num_missing_rows_skipped | 0
+grouping_cols            | state
+
      Review the output standardization table: 
      +SELECT * FROM iris_data_packed_standardization;
+
      +-[ RECORD 1 ]-------------------------------------------------------------------
+state | Alaska
+mean  | {5.40740740740741,2.95925925925926,2.94814814814815,0.833333333333333}
+std   | {0.628888452645665,0.470034875978888,1.39877469405147,0.536103914747325}
+-[ RECORD 2 ]-------------------------------------------------------------------
+state | Tennessee
+mean  | {5.516,3.04,3.108,0.872}
+std   | {0.55905634778617,0.523832034148353,1.43469021046357,0.564637937088893}
+
      5. +
    5. If the depedent variable is scalar integer, and you have not already encoded it, you can ask the preprocessor to encode it for you: 
      +DROP TABLE IF EXISTS iris_data_packed, iris_data_packed_summary, iris_data_packed_standardization;
+SELECT madlib.minibatch_preprocessor('iris_data',         -- Source table
+                                     'iris_data_packed',  -- Output table
+                                     'class',             -- Integer dependent variable
+                                     'attributes',        -- Independent variables
+                                     NULL,                -- Grouping
+                                     NULL,                -- Buffer size
+                                     TRUE                 -- Encode scalar int dependent variable
+                                     );
+
      Review the output summary table: 
      +SELECT * FROM iris_data_packed_summary;
+
      +-[ RECORD 1 ]------------+-----------------
+source_table             | iris_data
+output_table             | iris_data_packed
+dependent_varname        | class
+independent_varname      | attributes
+dependent_vartype        | integer
+buffer_size              | 26
+class_values             | {1,2}
+num_rows_processed       | 52
+num_missing_rows_skipped | 0
+grouping_cols            |
+
      6. +
    +
    +

    Literature
    +

    [1] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent, Geoffrey Hinton with Nitish Srivastava and Kevin Swersky, http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

    +

    Related Topics
    +

    minibatch_preprocessing.sql_in

    +

    Neural Networks

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__mlogreg.html b/docs/docs/v2.1.0/group__grp__mlogreg.html new file mode 100644 index 00000000..fe209e93 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__mlogreg.html @@ -0,0 +1,407 @@ + + + + + + + + +MADlib: Multinomial Logistic Regression + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Multinomial Logistic Regression
    Deprecated Modules
    +
    +
    +
    Warning
    This is an old implementation of multinomial logistic regression. Replacement of this function is available as the Multinomial regression module Multinomial Regression
    +
    Contents +

    Multinomial logistic regression is a widely used regression analysis tool that models the outcomes of categorical dependent random variables. The model assumes that the conditional mean of the dependent categorical variables is the logistic function of an affine combination of independent variables. Multinomial logistic regression finds the vector of coefficients that maximizes the likelihood of the observations.

    +

    Training Function
    The multinomial logistic regression training function has the following syntax: 
    +mlogregr_train(source_table,
+               output_table,
+               dependent_varname,
+               independent_varname,
+               ref_category,
+               optimizer_params
+              )
+
    Arguments
    +
    source_table
    +

    TEXT. The name of the table containing the input data.

    +

    +

    +
    +
    output_table
    +

    TEXT. The name of the generated table containing the output model. The output table produced by the multinomial logistic regression training function contains the following columns:

    + + + + + + + + + + + + + + + + + + + + +
    category INTEGER. The category. Categories are encoded as integers with values from {0, 1, 2,..., numCategories – 1}
    ref_category INTEGER. The reference category. Categories are encoded as integers with values from {0, 1, 2,..., numCategories – 1}
    coef FLOAT8[]. An array of coefficients, \( \boldsymbol c \).
    log_likelihood FLOAT8. The log-likelihood, \( l(\boldsymbol c) \).
    std_err FLOAT8[]. An array of the standard errors.
    z_stats FLOAT8[]. An array of the Wald z-statistics.
    p_values FLOAT8[]. An array of the Wald p-values.
    odds_ratios FLOAT8[]. An array of the odds ratios.
    condition_no FLOAT8. The condition number of the matrix, computed using the coefficients of the iteration immediately preceding convergence.
    num_iterations INTEGER. The number of iterations executed before the algorithm completed.
    +

    A summary table named <out_table>_summary is also created at the same time, and it contains the following columns:

    + + + + + + + + + + + + + + + + + +
    source_table The data source table name.
    out_table The output table name.
    dependent_varname The dependent variable.
    independent_varname The independent variables.
    optimizer_params The optimizer parameters. It is a copy of the optimizer_params in the training function's arguments.
    ref_category An integer, the value of reference category used.
    num_rows_processed INTEGER. The number of rows actually processed, which is equal to the total number of rows in the source table minus the number of skipped rows.
    num_missing_rows_skipped INTEGER. The number of rows skipped during the training. A row will be skipped if the ind_col is NULL or contains NULL values.
    +

    +
    +
    dependent_varname
    +

    TEXT. The name of the column containing the dependent variable.

    +

    +
    +
    independent_varname
    +

    TEXT. Expression list to evaluate for the independent variables. An intercept variable is not assumed. The number of independent variables cannot exceed 65535.

    +

    +
    +
    ref_category (optional)
    +

    INTEGER, default: 0. The reference category ranges from [0, numCategories – 1].

    +

    +
    +
    optimizer_params (optional)
    +
    VARCHAR, default: NULL, which uses the default values of optimizer parameters. It should be a string that contains pairs of 'key=value' separated by commas. Supported parameters with their default values: max_iter=20, optimizer='irls', precision=1e-4. Currently, only 'irls' and 'newton' are allowed for 'optimizer'.
    +
    +
    +
    Note
    Table names can be optionally schema qualified and table and column names should follow the same case-sensitivity and quoting rules as in the database.
    +

    Prediction Function
    The prediction function is provided to estimate the conditional mean given a new predictor. It has the following syntax: 
    +mlogregr_predict(
+    model_table,
+    new_data_table,
+    id_col_name,
+    output_table,
+    type)
+
    +

    Arguments

    +
    model_table
    +

    TEXT. Name of the table containing the multilogistic model. This should be the output table returned from mlogregr_train.

    +

    +
    +
    new_data_table
    +

    TEXT. Name of the table containing prediction data. This table is expected to contain the same features that were used during training. The table should also contain id_col_name used for identifying each row.

    +

    +
    +
    id_col_name
    +

    TEXT. Name of the column containing id information in the source data. This is a mandatory argument and is used for correlating prediction table rows with the source. The values of this column are expected to be unique for each tuple.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table to output prediction results to. If this table already exists then an error is returned. This output table contains the id_col_name column giving the 'id' for each prediction.

    +

    If type = 'response', then the table has a single additional column with the prediction value of the response. The type of this column depends on the type of the response variable used during training.

    +

    If type = 'prob', then the table has multiple additional columns, one for each possible category. The columns are labeled as 'estimated_prob_category_value', where category_value represents the values of categories (0 to K-1).

    +

    +
    +
    type
    +

    TEXT, optional, default: 'response'.

    +

    When type = 'prob', the probabilities of each category (including the reference category) is given.

    +

    When type = 'response', a single output is provided which represents the prediction category for each tuple. This represents the category with the highest probability.

    +
    +
    +

    Examples
    +
      +
    1. Create the training data table. 
      +DROP TABLE IF EXISTS test3;
+CREATE TABLE test3 (
+    feat1 INTEGER,
+    feat2 INTEGER,
+    cat INTEGER
+);
+INSERT INTO test3(feat1, feat2, cat) VALUES
+(1,35,1),
+(2,33,0),
+(3,39,1),
+(1,37,1),
+(2,31,1),
+(3,36,0),
+(2,36,1),
+(2,31,1),
+(2,41,1),
+(2,37,1),
+(1,44,1),
+(3,33,2),
+(1,31,1),
+(2,44,1),
+(1,35,1),
+(1,44,0),
+(1,46,0),
+(2,46,1),
+(2,46,2),
+(3,49,1),
+(2,39,0),
+(2,44,1),
+(1,47,1),
+(1,44,1),
+(1,37,2),
+(3,38,2),
+(1,49,0),
+(2,44,0),
+(3,61,2),
+(1,65,2),
+(3,67,1),
+(3,65,2),
+(1,65,2),
+(2,67,2),
+(1,65,2),
+(1,62,2),
+(3,52,2),
+(3,63,2),
+(2,59,2),
+(3,65,2),
+(2,59,0),
+(3,67,2),
+(3,67,2),
+(3,60,2),
+(3,67,2),
+(3,62,2),
+(2,54,2),
+(3,65,2),
+(3,62,2),
+(2,59,2),
+(3,60,2),
+(3,63,2),
+(3,65,2),
+(2,63,1),
+(2,67,2),
+(2,65,2),
+(2,62,2);
+
      2. +
    2. Run the multilogistic regression function. 
      +DROP TABLE IF EXISTS test3_output;
+DROP TABLE IF EXISTS test3_output_summary;
+SELECT madlib.mlogregr_train('test3',
+                             'test3_output',
+                             'cat',
+                             'ARRAY[1, feat1, feat2]',
+                             0,
+                             'max_iter=20, optimizer=irls, precision=0.0001'
+                             );
+
      3. +
    3. View the result: 
      +-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM test3_output;
+
      Results: 
      +-[ RECORD 1 ]--+------------------------------------------------------------
+category       | 1
+ref_category   | 0
+coef           | {1.45474045211601,0.0849956182104023,-0.0172383499601956}
+loglikelihood  | -39.14759930999
+std_err        | {2.13085072854143,0.585021661344715,0.0431487356292144}
+z_stats        | {0.682704063982831,0.145286275409074,-0.39950996729842}
+p_values       | {0.494793861210936,0.884484850387893,0.689517480964129}
+odd_ratios     | {4.28337158128448,1.08871229617973,0.982909380301134}
+condition_no   | 280069.034217586
+num_iterations | 5
+-[ RECORD 2 ]--+------------------------------------------------------------
+category       | 2
+ref_category   | 0
+coef           | {-7.12908167688326,0.87648787696783,0.127886153027713}
+loglikelihood  | -39.14759930999
+std_err        | {2.52104008297868,0.639575886323862,0.0445757462972303}
+z_stats        | {-2.82783352990566,1.37042045472615,2.86896269049475}
+p_values       | {0.00468641692252239,0.170555690550421,0.00411820373218956}
+odd_ratios     | {0.000801455044349486,2.40244718187161,1.13642361694409}
+condition_no   | 280069.034217586
+num_iterations | 5
+
      4. +
    4. View all parameters used during the training 
      +\x on
+SELECT * FROM test3_output_summary;
+
      Results: 
      +-[ RECORD 1 ]------------+--------------------------------------------------
+method                   | mlogregr
+source_table             | test3
+out_table                | test3_output
+dependent_varname        | cat
+independent_varname      | ARRAY[1, feat1, feat2]
+optimizer_params         | max_iter=20, optimizer=irls, precision=0.0001
+ref_category             | 0
+num_categories           | 3
+num_rows_processed       | 57
+num_missing_rows_skipped | 0
+variance_covariance      | {{4.54052482732554,3.01080140927409,-0.551901021610841,-0.380754019900586,-0.0784151362989211,-0.0510014701718268},{3.01080140927409,6.35564309998514,-0.351902272617974,-0.766730342510818,-0.051877550252329,-0.0954432017695571},{-0.551901021610841,-0.351902272617974,0.34225034424253,0.231740815080827,-0.00117521831508331,-0.00114043921343171},{-0.380754019900586,-0.766730342510818,0.231740815080827,0.409057314366954,-0.000556498286025567,-0.000404735750986327},{-0.0784151362989211,-0.051877550252329,-0.00117521831508331,-0.000556498286025569,0.00186181338639984,0.00121080293928445},{-0.0510014701718268,-0.0954432017695571,-0.00114043921343171,-0.000404735750986325,0.00121080293928446,0.00198699715795504}}
+coef                     | {{1.45474045211601,0.0849956182104023,-0.0172383499601956},{-7.12908167688326,0.87648787696783,0.127886153027713}}
+
      5. +
    +

    Technical Background
    Multinomial logistic regression models the outcomes of categorical dependent random variables (denoted \( Y \in \{ 0,1,2 \ldots k \} \)). The model assumes that the conditional mean of the dependent categorical variables is the logistic function of an affine combination of independent variables (usually denoted \( \boldsymbol x \)). That is,

    +\[ E[Y \mid \boldsymbol x] = \sigma(\boldsymbol c^T \boldsymbol x) \] +

    + for some unknown vector of coefficients \( \boldsymbol c \) and where \( \sigma(x) = \frac{1}{1 + \exp(-x)} \) is the logistic function. Multinomial logistic regression finds the vector of coefficients \( \boldsymbol c \) that maximizes the likelihood of the observations.
    +

    Let

      +
    • \( \boldsymbol y \in \{ 0,1 \}^{n \times k} \) denote the vector of observed dependent variables, with \( n \) rows and \( k \) columns, containing the observed values of the dependent variable,
      • +
    • \( X \in \mathbf R^{n \times k} \) denote the design matrix with \( k \) columns and \( n \) rows, containing all observed vectors of independent variables \( \boldsymbol x_i \) as rows.
      • +
    +

    By definition,

    +\[ P[Y = y_i | \boldsymbol x_i] = \sigma((-1)^{y_i} \cdot \boldsymbol c^T \boldsymbol x_i) \,. \] +

    +

    Maximizing the likelihood \( \prod_{i=1}^n \Pr(Y = y_i \mid \boldsymbol x_i) \) is equivalent to maximizing the log-likelihood \( \sum_{i=1}^n \log \Pr(Y = y_i \mid \boldsymbol x_i) \), which simplifies to

    +\[ l(\boldsymbol c) = -\sum_{i=1}^n \log(1 + \exp((-1)^{y_i} \cdot \boldsymbol c^T \boldsymbol x_i)) \,. \] +

    +

    The Hessian of this objective is \( H = -X^T A X \) where \( A = \text{diag}(a_1, \dots, a_n) \) is the diagonal matrix with \( a_i = \sigma(\boldsymbol c^T \boldsymbol x) \cdot \sigma(-\boldsymbol c^T \boldsymbol x) \,. \) Since \( H \) is non-positive definite, \( l(\boldsymbol c) \) is convex. There are many techniques for solving convex optimization problems. Currently, logistic regression in MADlib can use:

      +
    • Iteratively Reweighted Least Squares
      • +
    +

    We estimate the standard error for coefficient \( i \) as

    +\[ \mathit{se}(c_i) = \left( (X^T A X)^{-1} \right)_{ii} \,. \] +

    +

    The Wald z-statistic is

    +\[ z_i = \frac{c_i}{\mathit{se}(c_i)} \,. \] +

    +

    The Wald \( p \)-value for coefficient \( i \) gives the probability (under the assumptions inherent in the Wald test) of seeing a value at least as extreme as the one observed, provided that the null hypothesis ( \( c_i = 0 \)) is true. Letting \( F \) denote the cumulative density function of a standard normal distribution, the Wald \( p \)-value for coefficient \( i \) is therefore

    +\[ p_i = \Pr(|Z| \geq |z_i|) = 2 \cdot (1 - F( |z_i| )) \] +

    +

    where \( Z \) is a standard normally distributed random variable.

    +

    The odds ratio for coefficient \( i \) is estimated as \( \exp(c_i) \).

    +

    The condition number is computed as \( \kappa(X^T A X) \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration). A large condition number (say, more than 1000) indicates the presence of significant multicollinearity.

    +

    The multinomial logistic regression uses a default reference category of zero, and the regression coefficients in the output are in the order described below. For a problem with \( K \) dependent variables \( (1, ..., K) \) and \( J \) categories \( (0, ..., J-1) \), let \( {m_{k,j}} \) denote the coefficient for dependent variable \( k \) and category \( j \). The output is \( {m_{k_1, j_0}, m_{k_1, j_1} \ldots m_{k_1, j_{J-1}}, m_{k_2, j_0}, m_{k_2, j_1}, \ldots m_{k_2, j_{J-1}} \ldots m_{k_K, j_{J-1}}} \). The order is NOT CONSISTENT with the multinomial regression marginal effect calculation with function marginal_mlogregr. This is deliberate because the interfaces of all multinomial regressions (robust, clustered, ...) will be moved to match that used in marginal.

    +

    Literature
    +

    A collection of nice write-ups, with valuable pointers into further literature:

    +

    [1] Annette J. Dobson: An Introduction to Generalized Linear Models, Second Edition. Nov 2001

    +

    [2] Cosma Shalizi: Statistics 36-350: Data Mining, Lecture Notes, 18 November 2009, http://www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf

    +

    [3] Scott A. Czepiel: Maximum Likelihood Estimation of Logistic Regression Models: Theory and Implementation, Retrieved Jul 12 2012, http://czep.net/stat/mlelr.pdf

    +

    Related Topics
    +

    File multilogistic.sql_in documenting the multinomial logistic regression functions

    +

    Logistic Regression

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__model__prep.html b/docs/docs/v2.1.0/group__grp__model__prep.html new file mode 100644 index 00000000..8e3b6f9b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__model__prep.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: Model Preparation + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Model Preparation
    Deep Learning
    +
    +
    +

    Detailed Description

    +

    Prepare models and data for deep learning.

    + + + + + + + + + + + +

    +Modules

     Preprocess Data
     Prepare training data for use by deep learning modules.
     
     Define Model Architectures
     Function to load model architectures and weights into a table.
     
     Define Custom Functions
     Function to load serialized Python objects into a table.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__model__prep.js b/docs/docs/v2.1.0/group__grp__model__prep.js new file mode 100644 index 00000000..61cb681e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__model__prep.js @@ -0,0 +1,6 @@ +var group__grp__model__prep = +[ + [ "Preprocess Data", "group__grp__input__preprocessor__dl.html", null ], + [ "Define Model Architectures", "group__grp__keras__model__arch.html", null ], + [ "Define Custom Functions", "group__grp__custom__function.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__model__selection.html b/docs/docs/v2.1.0/group__grp__model__selection.html new file mode 100644 index 00000000..daf0532c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__model__selection.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: Train Multiple Models + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Train Multiple Models
    Deep Learning
    +
    +
    +

    Detailed Description

    +

    Train multiple deep learning models at the same time for model architecture search and hyperparameter selection.

    + + + + + + + + + + + +

    +Modules

     Define Model Configurations
     Generate configurations for model architecture search and hyperparameter tuning.
     
     Train Model Configurations
     Explore network architectures and hyperparameters by training many models a time.
     
     AutoML
     Functions to run automated machine learning (autoML) methods for model architecture search and hyperparameter tuning.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__model__selection.js b/docs/docs/v2.1.0/group__grp__model__selection.js new file mode 100644 index 00000000..642a74c3 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__model__selection.js @@ -0,0 +1,6 @@ +var group__grp__model__selection = +[ + [ "Define Model Configurations", "group__grp__keras__setup__model__selection.html", null ], + [ "Train Model Configurations", "group__grp__keras__run__model__selection.html", null ], + [ "AutoML", "group__grp__automl.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__multinom.html b/docs/docs/v2.1.0/group__grp__multinom.html new file mode 100644 index 00000000..838c9368 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__multinom.html @@ -0,0 +1,476 @@ + + + + + + + + +MADlib: Multinomial Regression + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Multinomial Regression
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    In statistics, multinomial regression is a classification method that generalizes binomial regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).

    +

    Training Function
    The multinomial regression training function has the following syntax: 
    +multinom(source_table,
+         model_table,
+         dependent_varname,
+         independent_varname,
+         ref_category,
+         link_func,
+         grouping_col,
+         optim_params,
+         verbose
+        )
+
    +

    Arguments

    +
    source_table
    +

    VARCHAR. Name of the table containing the training data.

    +

    +
    +
    model_table
    +

    VARCHAR. Name of the generated table containing the model.

    +

    The model table produced by multinom() contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + +
    <...>

    Grouping columns, if provided in input. This could be multiple columns depending on the grouping_col input.

    +

    +
    category

    VARCHAR. String representation of category value.

    +

    +
    coef

    FLOAT8[]. Vector of the coefficients in linear predictor.

    +

    +
    log_likelihood

    FLOAT8. The log-likelihood \( l(\boldsymbol \beta) \). The value will be the same across categories within the same group.

    +

    +
    std_err

    FLOAT8[]. Vector of the standard errors of the coefficients.

    +

    +
    z_stats

    FLOAT8[]. Vector of the z-statistics of the coefficients.

    +

    +
    p_values

    FLOAT8[]. Vector of the p-values of the coefficients.

    +

    +
    num_rows_processed

    BIGINT. Number of rows processed.

    +

    +
    num_rows_skipped

    BIGINT. Number of rows skipped due to missing values or failures.

    +

    +
    num_iterations INTEGER. Number of iterations actually completed. This would be different from the nIterations argument if a tolerance parameter is provided and the algorithm converges before all iterations are completed.
    +

    A summary table named <model_table>_summary is also created at the same time, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + +
    method

    VARCHAR. String describes the model: 'multinom'.

    +

    +
    source_table

    VARCHAR. Data source table name.

    +

    +
    model_table

    VARCHAR. Model table name.

    +

    +
    dependent_varname

    VARCHAR. Expression for dependent variable.

    +

    +
    independent_varname

    VARCHAR. Expression for independent variables.

    +

    +
    ref_category

    VARCHAR. String representation of reference category.

    +

    +
    link_func

    VARCHAR. String that contains link function parameters: only 'logit' is implemented now

    +

    +
    grouping_col

    VARCHAR. String representation of grouping columns.

    +

    +
    optimizer_params

    VARCHAR. String that contains optimizer parameters, and has the form of 'optimizer=..., max_iter=..., tolerance=...'.

    +

    +
    num_all_groups

    INTEGER. Number of groups in glm training.

    +

    +
    num_failed_groups

    INTEGER. Number of failed groups in glm training.

    +

    +
    total_rows_processed

    BIGINT. Total number of rows processed in all groups.

    +

    +
    total_rows_skipped

    BIGINT. Total number of rows skipped in all groups due to missing values or failures.

    +

    +
    +

    +
    +
    dependent_varname
    +

    VARCHAR. Name of the dependent variable column.

    +

    +
    +
    independent_varname
    +

    VARCHAR. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list.

    +

    +
    +
    link_function (optional)
    +

    VARCHAR, default: 'logit'. Parameters for link function. Currently, we support logit.

    +

    +
    +
    ref_category (optional)
    +

    VARCHAR, default: '0'. Parameters to specify the reference category.

    +

    +
    +
    grouping_col (optional)
    +

    VARCHAR, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated.

    +

    +
    +
    optim_params (optional)
    +

    VARCHAR, default: 'max_iter=100,optimizer=irls,tolerance=1e-6'. Parameters for optimizer. Currently, we support tolerance=[tolerance for relative error between log-likelihoods], max_iter=[maximum iterations to run], optimizer=irls.

    +

    +
    +
    verbose (optional)
    +
    BOOLEAN, default: FALSE. Provides verbose output of the results of training.
    +
    +
    Note
    For p-values, we just return the computation result directly. Other statistical packages, like 'R', produce the same result, but on printing the result to screen, another format function is used and any p-value that is smaller than the machine epsilon (the smallest positive floating-point number 'x' such that '1 + x != 1') will be printed on screen as "< xxx" (xxx is the value of the machine epsilon). Although the result may look different, they are in fact the same.
    +

    Prediction Function
    Multinomial regression prediction function has the following format: 
    +multinom_predict(model_table,
+                 predict_table_input,
+                 output_table,
+                 predict_type,
+                 verbose,
+                 id_column
+                )
+
    Arguments
    +
    model_table
    +

    TEXT. Name of the generated table containing the model, which is the output table from multinom().

    +

    +
    +
    predict_table_input
    +

    TEXT. The name of the table containing the data to predict on. The table must contain id column as the primary key.

    +

    +
    +
    output_table
    +

    TEXT. Name of the generated table containing the predicted values.

    +

    The model table produced by multinom_predict contains the following columns:

    + + + + + + + +
    id

    SERIAL. Column to identify the predicted value.

    +

    +
    category

    TEXT. Available if the predicted type = 'response'. Column contains the predicted categories

    +

    +
    category_value FLOAT8. The predicted probability for the specific category_value.
    +

    +
    +
    predict_type
    +
    TEXT. Either 'response' or 'probability'. Using 'response' will give the predicted category with the largest probability. Using probability will give the predicted probabilities for all categories
    +
    verbose
    +

    BOOLEAN. Control whether verbose is displayed. The default is FALSE.

    +

    +
    +
    id_column
    +
    TEXT. The name of the column in the input table.
    +
    +
    +

    Examples
    +
      +
    1. Create the training data table. 
      +DROP TABLE IF EXISTS test3;
+CREATE TABLE test3 (
+    feat1 INTEGER,
+    feat2 INTEGER,
+    cat INTEGER
+);
+INSERT INTO test3(feat1, feat2, cat) VALUES
+(1,35,1),
+(2,33,0),
+(3,39,1),
+(1,37,1),
+(2,31,1),
+(3,36,0),
+(2,36,1),
+(2,31,1),
+(2,41,1),
+(2,37,1),
+(1,44,1),
+(3,33,2),
+(1,31,1),
+(2,44,1),
+(1,35,1),
+(1,44,0),
+(1,46,0),
+(2,46,1),
+(2,46,2),
+(3,49,1),
+(2,39,0),
+(2,44,1),
+(1,47,1),
+(1,44,1),
+(1,37,2),
+(3,38,2),
+(1,49,0),
+(2,44,0),
+(3,61,2),
+(1,65,2),
+(3,67,1),
+(3,65,2),
+(1,65,2),
+(2,67,2),
+(1,65,2),
+(1,62,2),
+(3,52,2),
+(3,63,2),
+(2,59,2),
+(3,65,2),
+(2,59,0),
+(3,67,2),
+(3,67,2),
+(3,60,2),
+(3,67,2),
+(3,62,2),
+(2,54,2),
+(3,65,2),
+(3,62,2),
+(2,59,2),
+(3,60,2),
+(3,63,2),
+(3,65,2),
+(2,63,1),
+(2,67,2),
+(2,65,2),
+(2,62,2);
+
      2. +
    2. Run the multilogistic regression function. 
      +DROP TABLE IF EXISTS test3_output;
+DROP TABLE IF EXISTS test3_output_summary;
+SELECT madlib.multinom('test3',
+                       'test3_output',
+                       'cat',
+                       'ARRAY[1, feat1, feat2]',
+                       '0',
+                       'logit'
+                       );
+
      3. +
    3. View the regression results. 
      +-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM test3_output;
+
      Result: 
      +-[ RECORD 1 ]------+------------------------------------------------------------
+category           | 1
+coef               | {1.45474045165731,0.084995618282504,-0.0172383499512136}
+log_likelihood     | -39.1475993094045
+std_err            | {2.13085878785549,0.585023211942952,0.0431489262260687}
+z_stats            | {0.682701481650677,0.145285890452484,-0.399508202380224}
+p_values           | {0.494795493298706,0.884485154314181,0.689518781152604}
+num_rows_processed | 57
+num_rows_skipped   | 0
+iteration          | 6
+-[ RECORD 2 ]------+------------------------------------------------------------
+category           | 2
+coef               | {-7.1290816775109,0.876487877074751,0.127886153038661}
+log_likelihood     | -39.1475993094045
+std_err            | {2.52105418324135,0.639578886139654,0.0445760103748678}
+z_stats            | {-2.82781771407425,1.37041402721253,2.86894569440347}
+p_values           | {0.00468664844488755,0.170557695812408,0.00411842502754068}
+num_rows_processed | 57
+num_rows_skipped   | 0
+iteration          | 6
+
      4. +
    4. Predicting dependent variable using multinomial model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) 
      +\x off
+-- Add the id column for prediction function
+ALTER TABLE test3 ADD COLUMN id SERIAL;
+-- Predict probabilities for all categories using the original data
+SELECT madlib.multinom_predict('test3_output','test3', 'test3_prd_prob', 'probability');
+-- Display the predicted value
+SELECT * FROM test3_prd_prob;
+
      5. +
    +

    Technical Background
    When link = 'logit', multinomial logistic regression models the outcomes of categorical dependent random variables (denoted \( Y \in \{ 0,1,2 \ldots k \} \)). The model assumes that the conditional mean of the dependent categorical variables is the logistic function of an affine combination of independent variables (usually denoted \( \boldsymbol x \)). That is,

    +\[ E[Y \mid \boldsymbol x] = \sigma(\boldsymbol c^T \boldsymbol x) \] +

    + for some unknown vector of coefficients \( \boldsymbol c \) and where \( \sigma(x) = \frac{1}{1 + \exp(-x)} \) is the logistic function. Multinomial logistic regression finds the vector of coefficients \( \boldsymbol c \) that maximizes the likelihood of the observations.
    +

    Let

      +
    • \( \boldsymbol y \in \{ 0,1 \}^{n \times k} \) denote the vector of observed dependent variables, with \( n \) rows and \( k \) columns, containing the observed values of the dependent variable,
      • +
    • \( X \in \mathbf R^{n \times k} \) denote the design matrix with \( k \) columns and \( n \) rows, containing all observed vectors of independent variables \( \boldsymbol x_i \) as rows.
      • +
    +

    By definition,

    +\[ P[Y = y_i | \boldsymbol x_i] = \sigma((-1)^{y_i} \cdot \boldsymbol c^T \boldsymbol x_i) \,. \] +

    +

    Maximizing the likelihood \( \prod_{i=1}^n \Pr(Y = y_i \mid \boldsymbol x_i) \) is equivalent to maximizing the log-likelihood \( \sum_{i=1}^n \log \Pr(Y = y_i \mid \boldsymbol x_i) \), which simplifies to

    +\[ l(\boldsymbol c) = -\sum_{i=1}^n \log(1 + \exp((-1)^{y_i} \cdot \boldsymbol c^T \boldsymbol x_i)) \,. \] +

    +

    The Hessian of this objective is \( H = -X^T A X \) where \( A = \text{diag}(a_1, \dots, a_n) \) is the diagonal matrix with \( a_i = \sigma(\boldsymbol c^T \boldsymbol x) \cdot \sigma(-\boldsymbol c^T \boldsymbol x) \,. \) Since \( H \) is non-positive definite, \( l(\boldsymbol c) \) is convex. There are many techniques for solving convex optimization problems. Currently, logistic regression in MADlib can use:

      +
    • Iteratively Reweighted Least Squares
      • +
    +

    We estimate the standard error for coefficient \( i \) as

    +\[ \mathit{se}(c_i) = \left( (X^T A X)^{-1} \right)_{ii} \,. \] +

    +

    The Wald z-statistic is

    +\[ z_i = \frac{c_i}{\mathit{se}(c_i)} \,. \] +

    +

    The Wald \( p \)-value for coefficient \( i \) gives the probability (under the assumptions inherent in the Wald test) of seeing a value at least as extreme as the one observed, provided that the null hypothesis ( \( c_i = 0 \)) is true. Letting \( F \) denote the cumulative density function of a standard normal distribution, the Wald \( p \)-value for coefficient \( i \) is therefore

    +\[ p_i = \Pr(|Z| \geq |z_i|) = 2 \cdot (1 - F( |z_i| )) \] +

    +

    where \( Z \) is a standard normally distributed random variable.

    +

    The odds ratio for coefficient \( i \) is estimated as \( \exp(c_i) \).

    +

    The condition number is computed as \( \kappa(X^T A X) \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration). A large condition number (say, more than 1000) indicates the presence of significant multicollinearity.

    +

    The multinomial logistic regression uses a default reference category of zero, and the regression coefficients in the output are in the order described below. For a problem with \( K \) dependent variables \( (1, ..., K) \) and \( J \) categories \( (0, ..., J-1) \), let \( {m_{k,j}} \) denote the coefficient for dependent variable \( k \) and category \( j \). The output is \( {m_{k_1, j_0}, m_{k_1, j_1} \ldots m_{k_1, j_{J-1}}, m_{k_2, j_0}, m_{k_2, j_1}, \ldots m_{k_2, j_{J-1}} \ldots m_{k_K, j_{J-1}}} \). The order is NOT CONSISTENT with the multinomial regression marginal effect calculation with function marginal_mlogregr. This is deliberate because the interfaces of all multinomial regressions (robust, clustered, ...) will be moved to match that used in marginal.

    +

    Literature
    +

    A collection of nice write-ups, with valuable pointers into further literature:

    +

    [1] Annette J. Dobson: An Introduction to Generalized Linear Models, Second Edition. Nov 2001

    +

    [2] Cosma Shalizi: Statistics 36-350: Data Mining, Lecture Notes, 18 November 2009, http://www.stat.cmu.edu/~cshalizi/350/lectures/26/lecture-26.pdf

    +

    [3] Scott A. Czepiel: Maximum Likelihood Estimation of Logistic Regression Models: Theory and Implementation, Retrieved Jul 12 2012, http://czep.net/stat/mlelr.pdf

    +

    Related Topics
    +

    File multiresponseglm.sql_in documenting the multinomial regression functions

    +

    Logistic Regression

    +

    Ordinal Regression

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__nn.html b/docs/docs/v2.1.0/group__grp__nn.html new file mode 100644 index 00000000..e740a8c7 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__nn.html @@ -0,0 +1,1101 @@ + + + + + + + + +MADlib: Neural Network + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Neural Network
    Supervised Learning
    +
    +
    +
    Contents +

    Multilayer Perceptron (MLP) is a type of neural network that can be used for regression and classification.

    +

    MLPs consist of several fully connected hidden layers with non-linear activation functions. In the case of classification, the final layer of the neural net has as many nodes as classes, and the output of the neural net can be interpreted as the probability that a given input feature belongs to a specific class.

    +

    MLP can be used with or without mini-batching. The advantage of using mini-batching is that it can perform better than the default MADlib optimizer, because it uses more than one training example at a time, typically resulting faster and smoother convergence [3].

    +
    Note
    In order to use mini-batching, you must first run the Mini-Batch Preprocessor, which is a utility that prepares input data for use by models that support mini-batch as an optimization option, such as MLP. This is a one-time operation and you would only need to re-run the preprocessor if your input data has changed, or if you change the grouping parameter.
    +

    Classification Training Function
    The MLP classification training function has the following format:
    +
    +mlp_classification(
+    source_table,
+    output_table,
+    independent_varname,
+    dependent_varname,
+    hidden_layer_sizes,
+    optimizer_params,
+    activation,
+    weights,
+    warm_start,
+    verbose,
+    grouping_col
+    )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the training data. If you are using mini-batching, this is the name of the output table from the mini-batch preprocessor.

    +

    +
    +
    output_table
    +

    TEXT. Name of the output table containing the model. Details of the output table are shown below.

    +

    +
    +
    independent_varname
    +

    TEXT. Expression list to evaluate for the independent variables. It should be a numeric array expression. If you are using mini-batching, set this parameter to 'independent_varname' which is the hardcoded name of the column from the mini-batch preprocessor containing the packed independent variables.

    +
    Note
    If you are not using mini-batching, please note that an intercept variable should not be included as part of this expression - this is different from other MADlib modules. Also please note that independent variables should be encoded properly. All values are cast to DOUBLE PRECISION, so categorical variables should be one-hot or dummy encoded as appropriate. See Encoding Categorical Variables for more details.
    +
    +
    dependent_varname
    +

    TEXT. Name of the dependent variable column. For classification, supported types are: text, varchar, character varying, char, character integer, smallint, bigint, and boolean. If you are using mini-batching, set this parameter to 'dependent_varname' which is the hardcoded name of the column from the mini-batch preprocessor containing the packed dependent variables.

    +

    +
    +
    hidden_layer_sizes (optional)
    +

    INTEGER[], default: ARRAY[100]. The number of neurons in each hidden layer. The length of this array will determine the number of hidden layers. For example, ARRAY[5,10] means 2 hidden layers, one with 5 neurons and the other with 10 neurons. Use ARRAY[]::INTEGER[] for no hidden layers.

    +

    +
    +
    optimizer_params (optional)
    +

    TEXT, default: NULL. Parameters for optimization in a comma-separated string of key-value pairs. See the description below for details.

    +

    +
    +
    activation (optional)
    +

    TEXT, default: 'sigmoid'. Activation function. Currently three functions are supported: 'sigmoid' (default), 'relu', and 'tanh'. The text can be any prefix of the three strings; for e.g., specifying 's' will use sigmoid activation.

    +

    +
    +
    weights (optional)
    +
    TEXT, default: 1. Column name for giving different weights to different rows during training. E.g., a weight of two for a specific row is equivalent to dupicating that row. This weight is incorporated into the update during stochastic gradient descent (SGD), but is not be used for loss calculations. If not specified, weight for each row will default to 1 (equal weights). Column should be a numeric type.
    Note
    The 'weights' parameter cannot be used if you use mini-batching of the source dataset.
    +
    +
    warm_start (optional)
    +

    BOOLEAN, default: FALSE. Initalize neural network weights with the coefficients from the last call of the training function. If set to true, neural network weights will be initialized from the output_table generated by the previous run. Note that all parameters other than optimizer_params and verbose must remain constant between calls when warm_start is used.

    +
    Note
    The warm start feature works based on the name of the output_table. When using warm start, do not drop the output table or the output table summary before calling the training function, since these are needed to obtain the neural network weights from the previous run. If you are not using warm start, the output table and the output table summary must be dropped in the usual way before calling the training function.
    +

    +
    +
    verbose (optional)
    +
    BOOLEAN, default: FALSE. Provides verbose output of the results of training, including the value of loss at each iteration.
    Note
    There are some subtleties on the reported per-iteration loss values because we are working in a distributed system. When mini-batching is used (i.e., batch gradient descent), loss per iteration is an average of losses across all mini-batches and epochs on a segment. Losses across all segments then get averaged to give overall loss for the model for the iteration. This will tend to be a pessimistic estimate of loss. When mini-batching is not used (i.e., stochastic gradient descent), we use the model state from the previous iteration to compute the loss at the start of the current iteration on the whole data set. This is an accurate computation of loss for the iteration.
    +
    +
    grouping_col (optional)
    +
    TEXT, default: NULL. A single column or a list of comma-separated columns that divides the input data into discrete groups, resulting in one model per group. When this value is NULL, no grouping is used and a single model is generated for all data. If you are using mini-batching, you must have run the mini-batch preprocessor with exactly the same groups that you specify here for MLP training. If you change the groups, or remove the groups, then you must re- run the mini-batch preprocessor.
    +
    +

    Output tables
    + The model table produced by MLP contains the following columns:

    + + + + + + + + +
    coeffs FLOAT8[]. Flat array containing the weights of the neural net.
    n_iterations INTEGER. Number of iterations completed by the stochastic gradient descent algorithm. The algorithm either converged in this number of iterations or hit the maximum number specified in the optimization parameters.
    loss FLOAT8. The cross entropy loss over the training data. See Technical Background section below for more details.
    grouping columns If grouping_col is specified during training, a column for each grouping column is created.
    +

    A summary table named <output_table>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    source_table The source table.
    independent_varname The independent variables.
    dependent_varname The dependent variable.
    tolerance The tolerance as given in optimizer_params.
    learning_rate_init The initial learning rate as given in optimizer_params.
    learning_rate_policy The learning rate policy as given in optimizer_params.
    momentum Momentum value as given in optimizer_params.
    nesterov Nesterov value as given in optimizer_params.
    n_iterations The number of iterations run.
    n_tries The number of tries as given in optimizer_params.
    layer_sizes The number of units in each layer including the input and output layers.
    activation The activation function.
    is_classification True if the model was trained for classification, False if it was trained for regression.
    classes The classes which were trained against (empty for regression).
    weights The weight column used during training for giving different weights to different rows.
    grouping_col

    NULL if no grouping_col was specified during training, and a comma-separated list of grouping column names if not.

    +

    +
    +

    A standardization table named <output_table>_standardization is also create, that has the following columns:

    + + + + + + +
    mean The mean for all input features (used for normalization).
    std The standard deviation for all input features (used for normalization).
    grouping columns If grouping_col is specified during training, a column for each grouping column is created.
    +

    Regression Training Function
    The MLP regression training function has the following format: 
    +mlp_regression(
+    source_table,
+    output_table,
+    independent_varname,
+    dependent_varname,
+    hidden_layer_sizes,
+    optimizer_params,
+    activation,
+    weights,
+    warm_start,
+    verbose,
+    grouping_col
+    )
+
    +

    Arguments

    +

    Parameters for regression are largely the same as for classification. In the model table, the loss refers to mean square error instead of cross entropy loss. In the summary table, there is no classes column. The following arguments have specifications which differ from mlp_classification:

    +
    dependent_varname
    +
    TEXT. Name of the dependent variable column. For regression, supported types are any numeric type, or array of numeric types (for multiple regression).
    +
    +

    Optimizer Parameters
    Parameters in this section are supplied in the optimizer_params argument as a string containing a comma-delimited list of name-value pairs. All of these named parameters are optional and their order does not matter. You must use the format "<param_name> = <value>" to specify the value of a parameter, otherwise the parameter is ignored.
    +
    +  'solver = <value>,
+   learning_rate_init = <value>,
+   learning_rate_policy = <value>,
+   gamma = <value>,
+   power = <value>,
+   iterations_per_step = <value>,
+   n_iterations = <value>,
+   n_tries = <value>,
+   lambda = <value>,
+   tolerance = <value>,
+   batch_size = <value>,
+   n_epochs = <value>,
+   momentum = <value>,
+   nesterov = <value>',
+   rho = <value>,
+   beta1 = <value>,
+   beta2 = <value>,
+   eps = <value>'
+

    Optimizer Parameters

    +
    solver
    +

    Default: sgd. One of 'sgd', 'rmsprop' or 'adam' or any prefix of these (e.g., 'rmsp' means 'rmsprop'). These are defined below:

      +
    • 'sgd': stochastic gradient descent
      • +
    • 'rmsprop': RMSprop algorithm proposed by Hinton et al. [3]
      • +
    • 'adam': Adam algorithm proposed by Kingma and Ba [4]
      • +
    +
    Note
    rmsprop and adam solvers only work with minibatched data. In addition, they do not support momentum. Please see the references for the explanations on these constraints.
    +
    +
    learning_rate_init
    +

    Default: 0.001. Also known as the learning rate. A small value is usually desirable to ensure convergence, while a large value provides more room for progress during training. Since the best value depends on the condition number of the data, in practice one often tunes this parameter.

    +

    +
    +
    learning_rate_policy
    +

    Default: constant. One of 'constant', 'exp', 'inv' or 'step' or any prefix of these (e.g., 's' means 'step'). These are defined below, where 'iter' is the current iteration:

      +
    • 'constant': learning_rate = learning_rate_init
      • +
    • 'exp': learning_rate = learning_rate_init * gamma^(iter)
      • +
    • 'inv': learning_rate = learning_rate_init * (iter+1)^(-power)
      • +
    • 'step': learning_rate = learning_rate_init * gamma^(floor(iter/iterations_per_step))
      • +
    +

    +
    +
    gamma
    +

    Default: 0.1. Decay rate for learning rate when learning_rate_policy is 'exp' or 'step'.

    +

    +
    +
    power
    +

    Default: 0.5. Exponent for learning_rate_policy = 'inv'.

    +

    +
    +
    iterations_per_step
    +

    Default: 100. Number of iterations to run before decreasing the learning rate by a factor of gamma. Valid for learning rate policy = 'step'.

    +

    +
    +
    n_iterations
    +

    Default: 100. The maximum number of iterations allowed.

    +

    +
    +
    n_tries
    +

    Default: 1. Number of times to retrain the network with randomly initialized neural network weights.

    +

    +
    +
    lambda
    +

    Default: 0. The regularization coefficient for L2 regularization.

    +

    +
    +
    tolerance
    +

    Default: 0.001. The criterion to end iterations. The training stops whenever the difference between the training models of two consecutive iterations is smaller than tolerance or the iteration number is larger than n_iterations. If you want to run the full number of iterations specified in n_interations, set tolerance=0.0

    +

    +
    +
    batch_size
    +

    Default: min(200, buffer_size) where buffer_size is set in the mini-batch preprocessor. The 'batch_size' is the size of the mini-batch used in the optimizer. This parameter is only used in the case of mini-batching.

    +

    +
    +
    n_epochs
    +

    Default: 1. Represents the number of times each batch is used by the optimizer. This parameter is only used in the case of mini-batching.

    +

    +
    +
    momentum
    +

    Default: 0.9. Momentum can help accelerate learning and avoid local minima when using gradient descent. Value must be in the range 0 to 1, where 0 means no momentum.

    +

    +
    +
    nesterov
    +

    Default: TRUE. Only used when the 'momentum' parameter is > 0. Nesterov momentum can provide better results than using classical momentum alone, due to its look-ahead characteristics. In classical momentum we correct the velocity and then update the model with that velocity, whereas in Nesterov Accelerated Gradient method, we first move the model in the direction of velocity, compute the gradient using this updated model, and then add this gradient back into the model. The main difference being that in classical momentum, we compute the gradient before updating the model whereas in nesterov we first update the model and then compute the gradient from the updated position.

    +

    +
    +
    rho
    +

    Default: 0.9. Moving average parameter for the RMSprop solver.

    +

    +
    +
    beta1
    +

    Default: 0.9. The exponential decay rate for the first moment estimates.

    +

    +
    +
    beta2
    +

    Default: 0.999. The exponential decay rate for the second moment estimates.

    +

    +
    +
    eps
    +
    Default: 1e-7. Constant for numerical stability in adam and rmsprop solvers.
    +
    +

    Prediction Function
    Used to generate predictions on novel data given a previously trained model. The same syntax is used for classification and regression. 
    +mlp_predict(
+    model_table,
+    data_table,
+    id_col_name,
+    output_table,
+    pred_type
+    )
+
    +

    Arguments

    +
    model_table
    +

    TEXT. Model table produced by the training function.

    +

    +
    +
    data_table
    +

    TEXT. Name of the table containing the data for prediction. This table is expected to contain the same input features that were used during training. The table should also contain id_col_name used for identifying each row.

    +

    +
    +
    id_col_name
    +

    TEXT. The name of the id column in data_table.

    +

    +
    +
    output_table
    +
    TEXT. Name of the table where output predictions are written. If this table name is already in use, an error is returned. Table contains: + + + + + + +
    id Gives the 'id' for each prediction, corresponding to each row from the data_table.
    estimated_COL_NAME (For pred_type='response') The estimated class for classification or value for regression, where COL_NAME is the name of the column to be predicted from training data.
    prob_CLASS

    (For pred_type='prob' for classification) The probability of a given class CLASS as given by softmax. There will be one column for each class in the training data.

    +

    +
    +
    +
    pred_type
    +
    TEXT. The type of output requested: 'response' gives the actual prediction, 'prob' gives the probability of each class. For regression, only type='response' is defined.
    +
    +

    Examples
    +

    Classification without Mini-Batching

    +
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS iris_data;
+CREATE TABLE iris_data(
+    id serial,
+    attributes numeric[],
+    class_text varchar,
+    class integer,
+    state varchar
+);
+INSERT INTO iris_data(id, attributes, class_text, class, state) VALUES
+(1,ARRAY[5.0,3.2,1.2,0.2],'Iris_setosa',1,'Alaska'),
+(2,ARRAY[5.5,3.5,1.3,0.2],'Iris_setosa',1,'Alaska'),
+(3,ARRAY[4.9,3.1,1.5,0.1],'Iris_setosa',1,'Alaska'),
+(4,ARRAY[4.4,3.0,1.3,0.2],'Iris_setosa',1,'Alaska'),
+(5,ARRAY[5.1,3.4,1.5,0.2],'Iris_setosa',1,'Alaska'),
+(6,ARRAY[5.0,3.5,1.3,0.3],'Iris_setosa',1,'Alaska'),
+(7,ARRAY[4.5,2.3,1.3,0.3],'Iris_setosa',1,'Alaska'),
+(8,ARRAY[4.4,3.2,1.3,0.2],'Iris_setosa',1,'Alaska'),
+(9,ARRAY[5.0,3.5,1.6,0.6],'Iris_setosa',1,'Alaska'),
+(10,ARRAY[5.1,3.8,1.9,0.4],'Iris_setosa',1,'Alaska'),
+(11,ARRAY[4.8,3.0,1.4,0.3],'Iris_setosa',1,'Alaska'),
+(12,ARRAY[5.1,3.8,1.6,0.2],'Iris_setosa',1,'Alaska'),
+(13,ARRAY[5.7,2.8,4.5,1.3],'Iris_versicolor',2,'Alaska'),
+(14,ARRAY[6.3,3.3,4.7,1.6],'Iris_versicolor',2,'Alaska'),
+(15,ARRAY[4.9,2.4,3.3,1.0],'Iris_versicolor',2,'Alaska'),
+(16,ARRAY[6.6,2.9,4.6,1.3],'Iris_versicolor',2,'Alaska'),
+(17,ARRAY[5.2,2.7,3.9,1.4],'Iris_versicolor',2,'Alaska'),
+(18,ARRAY[5.0,2.0,3.5,1.0],'Iris_versicolor',2,'Alaska'),
+(19,ARRAY[5.9,3.0,4.2,1.5],'Iris_versicolor',2,'Alaska'),
+(20,ARRAY[6.0,2.2,4.0,1.0],'Iris_versicolor',2,'Alaska'),
+(21,ARRAY[6.1,2.9,4.7,1.4],'Iris_versicolor',2,'Alaska'),
+(22,ARRAY[5.6,2.9,3.6,1.3],'Iris_versicolor',2,'Alaska'),
+(23,ARRAY[6.7,3.1,4.4,1.4],'Iris_versicolor',2,'Alaska'),
+(24,ARRAY[5.6,3.0,4.5,1.5],'Iris_versicolor',2,'Alaska'),
+(25,ARRAY[5.8,2.7,4.1,1.0],'Iris_versicolor',2,'Alaska'),
+(26,ARRAY[6.2,2.2,4.5,1.5],'Iris_versicolor',2,'Alaska'),
+(27,ARRAY[5.6,2.5,3.9,1.1],'Iris_versicolor',2,'Alaska'),
+(28,ARRAY[5.0,3.4,1.5,0.2],'Iris_setosa',1,'Tennessee'),
+(29,ARRAY[4.4,2.9,1.4,0.2],'Iris_setosa',1,'Tennessee'),
+(30,ARRAY[4.9,3.1,1.5,0.1],'Iris_setosa',1,'Tennessee'),
+(31,ARRAY[5.4,3.7,1.5,0.2],'Iris_setosa',1,'Tennessee'),
+(32,ARRAY[4.8,3.4,1.6,0.2],'Iris_setosa',1,'Tennessee'),
+(33,ARRAY[4.8,3.0,1.4,0.1],'Iris_setosa',1,'Tennessee'),
+(34,ARRAY[4.3,3.0,1.1,0.1],'Iris_setosa',1,'Tennessee'),
+(35,ARRAY[5.8,4.0,1.2,0.2],'Iris_setosa',1,'Tennessee'),
+(36,ARRAY[5.7,4.4,1.5,0.4],'Iris_setosa',1,'Tennessee'),
+(37,ARRAY[5.4,3.9,1.3,0.4],'Iris_setosa',1,'Tennessee'),
+(38,ARRAY[6.0,2.9,4.5,1.5],'Iris_versicolor',2,'Tennessee'),
+(39,ARRAY[5.7,2.6,3.5,1.0],'Iris_versicolor',2,'Tennessee'),
+(40,ARRAY[5.5,2.4,3.8,1.1],'Iris_versicolor',2,'Tennessee'),
+(41,ARRAY[5.5,2.4,3.7,1.0],'Iris_versicolor',2,'Tennessee'),
+(42,ARRAY[5.8,2.7,3.9,1.2],'Iris_versicolor',2,'Tennessee'),
+(43,ARRAY[6.0,2.7,5.1,1.6],'Iris_versicolor',2,'Tennessee'),
+(44,ARRAY[5.4,3.0,4.5,1.5],'Iris_versicolor',2,'Tennessee'),
+(45,ARRAY[6.0,3.4,4.5,1.6],'Iris_versicolor',2,'Tennessee'),
+(46,ARRAY[6.7,3.1,4.7,1.5],'Iris_versicolor',2,'Tennessee'),
+(47,ARRAY[6.3,2.3,4.4,1.3],'Iris_versicolor',2,'Tennessee'),
+(48,ARRAY[5.6,3.0,4.1,1.3],'Iris_versicolor',2,'Tennessee'),
+(49,ARRAY[5.5,2.5,4.0,1.3],'Iris_versicolor',2,'Tennessee'),
+(50,ARRAY[5.5,2.6,4.4,1.2],'Iris_versicolor',2,'Tennessee'),
+(51,ARRAY[6.1,3.0,4.6,1.4],'Iris_versicolor',2,'Tennessee'),
+(52,ARRAY[5.8,2.6,4.0,1.2],'Iris_versicolor',2,'Tennessee');
+
      2. +
    2. Generate a multilayer perceptron with a single hidden layer of 5 units. Use the attributes column as the independent variables, and use the class column as the classification. Set the tolerance to 0 so that 500 iterations will be run. Use a hyperbolic tangent activation function. The model will be written to mlp_model. 
      +DROP TABLE IF EXISTS mlp_model, mlp_model_summary, mlp_model_standardization;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.mlp_classification(
+    'iris_data',      -- Source table
+    'mlp_model',      -- Destination table
+    'attributes',     -- Input features
+    'class_text',     -- Label
+    ARRAY[5],         -- Number of units per layer
+    'learning_rate_init=0.003,
+    n_iterations=500,
+    tolerance=0',     -- Optimizer params
+    'tanh',           -- Activation function
+    NULL,             -- Default weight (1)
+    FALSE,            -- No warm start
+    FALSE             -- Not verbose
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_model;
+
      +-[ RECORD 1 ]--+------------------------------------------------------------------------------------
+coeff          | {-0.40378996718,0.0157490328855,-0.298904053444,-0.984152185093,-0.657684089715 ...
+loss           | 0.0103518565103
+num_iterations | 500
+
      View the model summary table: 
      +SELECT * FROM mlp_model_summary;
+
      +-[ RECORD 1 ]--------+------------------------------
+source_table         | iris_data
+independent_varname  | attributes
+dependent_varname    | class_text
+dependent_vartype    | character varying
+tolerance            | 0
+learning_rate_init   | 0.003
+learning_rate_policy | constant
+momentum             | 0.9
+nesterov             | t
+n_iterations         | 500
+n_tries              | 1
+layer_sizes          | {4,5,2}
+activation           | tanh
+is_classification    | t
+classes              | {Iris_setosa,Iris_versicolor}
+weights              | 1
+grouping_col         | NULL
+
      View the model standardization table: 
      +SELECT * FROM mlp_model_standardization;
+
      +-[ RECORD 1 ]------------------------------------------------------------------
+mean | {5.45961538461539,2.99807692307692,3.025,0.851923076923077}
+std  | {0.598799958694505,0.498262513685689,1.41840579525043,0.550346179381454}
+
      3. +
    3. Now let's use the model to predict. In the following example we will use the training data set for prediction as well, which is not usual but serves to show the syntax. The prediction is in the estimated_class_text column with the actual value in the class_text column. 
      +DROP TABLE IF EXISTS mlp_prediction;
+\x off
+SELECT madlib.mlp_predict(
+         'mlp_model',         -- Model table
+         'iris_data',         -- Test data table
+         'id',                -- Id column in test table
+         'mlp_prediction',    -- Output table for predictions
+         'response'           -- Output classes, not probabilities
+     );
+SELECT * FROM mlp_prediction JOIN iris_data USING (id) ORDER BY id;
+
      + id | estimated_class_text |    attributes     |   class_text    | class |   state
+----+----------------------+-------------------+-----------------+-------+-----------
+  1 | Iris_setosa          | {5.0,3.2,1.2,0.2} | Iris_setosa     |     1 | Alaska
+  2 | Iris_setosa          | {5.5,3.5,1.3,0.2} | Iris_setosa     |     1 | Alaska
+  3 | Iris_setosa          | {4.9,3.1,1.5,0.1} | Iris_setosa     |     1 | Alaska
+  4 | Iris_setosa          | {4.4,3.0,1.3,0.2} | Iris_setosa     |     1 | Alaska
+  5 | Iris_setosa          | {5.1,3.4,1.5,0.2} | Iris_setosa     |     1 | Alaska
+  6 | Iris_setosa          | {5.0,3.5,1.3,0.3} | Iris_setosa     |     1 | Alaska
+  7 | Iris_setosa          | {4.5,2.3,1.3,0.3} | Iris_setosa     |     1 | Alaska
+  8 | Iris_setosa          | {4.4,3.2,1.3,0.2} | Iris_setosa     |     1 | Alaska
+  9 | Iris_setosa          | {5.0,3.5,1.6,0.6} | Iris_setosa     |     1 | Alaska
+ 10 | Iris_setosa          | {5.1,3.8,1.9,0.4} | Iris_setosa     |     1 | Alaska
+ 11 | Iris_setosa          | {4.8,3.0,1.4,0.3} | Iris_setosa     |     1 | Alaska
+ 12 | Iris_setosa          | {5.1,3.8,1.6,0.2} | Iris_setosa     |     1 | Alaska
+ 13 | Iris_versicolor      | {5.7,2.8,4.5,1.3} | Iris_versicolor |     2 | Alaska
+ 14 | Iris_versicolor      | {6.3,3.3,4.7,1.6} | Iris_versicolor |     2 | Alaska
+ 15 | Iris_versicolor      | {4.9,2.4,3.3,1.0} | Iris_versicolor |     2 | Alaska
+ 16 | Iris_versicolor      | {6.6,2.9,4.6,1.3} | Iris_versicolor |     2 | Alaska
+ 17 | Iris_versicolor      | {5.2,2.7,3.9,1.4} | Iris_versicolor |     2 | Alaska
+ 18 | Iris_versicolor      | {5.0,2.0,3.5,1.0} | Iris_versicolor |     2 | Alaska
+ 19 | Iris_versicolor      | {5.9,3.0,4.2,1.5} | Iris_versicolor |     2 | Alaska
+ 20 | Iris_versicolor      | {6.0,2.2,4.0,1.0} | Iris_versicolor |     2 | Alaska
+ 21 | Iris_versicolor      | {6.1,2.9,4.7,1.4} | Iris_versicolor |     2 | Alaska
+ 22 | Iris_versicolor      | {5.6,2.9,3.6,1.3} | Iris_versicolor |     2 | Alaska
+ 23 | Iris_versicolor      | {6.7,3.1,4.4,1.4} | Iris_versicolor |     2 | Alaska
+ 24 | Iris_versicolor      | {5.6,3.0,4.5,1.5} | Iris_versicolor |     2 | Alaska
+ 25 | Iris_versicolor      | {5.8,2.7,4.1,1.0} | Iris_versicolor |     2 | Alaska
+ 26 | Iris_versicolor      | {6.2,2.2,4.5,1.5} | Iris_versicolor |     2 | Alaska
+ 27 | Iris_versicolor      | {5.6,2.5,3.9,1.1} | Iris_versicolor |     2 | Alaska
+ 28 | Iris_setosa          | {5.0,3.4,1.5,0.2} | Iris_setosa     |     1 | Tennessee
+ 29 | Iris_setosa          | {4.4,2.9,1.4,0.2} | Iris_setosa     |     1 | Tennessee
+ 30 | Iris_setosa          | {4.9,3.1,1.5,0.1} | Iris_setosa     |     1 | Tennessee
+ 31 | Iris_setosa          | {5.4,3.7,1.5,0.2} | Iris_setosa     |     1 | Tennessee
+ 32 | Iris_setosa          | {4.8,3.4,1.6,0.2} | Iris_setosa     |     1 | Tennessee
+ 33 | Iris_setosa          | {4.8,3.0,1.4,0.1} | Iris_setosa     |     1 | Tennessee
+ 34 | Iris_setosa          | {4.3,3.0,1.1,0.1} | Iris_setosa     |     1 | Tennessee
+ 35 | Iris_setosa          | {5.8,4.0,1.2,0.2} | Iris_setosa     |     1 | Tennessee
+ 36 | Iris_setosa          | {5.7,4.4,1.5,0.4} | Iris_setosa     |     1 | Tennessee
+ 37 | Iris_setosa          | {5.4,3.9,1.3,0.4} | Iris_setosa     |     1 | Tennessee
+ 38 | Iris_versicolor      | {6.0,2.9,4.5,1.5} | Iris_versicolor |     2 | Tennessee
+ 39 | Iris_versicolor      | {5.7,2.6,3.5,1.0} | Iris_versicolor |     2 | Tennessee
+ 40 | Iris_versicolor      | {5.5,2.4,3.8,1.1} | Iris_versicolor |     2 | Tennessee
+ 41 | Iris_versicolor      | {5.5,2.4,3.7,1.0} | Iris_versicolor |     2 | Tennessee
+ 42 | Iris_versicolor      | {5.8,2.7,3.9,1.2} | Iris_versicolor |     2 | Tennessee
+ 43 | Iris_versicolor      | {6.0,2.7,5.1,1.6} | Iris_versicolor |     2 | Tennessee
+ 44 | Iris_versicolor      | {5.4,3.0,4.5,1.5} | Iris_versicolor |     2 | Tennessee
+ 45 | Iris_versicolor      | {6.0,3.4,4.5,1.6} | Iris_versicolor |     2 | Tennessee
+ 46 | Iris_versicolor      | {6.7,3.1,4.7,1.5} | Iris_versicolor |     2 | Tennessee
+ 47 | Iris_versicolor      | {6.3,2.3,4.4,1.3} | Iris_versicolor |     2 | Tennessee
+ 48 | Iris_versicolor      | {5.6,3.0,4.1,1.3} | Iris_versicolor |     2 | Tennessee
+ 49 | Iris_versicolor      | {5.5,2.5,4.0,1.3} | Iris_versicolor |     2 | Tennessee
+ 50 | Iris_versicolor      | {5.5,2.6,4.4,1.2} | Iris_versicolor |     2 | Tennessee
+ 51 | Iris_versicolor      | {6.1,3.0,4.6,1.4} | Iris_versicolor |     2 | Tennessee
+ 52 | Iris_versicolor      | {5.8,2.6,4.0,1.2} | Iris_versicolor |     2 | Tennessee
+(52 rows)
+
      Count the misclassifications: 
      +SELECT COUNT(*) FROM mlp_prediction JOIN iris_data USING (id)
+WHERE mlp_prediction.estimated_class_text != iris_data.class_text;
+
      + count
+-------+
+     0
+
      4. +
    +

    Classification with Mini-Batching

    +
      +
    1. Use the same data set as above. Call mini-batch preprocessor: 
      +DROP TABLE IF EXISTS iris_data_packed, iris_data_packed_summary, iris_data_packed_standardization;
+SELECT madlib.minibatch_preprocessor('iris_data',         -- Source table
+                                     'iris_data_packed',  -- Output table
+                                     'class_text',        -- Dependent variable
+                                     'attributes'        -- Independent variables
+                                    );
+
      2. +
    2. Train the classification model using similar parameters as before: 
      +DROP TABLE IF EXISTS mlp_model, mlp_model_summary, mlp_model_standardization;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.mlp_classification(
+    'iris_data_packed',      -- Output table from mini-batch preprocessor
+    'mlp_model',             -- Destination table
+    'independent_varname',   -- Hardcode to this, from table iris_data_packed
+    'dependent_varname',     -- Hardcode to this, from table iris_data_packed
+    ARRAY[5],                -- Number of units per layer
+    'learning_rate_init=0.1,
+    n_iterations=500,
+    tolerance=0',            -- Optimizer params
+    'tanh',                  -- Activation function
+    NULL,                    -- Default weight (1)
+    FALSE,                   -- No warm start
+    FALSE                    -- Not verbose
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_model;
+
      +-[ RECORD 1 ]--+------------------------------------------------------------------------------------
+coeff          | {-0.0780564661828377,-0.0781452670639994,0.3083605989842 ...
+loss           | 0.00563534904146765
+num_iterations | 500
+
      3. +
    3. Now let's use the model to predict. As before we will use the training data set for prediction as well, which is not usual but serves to show the syntax. The prediction is in the estimated_class_text column with the actual value in the class_text column. 
      +DROP TABLE IF EXISTS mlp_prediction;
+\x off
+SELECT madlib.mlp_predict(
+         'mlp_model',         -- Model table
+         'iris_data',         -- Test data table
+         'id',                -- Id column in test table
+         'mlp_prediction',    -- Output table for predictions
+         'response'           -- Output classes, not probabilities
+     );
+SELECT * FROM mlp_prediction JOIN iris_data USING (id) ORDER BY id;
+
      + id | estimated_class_text |    attributes     |   class_text    | class |   state
+----+----------------------+-------------------+-----------------+-------+-----------
+  1 | Iris_setosa          | {5.0,3.2,1.2,0.2} | Iris_setosa     |     1 | Alaska
+  2 | Iris_setosa          | {5.5,3.5,1.3,0.2} | Iris_setosa     |     1 | Alaska
+  3 | Iris_setosa          | {4.9,3.1,1.5,0.1} | Iris_setosa     |     1 | Alaska
+  4 | Iris_setosa          | {4.4,3.0,1.3,0.2} | Iris_setosa     |     1 | Alaska
+  5 | Iris_setosa          | {5.1,3.4,1.5,0.2} | Iris_setosa     |     1 | Alaska
+  6 | Iris_setosa          | {5.0,3.5,1.3,0.3} | Iris_setosa     |     1 | Alaska
+  7 | Iris_setosa          | {4.5,2.3,1.3,0.3} | Iris_setosa     |     1 | Alaska
+  8 | Iris_setosa          | {4.4,3.2,1.3,0.2} | Iris_setosa     |     1 | Alaska
+  9 | Iris_setosa          | {5.0,3.5,1.6,0.6} | Iris_setosa     |     1 | Alaska
+ 10 | Iris_setosa          | {5.1,3.8,1.9,0.4} | Iris_setosa     |     1 | Alaska
+ 11 | Iris_setosa          | {4.8,3.0,1.4,0.3} | Iris_setosa     |     1 | Alaska
+ 12 | Iris_setosa          | {5.1,3.8,1.6,0.2} | Iris_setosa     |     1 | Alaska
+ 13 | Iris_versicolor      | {5.7,2.8,4.5,1.3} | Iris_versicolor |     2 | Alaska
+ 14 | Iris_versicolor      | {6.3,3.3,4.7,1.6} | Iris_versicolor |     2 | Alaska
+ 15 | Iris_versicolor      | {4.9,2.4,3.3,1.0} | Iris_versicolor |     2 | Alaska
+ 16 | Iris_versicolor      | {6.6,2.9,4.6,1.3} | Iris_versicolor |     2 | Alaska
+ 17 | Iris_versicolor      | {5.2,2.7,3.9,1.4} | Iris_versicolor |     2 | Alaska
+ 18 | Iris_versicolor      | {5.0,2.0,3.5,1.0} | Iris_versicolor |     2 | Alaska
+ 19 | Iris_versicolor      | {5.9,3.0,4.2,1.5} | Iris_versicolor |     2 | Alaska
+ 20 | Iris_versicolor      | {6.0,2.2,4.0,1.0} | Iris_versicolor |     2 | Alaska
+ 21 | Iris_versicolor      | {6.1,2.9,4.7,1.4} | Iris_versicolor |     2 | Alaska
+ 22 | Iris_versicolor      | {5.6,2.9,3.6,1.3} | Iris_versicolor |     2 | Alaska
+ 23 | Iris_versicolor      | {6.7,3.1,4.4,1.4} | Iris_versicolor |     2 | Alaska
+ 24 | Iris_versicolor      | {5.6,3.0,4.5,1.5} | Iris_versicolor |     2 | Alaska
+ 25 | Iris_versicolor      | {5.8,2.7,4.1,1.0} | Iris_versicolor |     2 | Alaska
+ 26 | Iris_versicolor      | {6.2,2.2,4.5,1.5} | Iris_versicolor |     2 | Alaska
+ 27 | Iris_versicolor      | {5.6,2.5,3.9,1.1} | Iris_versicolor |     2 | Alaska
+ 28 | Iris_setosa          | {5.0,3.4,1.5,0.2} | Iris_setosa     |     1 | Tennessee
+ 29 | Iris_setosa          | {4.4,2.9,1.4,0.2} | Iris_setosa     |     1 | Tennessee
+ 30 | Iris_setosa          | {4.9,3.1,1.5,0.1} | Iris_setosa     |     1 | Tennessee
+ 31 | Iris_setosa          | {5.4,3.7,1.5,0.2} | Iris_setosa     |     1 | Tennessee
+ 32 | Iris_setosa          | {4.8,3.4,1.6,0.2} | Iris_setosa     |     1 | Tennessee
+ 33 | Iris_setosa          | {4.8,3.0,1.4,0.1} | Iris_setosa     |     1 | Tennessee
+ 34 | Iris_setosa          | {4.3,3.0,1.1,0.1} | Iris_setosa     |     1 | Tennessee
+ 35 | Iris_setosa          | {5.8,4.0,1.2,0.2} | Iris_setosa     |     1 | Tennessee
+ 36 | Iris_setosa          | {5.7,4.4,1.5,0.4} | Iris_setosa     |     1 | Tennessee
+ 37 | Iris_setosa          | {5.4,3.9,1.3,0.4} | Iris_setosa     |     1 | Tennessee
+ 38 | Iris_versicolor      | {6.0,2.9,4.5,1.5} | Iris_versicolor |     2 | Tennessee
+ 39 | Iris_versicolor      | {5.7,2.6,3.5,1.0} | Iris_versicolor |     2 | Tennessee
+ 40 | Iris_versicolor      | {5.5,2.4,3.8,1.1} | Iris_versicolor |     2 | Tennessee
+ 41 | Iris_versicolor      | {5.5,2.4,3.7,1.0} | Iris_versicolor |     2 | Tennessee
+ 42 | Iris_versicolor      | {5.8,2.7,3.9,1.2} | Iris_versicolor |     2 | Tennessee
+ 43 | Iris_versicolor      | {6.0,2.7,5.1,1.6} | Iris_versicolor |     2 | Tennessee
+ 44 | Iris_versicolor      | {5.4,3.0,4.5,1.5} | Iris_versicolor |     2 | Tennessee
+ 45 | Iris_versicolor      | {6.0,3.4,4.5,1.6} | Iris_versicolor |     2 | Tennessee
+ 46 | Iris_versicolor      | {6.7,3.1,4.7,1.5} | Iris_versicolor |     2 | Tennessee
+ 47 | Iris_versicolor      | {6.3,2.3,4.4,1.3} | Iris_versicolor |     2 | Tennessee
+ 48 | Iris_versicolor      | {5.6,3.0,4.1,1.3} | Iris_versicolor |     2 | Tennessee
+ 49 | Iris_versicolor      | {5.5,2.5,4.0,1.3} | Iris_versicolor |     2 | Tennessee
+ 50 | Iris_versicolor      | {5.5,2.6,4.4,1.2} | Iris_versicolor |     2 | Tennessee
+ 51 | Iris_versicolor      | {6.1,3.0,4.6,1.4} | Iris_versicolor |     2 | Tennessee
+ 52 | Iris_versicolor      | {5.8,2.6,4.0,1.2} | Iris_versicolor |     2 | Tennessee
+(52 rows)
+
      Count the misclassifications: 
      +SELECT COUNT(*) FROM mlp_prediction JOIN iris_data USING (id)
+WHERE mlp_prediction.estimated_class_text != iris_data.class_text;
+
      + count
+-------+
+     0
+
      4. +
    +

    Classification with Other Parameters

    +
      +
    1. Now, use the n_tries optimizer parameter to learn and choose the best model among n_tries number of models learnt by the algorithm. Run only for 50 iterations and choose the best model from this short run. Note we are not using mini-batching here. 
      +DROP TABLE IF EXISTS mlp_model, mlp_model_summary, mlp_model_standardization;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.mlp_classification(
+    'iris_data',      -- Source table
+    'mlp_model',      -- Destination table
+    'attributes',     -- Input features
+    'class_text',     -- Label
+    ARRAY[5],         -- Number of units per layer
+    'learning_rate_init=0.003,
+    n_iterations=50,
+    tolerance=0,
+    n_tries=3',       -- Optimizer params, with n_tries
+    'tanh',           -- Activation function
+    NULL,             -- Default weight (1)
+    FALSE,            -- No warm start
+    FALSE             -- Not verbose
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_model;
+
      +-[ RECORD 1 ]--+------------------------------------------------------------------------------------
+coeff          | {0.000156316559088915,0.131131017223563,-0.293990512682215 ...
+loss           | 0.142238768280717
+num_iterations | 50
+
      2. +
    2. Next, use the warm_start parameter to start learning a new model, using the coefficients already present in mlp_model. Note that we must not drop the mlp_model table, and cannot use the n_tries parameter if warm_start is used. 
      +SELECT madlib.mlp_classification(
+    'iris_data',      -- Source table
+    'mlp_model',      -- Destination table
+    'attributes',     -- Input features
+    'class_text',     -- Label
+    ARRAY[5],         -- Number of units per layer
+    'learning_rate_init=0.003,
+    n_iterations=450,
+    tolerance=0',     -- Optimizer params
+    'tanh',           -- Activation function
+    NULL,             -- Default weight (1)
+    TRUE,             -- Warm start
+    FALSE             -- Not verbose
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_model;
+
      +-[ RECORD 1 ]--+------------------------------------------------------------------------------------
+coeff          | {0.0883013960215441,0.235944854050211,-0.398126039487036 ...
+loss           | 0.00818899646775659
+num_iterations | 450
+
      Notice that the loss is lower compared to the previous example, despite having the same values for every other parameter. This is because the algorithm learned three different models starting with a different set of initial weights for the coefficients, and chose the best model among them as the initial weights for the coefficients when run with warm start.
      3. +
    3. Next, test adam solver for adaptive learning rates. Note that we are using the minibatched dataset. 
      +DROP TABLE IF EXISTS mlp_model, mlp_model_summary, mlp_model_standardization;
+SELECT madlib.mlp_classification(
+    'iris_data_packed',      -- Output table from mini-batch preprocessor
+    'mlp_model',             -- Destination table
+    'independent_varname',   -- Hardcode to this, from table iris_data_packed
+    'dependent_varname',     -- Hardcode to this, from table iris_data_packed
+    ARRAY[5],                -- Number of units per layer
+    'learning_rate_init=0.1,
+    n_iterations=500,
+    tolerance=0.0001,
+    solver=adam',            -- Optimizer params
+    'tanh',                  -- Activation function
+    NULL,                    -- Default weight (1)
+    FALSE,                   -- No warm start
+    FALSE                    -- Not verbose
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_model;
+
      +-[ RECORD 1 ]--+------------------------------------------------------------------------------------
+coeff          | {5.39258022025872,0.674679083739714,-2.59002712311116 ...
+loss           | 0.155612432637527
+num_iterations | 500
+
      4. +
    +

    Classification with Grouping

    +
      +
    1. Next, group the training data by state, and learn a different model for each state. Note we are not using mini-batching in this example. 
      +DROP TABLE IF EXISTS mlp_model_group, mlp_model_group_summary, mlp_model_group_standardization;
+-- Set seed so results are reproducible
+SELECT setseed(0);
+SELECT madlib.mlp_classification(
+    'iris_data',        -- Source table
+    'mlp_model_group',  -- Destination table
+    'attributes',       -- Input features
+    'class_text',       -- Label
+    ARRAY[5],           -- Number of units per layer
+    'learning_rate_init=0.003,
+    n_iterations=500,   -- Optimizer params
+    tolerance=0',
+    'tanh',             -- Activation function
+    NULL,               -- Default weight (1)
+    FALSE,              -- No warm start
+    FALSE,              -- Not verbose
+    'state'             -- Grouping column
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_model_group ORDER BY state;
+
      +-[ RECORD 1 ]--+------------------------------------------------------------------------------------
+state          | Alaska
+coeff          | {-0.51246602223,-0.78952457411,0.454192045225,0.223214894458,0.188804700547 ...
+loss           | 0.0225081995679
+num_iterations | 500
+-[ RECORD 2 ]--+------------------------------------------------------------------------------------
+state          | Tennessee
+coeff          | {-0.215009937565,0.116581594162,-0.397643279185,0.919193295184,-0.0811341736111 ...
+loss           | 0.0182854983946
+num_iterations | 500
+
      A separate model is learnt for each state, and the result table displays the name of the state (grouping column) associated with the model.
      2. +
    2. Prediction based on grouping using the state column: 
      +\x off
+DROP TABLE IF EXISTS mlp_prediction;
+SELECT madlib.mlp_predict(
+         'mlp_model_group',   -- Model table
+         'iris_data',         -- Test data table
+         'id',                -- Id column in test table
+         'mlp_prediction',    -- Output table for predictions
+         'response'           -- Output classes, not probabilities
+     );
+SELECT * FROM mlp_prediction JOIN iris_data USING (state,id) ORDER BY state, id;
+
      Result for the classification model: 
      +   state   | id | estimated_class_text |    attributes     |   class_text    | class
+-----------+----+----------------------+-------------------+-----------------+-------
+ Alaska    |  1 | Iris_setosa          | {5.0,3.2,1.2,0.2} | Iris_setosa     |     1
+ Alaska    |  2 | Iris_setosa          | {5.5,3.5,1.3,0.2} | Iris_setosa     |     1
+ Alaska    |  3 | Iris_setosa          | {4.9,3.1,1.5,0.1} | Iris_setosa     |     1
+ Alaska    |  4 | Iris_setosa          | {4.4,3.0,1.3,0.2} | Iris_setosa     |     1
+ Alaska    |  5 | Iris_setosa          | {5.1,3.4,1.5,0.2} | Iris_setosa     |     1
+ Alaska    |  6 | Iris_setosa          | {5.0,3.5,1.3,0.3} | Iris_setosa     |     1
+ Alaska    |  7 | Iris_setosa          | {4.5,2.3,1.3,0.3} | Iris_setosa     |     1
+ Alaska    |  8 | Iris_setosa          | {4.4,3.2,1.3,0.2} | Iris_setosa     |     1
+ Alaska    |  9 | Iris_setosa          | {5.0,3.5,1.6,0.6} | Iris_setosa     |     1
+ Alaska    | 10 | Iris_setosa          | {5.1,3.8,1.9,0.4} | Iris_setosa     |     1
+ Alaska    | 11 | Iris_setosa          | {4.8,3.0,1.4,0.3} | Iris_setosa     |     1
+ Alaska    | 12 | Iris_setosa          | {5.1,3.8,1.6,0.2} | Iris_setosa     |     1
+ Alaska    | 13 | Iris_versicolor      | {5.7,2.8,4.5,1.3} | Iris_versicolor |     2
+ Alaska    | 14 | Iris_versicolor      | {6.3,3.3,4.7,1.6} | Iris_versicolor |     2
+ Alaska    | 15 | Iris_versicolor      | {4.9,2.4,3.3,1.0} | Iris_versicolor |     2
+ Alaska    | 16 | Iris_versicolor      | {6.6,2.9,4.6,1.3} | Iris_versicolor |     2
+ Alaska    | 17 | Iris_versicolor      | {5.2,2.7,3.9,1.4} | Iris_versicolor |     2
+ Alaska    | 18 | Iris_versicolor      | {5.0,2.0,3.5,1.0} | Iris_versicolor |     2
+ Alaska    | 19 | Iris_versicolor      | {5.9,3.0,4.2,1.5} | Iris_versicolor |     2
+ Alaska    | 20 | Iris_versicolor      | {6.0,2.2,4.0,1.0} | Iris_versicolor |     2
+ Alaska    | 21 | Iris_versicolor      | {6.1,2.9,4.7,1.4} | Iris_versicolor |     2
+ Alaska    | 22 | Iris_versicolor      | {5.6,2.9,3.6,1.3} | Iris_versicolor |     2
+ Alaska    | 23 | Iris_versicolor      | {6.7,3.1,4.4,1.4} | Iris_versicolor |     2
+ Alaska    | 24 | Iris_versicolor      | {5.6,3.0,4.5,1.5} | Iris_versicolor |     2
+ Alaska    | 25 | Iris_versicolor      | {5.8,2.7,4.1,1.0} | Iris_versicolor |     2
+ Alaska    | 26 | Iris_versicolor      | {6.2,2.2,4.5,1.5} | Iris_versicolor |     2
+ Alaska    | 27 | Iris_versicolor      | {5.6,2.5,3.9,1.1} | Iris_versicolor |     2
+ Tennessee | 28 | Iris_setosa          | {5.0,3.4,1.5,0.2} | Iris_setosa     |     1
+ Tennessee | 29 | Iris_setosa          | {4.4,2.9,1.4,0.2} | Iris_setosa     |     1
+ Tennessee | 30 | Iris_setosa          | {4.9,3.1,1.5,0.1} | Iris_setosa     |     1
+ Tennessee | 31 | Iris_setosa          | {5.4,3.7,1.5,0.2} | Iris_setosa     |     1
+ Tennessee | 32 | Iris_setosa          | {4.8,3.4,1.6,0.2} | Iris_setosa     |     1
+ Tennessee | 33 | Iris_setosa          | {4.8,3.0,1.4,0.1} | Iris_setosa     |     1
+ Tennessee | 34 | Iris_setosa          | {4.3,3.0,1.1,0.1} | Iris_setosa     |     1
+ Tennessee | 35 | Iris_setosa          | {5.8,4.0,1.2,0.2} | Iris_setosa     |     1
+ Tennessee | 36 | Iris_setosa          | {5.7,4.4,1.5,0.4} | Iris_setosa     |     1
+ Tennessee | 37 | Iris_setosa          | {5.4,3.9,1.3,0.4} | Iris_setosa     |     1
+ Tennessee | 38 | Iris_versicolor      | {6.0,2.9,4.5,1.5} | Iris_versicolor |     2
+ Tennessee | 39 | Iris_versicolor      | {5.7,2.6,3.5,1.0} | Iris_versicolor |     2
+ Tennessee | 40 | Iris_versicolor      | {5.5,2.4,3.8,1.1} | Iris_versicolor |     2
+ Tennessee | 41 | Iris_versicolor      | {5.5,2.4,3.7,1.0} | Iris_versicolor |     2
+ Tennessee | 42 | Iris_versicolor      | {5.8,2.7,3.9,1.2} | Iris_versicolor |     2
+ Tennessee | 43 | Iris_versicolor      | {6.0,2.7,5.1,1.6} | Iris_versicolor |     2
+ Tennessee | 44 | Iris_versicolor      | {5.4,3.0,4.5,1.5} | Iris_versicolor |     2
+ Tennessee | 45 | Iris_versicolor      | {6.0,3.4,4.5,1.6} | Iris_versicolor |     2
+ Tennessee | 46 | Iris_versicolor      | {6.7,3.1,4.7,1.5} | Iris_versicolor |     2
+ Tennessee | 47 | Iris_versicolor      | {6.3,2.3,4.4,1.3} | Iris_versicolor |     2
+ Tennessee | 48 | Iris_versicolor      | {5.6,3.0,4.1,1.3} | Iris_versicolor |     2
+ Tennessee | 49 | Iris_versicolor      | {5.5,2.5,4.0,1.3} | Iris_versicolor |     2
+ Tennessee | 50 | Iris_versicolor      | {5.5,2.6,4.4,1.2} | Iris_versicolor |     2
+ Tennessee | 51 | Iris_versicolor      | {6.1,3.0,4.6,1.4} | Iris_versicolor |     2
+ Tennessee | 52 | Iris_versicolor      | {5.8,2.6,4.0,1.2} | Iris_versicolor |     2
+(52 rows)
+
      3. +
    +

    Regression without Mini-Batching

    +
      +
    1. Create a dataset with housing prices data. 
      +DROP TABLE IF EXISTS lin_housing;
+CREATE TABLE lin_housing (id serial, x numeric[], zipcode int, y float8);
+INSERT INTO lin_housing(id, x, zipcode, y) VALUES
+(1,ARRAY[1,0.00632,18.00,2.310,0,0.5380,6.5750,65.20,4.0900,1,296.0,15.30,396.90,4.98],94016,24.00),
+(2,ARRAY[1,0.02731,0.00,7.070,0,0.4690,6.4210,78.90,4.9671,2,242.0,17.80,396.90,9.14],94016,21.60),
+(3,ARRAY[1,0.02729,0.00,7.070,0,0.4690,7.1850,61.10,4.9671,2,242.0,17.80,392.83,4.03],94016,34.70),
+(4,ARRAY[1,0.03237,0.00,2.180,0,0.4580,6.9980,45.80,6.0622,3,222.0,18.70,394.63,2.94],94016,33.40),
+(5,ARRAY[1,0.06905,0.00,2.180,0,0.4580,7.1470,54.20,6.0622,3,222.0,18.70,396.90,5.33],94016,36.20),
+(6,ARRAY[1,0.02985,0.00,2.180,0,0.4580,6.4300,58.70,6.0622,3,222.0,18.70,394.12,5.21],94016,28.70),
+(7,ARRAY[1,0.08829,12.50,7.870,0,0.5240,6.0120,66.60,5.5605,5,311.0,15.20,395.60,12.43],94016,22.90),
+(8,ARRAY[1,0.14455,12.50,7.870,0,0.5240,6.1720,96.10,5.9505,5,311.0,15.20,396.90,19.15],94016,27.10),
+(9,ARRAY[1,0.21124,12.50,7.870,0,0.5240,5.6310,100.00,6.0821,5,311.0,15.20,386.63,29.93],94016,16.50),
+(10,ARRAY[1,0.17004,12.50,7.870,0,0.5240,6.0040,85.90,6.5921,5,311.0,15.20,386.71,17.10],94016,18.90),
+(11,ARRAY[1,0.22489,12.50,7.870,0,0.5240,6.3770,94.30,6.3467,5,311.0,15.20,392.52,20.45],94016,15.00),
+(12,ARRAY[1,0.11747,12.50,7.870,0,0.5240,6.0090,82.90,6.2267,5,311.0,15.20,396.90,13.27],20001,18.90),
+(13,ARRAY[1,0.09378,12.50,7.870,0,0.5240,5.8890,39.00,5.4509,5,311.0,15.20,390.50,15.71],20001,21.70),
+(14,ARRAY[1,0.62976,0.00,8.140,0,0.5380,5.9490,61.80,4.7075,4,307.0,21.00,396.90,8.26],20001,20.40),
+(15,ARRAY[1,0.63796,0.00,8.140,0,0.5380,6.0960,84.50,4.4619,4,307.0,21.00,380.02,10.26],20001,18.20),
+(16,ARRAY[1,0.62739,0.00,8.140,0,0.5380,5.8340,56.50,4.4986,4,307.0,21.00,395.62,8.47],20001,19.90),
+(17,ARRAY[1,1.05393,0.00,8.140,0,0.5380,5.9350,29.30,4.4986,4,307.0,21.00,386.85,6.58],20001, 23.10),
+(18,ARRAY[1,0.78420,0.00,8.140,0,0.5380,5.9900,81.70,4.2579,4,307.0,21.00,386.75,14.67],20001,17.50),
+(19,ARRAY[1,0.80271,0.00,8.140,0,0.5380,5.4560,36.60,3.7965,4,307.0,21.00,288.99,11.69],20001,20.20),
+(20,ARRAY[1,0.72580,0.00,8.140,0,0.5380,5.7270,69.50,3.7965,4,307.0,21.00,390.95,11.28],20001,18.20);
+
      2. +
    2. Now train a regression model using a multilayer perceptron with two hidden layers of twenty five nodes each: 
      +DROP TABLE IF EXISTS mlp_regress, mlp_regress_summary, mlp_regress_standardization;
+SELECT setseed(0);
+SELECT madlib.mlp_regression(
+    'lin_housing',    -- Source table
+    'mlp_regress',    -- Desination table
+    'x',              -- Input features
+    'y',              -- Dependent variable
+    ARRAY[25,25],     -- Number of units per layer
+    'learning_rate_init=0.001,
+    n_iterations=500,
+    lambda=0.001,
+    tolerance=0',     -- Optimizer params
+    'relu',           -- Activation function
+    NULL,             -- Default weight (1)
+    FALSE,            -- No warm start
+    FALSE             -- Not verbose
+);
+
      View the model: 
      +\x on
+SELECT * FROM mlp_regress;
+
      +[ RECORD 1 ]--+-------------------------------------------------------------------------------------
+coeff          | {-0.250057620174,0.0630805938982,-0.290635490112,-0.382966162592,-0.212206338909...
+loss           | 1.07042781236
+num_iterations | 500
+
      3. +
    3. Prediction using the regression model: 
      +DROP TABLE IF EXISTS mlp_regress_prediction;
+SELECT madlib.mlp_predict(
+         'mlp_regress',               -- Model table
+         'lin_housing',               -- Test data table
+         'id',                        -- Id column in test table
+         'mlp_regress_prediction',    -- Output table for predictions
+         'response'                   -- Output values, not probabilities
+     );
+
      View results: 
      +\x off
+SELECT * FROM lin_housing JOIN mlp_regress_prediction USING (id) ORDER BY id;
+
      + id |                                         x                                        | zipcode |  y   |   estimated_y
+----+----------------------------------------------------------------------------------+---------+------+------------------
+  1 | {1,0.00632,18.00,2.310,0,0.5380,6.5750,65.20,4.0900,1,296.0,15.30,396.90,4.98}   |   94016 |   24 | 23.9989087488259
+  2 | {1,0.02731,0.00,7.070,0,0.4690,6.4210,78.90,4.9671,2,242.0,17.80,396.90,9.14}    |   94016 | 21.6 | 21.5983177932005
+  3 | {1,0.02729,0.00,7.070,0,0.4690,7.1850,61.10,4.9671,2,242.0,17.80,392.83,4.03}    |   94016 | 34.7 | 34.7102398021623
+  4 | {1,0.03237,0.00,2.180,0,0.4580,6.9980,45.80,6.0622,3,222.0,18.70,394.63,2.94}    |   94016 | 33.4 | 33.4221257351015
+  5 | {1,0.06905,0.00,2.180,0,0.4580,7.1470,54.20,6.0622,3,222.0,18.70,396.90,5.33}    |   94016 | 36.2 | 36.1523886001663
+  6 | {1,0.02985,0.00,2.180,0,0.4580,6.4300,58.70,6.0622,3,222.0,18.70,394.12,5.21}    |   94016 | 28.7 |  28.723894783928
+  7 | {1,0.08829,12.50,7.870,0,0.5240,6.0120,66.60,5.5605,5,311.0,15.20,395.60,12.43}  |   94016 | 22.9 | 22.6515242795835
+  8 | {1,0.14455,12.50,7.870,0,0.5240,6.1720,96.10,5.9505,5,311.0,15.20,396.90,19.15}  |   94016 | 27.1 | 25.7615314879354
+  9 | {1,0.21124,12.50,7.870,0,0.5240,5.6310,100.00,6.0821,5,311.0,15.20,386.63,29.93} |   94016 | 16.5 | 15.7368298351732
+ 10 | {1,0.17004,12.50,7.870,0,0.5240,6.0040,85.90,6.5921,5,311.0,15.20,386.71,17.10}  |   94016 | 18.9 | 16.8850496141437
+ 11 | {1,0.22489,12.50,7.870,0,0.5240,6.3770,94.30,6.3467,5,311.0,15.20,392.52,20.45}  |   94016 |   15 | 14.9150416339458
+ 12 | {1,0.11747,12.50,7.870,0,0.5240,6.0090,82.90,6.2267,5,311.0,15.20,396.90,13.27}  |   20001 | 18.9 | 19.4541629864106
+ 13 | {1,0.09378,12.50,7.870,0,0.5240,5.8890,39.00,5.4509,5,311.0,15.20,390.50,15.71}  |   20001 | 21.7 |  21.715554997762
+ 14 | {1,0.62976,0.00,8.140,0,0.5380,5.9490,61.80,4.7075,4,307.0,21.00,396.90,8.26}    |   20001 | 20.4 | 20.3181247234996
+ 15 | {1,0.63796,0.00,8.140,0,0.5380,6.0960,84.50,4.4619,4,307.0,21.00,380.02,10.26}   |   20001 | 18.2 | 18.5026399122209
+ 16 | {1,0.62739,0.00,8.140,0,0.5380,5.8340,56.50,4.4986,4,307.0,21.00,395.62,8.47}    |   20001 | 19.9 | 19.9131696333521
+ 17 | {1,1.05393,0.00,8.140,0,0.5380,5.9350,29.30,4.4986,4,307.0,21.00,386.85,6.58}    |   20001 | 23.1 | 23.1757650468106
+ 18 | {1,0.78420,0.00,8.140,0,0.5380,5.9900,81.70,4.2579,4,307.0,21.00,386.75,14.67}   |   20001 | 17.5 | 17.2671872543377
+ 19 | {1,0.80271,0.00,8.140,0,0.5380,5.4560,36.60,3.7965,4,307.0,21.00,288.99,11.69}   |   20001 | 20.2 | 20.1073474558796
+ 20 | {1,0.72580,0.00,8.140,0,0.5380,5.7270,69.50,3.7965,4,307.0,21.00,390.95,11.28}   |   20001 | 18.2 | 18.2143446340975
+(20 rows)
+
      RMS error: 
      +SELECT SQRT(AVG((y-estimated_y)*(y-estimated_y))) as rms_error FROM lin_housing
+JOIN mlp_regress_prediction USING (id);
+
      +    rms_error
+------------------+
+ 0.544960829104004
+
      4. +
    +

    Regression with Mini-Batching

    +
      +
    1. Call min-batch preprocessor using the same data set as above: 
      +DROP TABLE IF EXISTS lin_housing_packed, lin_housing_packed_summary, lin_housing_packed_standardization;
+SELECT madlib.minibatch_preprocessor('lin_housing',         -- Source table
+                                     'lin_housing_packed',  -- Output table
+                                     'y',                   -- Dependent variable
+                                     'x'                   -- Independent variables
+                                     );
+
      2. +
    2. Train regression model with mini-batching 
      +DROP TABLE IF EXISTS mlp_regress, mlp_regress_summary, mlp_regress_standardization;
+SELECT setseed(0);
+SELECT madlib.mlp_regression(
+    'lin_housing_packed',    -- Source table
+    'mlp_regress',           -- Desination table
+    'independent_varname',   -- Hardcode to this, from table lin_housing_packed
+    'dependent_varname',     -- Hardcode to this, from table lin_housing_packed
+    ARRAY[25,25],            -- Number of units per layer
+    'learning_rate_init=0.01,
+    n_iterations=500,
+    lambda=0.001,
+    tolerance=0',            -- Optimizer params
+    'tanh',                  -- Activation function
+    NULL,                    -- Default weight (1)
+    FALSE,                   -- No warm start
+    FALSE                    -- Not verbose
+);
+
      View model: 
      +\x on
+SELECT * FROM mlp_regress;
+
      +-[ RECORD 1 ]--+-------------------------------------------------------------
+coeff          | {0.0395865908810001,-0.164860448878703,-0.132787863194324...
+loss           | 0.0442383714892138
+num_iterations | 500
+
      3. +
    3. Prediction for regression: 
      +DROP TABLE IF EXISTS mlp_regress_prediction;
+SELECT madlib.mlp_predict(
+         'mlp_regress',               -- Model table
+         'lin_housing',               -- Test data table
+         'id',                        -- Id column in test table
+         'mlp_regress_prediction',    -- Output table for predictions
+         'response'                   -- Output values, not probabilities
+     );
+\x off
+SELECT *, ABS(y-estimated_y) as abs_diff FROM lin_housing JOIN mlp_regress_prediction USING (id) ORDER BY id;
+
      + id |                                        x                                         | zipcode |  y   | zipcode |   estimated_y    |      abs_diff
+----+----------------------------------------------------------------------------------+---------+------+---------+------------------+--------------------
+  1 | {1,0.00632,18.00,2.310,0,0.5380,6.5750,65.20,4.0900,1,296.0,15.30,396.90,4.98}   |   94016 |   24 |   94016 | 23.9714991250013 | 0.0285008749987092
+  2 | {1,0.02731,0.00,7.070,0,0.4690,6.4210,78.90,4.9671,2,242.0,17.80,396.90,9.14}    |   94016 | 21.6 |   94016 | 22.3655180133895 |  0.765518013389535
+  3 | {1,0.02729,0.00,7.070,0,0.4690,7.1850,61.10,4.9671,2,242.0,17.80,392.83,4.03}    |   94016 | 34.7 |   94016 | 33.8620767428645 |  0.837923257135465
+  4 | {1,0.03237,0.00,2.180,0,0.4580,6.9980,45.80,6.0622,3,222.0,18.70,394.63,2.94}    |   94016 | 33.4 |   94016 | 35.3094157686524 |   1.90941576865244
+  5 | {1,0.06905,0.00,2.180,0,0.4580,7.1470,54.20,6.0622,3,222.0,18.70,396.90,5.33}    |   94016 | 36.2 |   94016 | 35.0379122731818 |   1.16208772681817
+  6 | {1,0.02985,0.00,2.180,0,0.4580,6.4300,58.70,6.0622,3,222.0,18.70,394.12,5.21}    |   94016 | 28.7 |   94016 | 27.5207943492151 |   1.17920565078487
+  7 | {1,0.08829,12.50,7.870,0,0.5240,6.0120,66.60,5.5605,5,311.0,15.20,395.60,12.43}  |   94016 | 22.9 |   94016 | 24.9841422781166 |    2.0841422781166
+  8 | {1,0.14455,12.50,7.870,0,0.5240,6.1720,96.10,5.9505,5,311.0,15.20,396.90,19.15}  |   94016 | 27.1 |   94016 | 24.5403994064793 |   2.55960059352067
+  9 | {1,0.21124,12.50,7.870,0,0.5240,5.6310,100.00,6.0821,5,311.0,15.20,386.63,29.93} |   94016 | 16.5 |   94016 | 17.2588278443879 |   0.75882784438787
+ 10 | {1,0.17004,12.50,7.870,0,0.5240,6.0040,85.90,6.5921,5,311.0,15.20,386.71,17.10}  |   94016 | 18.9 |   94016 | 17.0600407532569 |    1.8399592467431
+ 11 | {1,0.22489,12.50,7.870,0,0.5240,6.3770,94.30,6.3467,5,311.0,15.20,392.52,20.45}  |   94016 |   15 |   94016 | 15.2284207930287 |  0.228420793028732
+ 12 | {1,0.11747,12.50,7.870,0,0.5240,6.0090,82.90,6.2267,5,311.0,15.20,396.90,13.27}  |   20001 | 18.9 |   20001 | 19.2272848285357 |  0.327284828535671
+ 13 | {1,0.09378,12.50,7.870,0,0.5240,5.8890,39.00,5.4509,5,311.0,15.20,390.50,15.71}  |   20001 | 21.7 |   20001 | 21.3979318641202 |  0.302068135879811
+ 14 | {1,0.62976,0.00,8.140,0,0.5380,5.9490,61.80,4.7075,4,307.0,21.00,396.90,8.26}    |   20001 | 20.4 |   20001 | 19.7743403979155 |  0.625659602084532
+ 15 | {1,0.63796,0.00,8.140,0,0.5380,6.0960,84.50,4.4619,4,307.0,21.00,380.02,10.26}   |   20001 | 18.2 |   20001 | 18.7400800902121 |  0.540080090212125
+ 16 | {1,0.62739,0.00,8.140,0,0.5380,5.8340,56.50,4.4986,4,307.0,21.00,395.62,8.47}    |   20001 | 19.9 |   20001 | 19.6187933144569 |  0.281206685543061
+ 17 | {1,1.05393,0.00,8.140,0,0.5380,5.9350,29.30,4.4986,4,307.0,21.00,386.85,6.58}    |   20001 | 23.1 |   20001 | 23.3492239648177 |  0.249223964817737
+ 18 | {1,0.78420,0.00,8.140,0,0.5380,5.9900,81.70,4.2579,4,307.0,21.00,386.75,14.67}   |   20001 | 17.5 |   20001 | 17.0806608347814 |  0.419339165218577
+ 19 | {1,0.80271,0.00,8.140,0,0.5380,5.4560,36.60,3.7965,4,307.0,21.00,288.99,11.69}   |   20001 | 20.2 |   20001 | 20.1559086626409 |  0.044091337359113
+ 20 | {1,0.72580,0.00,8.140,0,0.5380,5.7270,69.50,3.7965,4,307.0,21.00,390.95,11.28}   |   20001 | 18.2 |   20001 | 18.6980897920022 |  0.498089792002183
+(20 rows)
+
      RMS error: 
      +SELECT SQRT(AVG((y-estimated_y)*(y-estimated_y))) as rms_error FROM lin_housing
+JOIN mlp_regress_prediction USING (id);
+
      +     rms_error
+-------------------+
+ 0.912158035902468
+(1 row)
+
      4. +
    +

    Note that the results you get for all examples may vary with the database you are using.

    +

    Technical Background
    +

    To train a neural net, the loss function is minimized using stochastic gradient descent. In the case of classification, the loss function is cross entropy. For regression, mean square error is used. Weights in the neural net are updated via the backpropogation process, which uses dynamic programming to compute the partial derivative of each weight with respect to the overall loss. This partial derivative incorporates the activation function used, which requires that the activation function be differentiable.

    +

    For an overview of multilayer perceptrons, see [1].

    +

    For details on backpropogation, see [2].

    +

    On the effect of database cluster size: as the database cluster size increases, the per iteration loss will be higher since the model only sees 1/n of the data, where n is the number of segments. However, each iteration runs faster than single node because it is only traversing 1/n of the data. For large data sets, all else being equal, a bigger cluster will achieve a given accuracy faster than a single node although it may take more iterations to achieve that accuracy.

    +

    Literature
    +

    [1] https://en.wikipedia.org/wiki/Multilayer_perceptron

    +

    [2] Yu Hen Hu. "Lecture 11. MLP (III): Back-Propagation." University of Wisconsin Madison: Computer-Aided Engineering. Web. 12 July 2017, http://homepages.cae.wisc.edu/~ece539/videocourse/notes/pdf/lec%2011%20MLP%20(3)%20BP.pdf

    +

    [3] "Neural Networks for Machine Learning", Lectures 6a and 6b on mini-batch gradient descent, Geoffrey Hinton with Nitish Srivastava and Kevin Swersky, http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf

    +

    [4] Kingma, D. P., & Ba, J. L. (2015), "Adam: a Method for Stochastic Optimization," International Conference on Learning Representations, 1–13.

    +

    Related Topics
    +

    File mlp.sql_in documenting the training function

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__ordinal.html b/docs/docs/v2.1.0/group__grp__ordinal.html new file mode 100644 index 00000000..fe0497dc --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__ordinal.html @@ -0,0 +1,459 @@ + + + + + + + + +MADlib: Ordinal Regression + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    +
    Ordinal Regression
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    In statistics, ordinal regression is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant. The two most common types of ordinal regression models are ordered logit, which applies to data that meet the proportional odds assumption, and ordered probit.

    +

    Training Function
    The ordinal regression training function has the following syntax: 
    +ordinal(source_table,
+         model_table,
+         dependent_varname,
+         independent_varname,
+         cat_order,
+         link_func,
+         grouping_col,
+         optim_params,
+         verbose
+        )
+
    +

    Arguments

    +
    source_table
    +

    VARCHAR. Name of the table containing the training data.

    +

    +
    +
    model_table
    +

    VARCHAR. Name of the generated table containing the model.

    +

    The model table produced by ordinal() contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    <...>

    Grouping columns, if provided in input. This could be multiple columns depending on the grouping_col input.

    +

    +
    coef_threshold

    FLOAT8[]. Vector of the threshold coefficients in linear predictor. The threshold coefficients are the intercepts specific to each categorical levels

    +

    +
    std_err_threshold

    FLOAT8[]. Vector of the threshold standard errors of the threshold coefficients.

    +

    +
    z_stats_threshold

    FLOAT8[]. Vector of the threshold z-statistics of the thresholdcoefficients.

    +

    +
    p_values_threshold

    FLOAT8[]. Vector of the threshold p-values of the threshold coefficients.

    +

    +
    log_likelihood

    FLOAT8. The log-likelihood \( l(\boldsymbol \beta) \). The value will be the same across categories within the same group.

    +

    +
    coef_feature

    FLOAT8[]. Vector of the feature coefficients in linear predictor. The feature coefficients are the coefficients for the independent variables. They are the same across categories.

    +

    +
    std_err_feature

    FLOAT8[]. Vector of the feature standard errors of the feature coefficients.

    +

    +
    z_stats_feature

    FLOAT8[]. Vector of the feature z-statistics of the feature coefficients.

    +

    +
    p_values_feature

    FLOAT8[]. Vector of the feature p-values of the feature coefficients.

    +

    +
    num_rows_processed

    BIGINT. Number of rows processed.

    +

    +
    num_rows_skipped

    BIGINT. Number of rows skipped due to missing values or failures.

    +

    +
    num_iterations INTEGER. Number of iterations actually completed. This would be different from the nIterations argument if a tolerance parameter is provided and the algorithm converges before all iterations are completed.
    +

    A summary table named <model_table>_summary is also created at the same time, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + +
    method

    VARCHAR. String describes the model: 'ordinal'.

    +

    +
    source_table

    VARCHAR. Data source table name.

    +

    +
    model_table

    VARCHAR. Model table name.

    +

    +
    dependent_varname

    VARCHAR. Expression for dependent variable.

    +

    +
    independent_varname

    VARCHAR. Expression for independent variables. The independent variables should not include intercept term. Otherwise there will be an error message indicating Hessian matrix is not finite. In that case, the user should drop the intercept and rerun the function agian.

    +

    +
    cat_order

    VARCHAR. String representation of category order. Default is the sorted categories in data using python sort

    +

    +
    link_func

    VARCHAR. String that contains link function parameters: 'logit' and 'probit' links are implemented now

    +

    +
    grouping_col

    VARCHAR. String representation of grouping columns.

    +

    +
    optimizer_params

    VARCHAR. String that contains optimizer parameters, and has the form of 'optimizer=..., max_iter=..., tolerance=...'.

    +

    +
    num_all_groups

    INTEGER. Number of groups in ordinal regression training.

    +

    +
    num_failed_groups

    INTEGER. Number of failed groups in ordinal regression training.

    +

    +
    total_rows_processed

    BIGINT. Total number of rows processed in all groups.

    +

    +
    total_rows_skipped

    BIGINT. Total number of rows skipped in all groups due to missing values or failures.

    +

    +
    +

    +
    +
    dependent_varname
    +

    VARCHAR. Name of the dependent variable column.

    +

    +
    +
    independent_varname
    +

    VARCHAR. Expression list to evaluate for the independent variables. The intercept should not be included here since the cumulative probability force to have intercepts for each category level.

    +

    +
    +
    cat_order
    +

    VARCHAR, String that represents the order of category. The order is specified by charactor '<'.

    +

    +
    +
    link_function (optional)
    +

    VARCHAR, default: 'logit'. Parameters for link function. Currently, we support logit and probit.

    +

    +
    +
    grouping_col (optional)
    +

    VARCHAR, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated.

    +

    +
    +
    optim_params (optional)
    +

    VARCHAR, default: 'max_iter=100,optimizer=irls,tolerance=1e-6'. Parameters for optimizer. Currently, we support tolerance=[tolerance for relative error between log-likelihoods], max_iter=[maximum iterations to run], optimizer=irls.

    +

    +
    +
    verbose (optional)
    +
    BOOLEAN, default: FALSE. Provides verbose output of the results of training.
    +
    +
    Note
    To calculate the standard error the coefficient, we are using the square root of the diagnal elements of the expected Fisher information matrix, which is a by-product of iteratively reweighted least square. This method is used in the original ordinal regression paper by McCullagh(1980). In some software like Stata, the standard error is calculated by the observed information matrix, which is supported by Efron and Hinkley (1978). In R, polr() uses the approximated observed information matrix while the optimization is achieved by first order optimization method. Therefore, there will be some difference on standard error, z-stats and p-value from other software.
    +

    Prediction Function
    Ordinal regression prediction function has the following format: 
    +ordinal_predict(
+                    model_table,
+                    predict_table_input,
+                    output_table,
+                    predict_type,
+                    verbose
+               )
+
    Arguments
    +
    model_table
    +

    TEXT. Name of the generated table containing the model, which is the output table from ordinal().

    +

    +
    +
    predict_table_input
    +

    TEXT. The name of the table containing the data to predict on. The table must contain id column as the primary key.

    +

    +
    +
    output_table
    +

    TEXT. Name of the generated table containing the predicted values.

    +

    The model table produced by ordinal_predict contains the following columns:

    + + + + + + + +
    id

    SERIAL. Column to identify the predicted value.

    +

    +
    category

    TEXT. Available if the predicted type = 'response'. Column contains the predicted categories

    +

    +
    category_value FLOAT8. The predicted probability for the specific category_value.
    +

    +
    +
    predict_type
    +

    TEXT. Either 'response' or 'probability'. Using 'response' will give the predicted category with the largest probability. Using probability will give the predicted probabilities for all categories

    +

    +
    +
    verbose
    +
    BOOLEAN. Whether verbose is displayed
    +
    +
    +

    Examples
    +
      +
    1. Create the training data table. 
      +DROP TABLE IF EXISTS test3;
+CREATE TABLE test3 (
+    feat1 INTEGER,
+    feat2 INTEGER,
+    cat INTEGER
+);
+INSERT INTO test3(feat1, feat2, cat) VALUES
+(1,35,1),
+(2,33,0),
+(3,39,1),
+(1,37,1),
+(2,31,1),
+(3,36,0),
+(2,36,1),
+(2,31,1),
+(2,41,1),
+(2,37,1),
+(1,44,1),
+(3,33,2),
+(1,31,1),
+(2,44,1),
+(1,35,1),
+(1,44,0),
+(1,46,0),
+(2,46,1),
+(2,46,2),
+(3,49,1),
+(2,39,0),
+(2,44,1),
+(1,47,1),
+(1,44,1),
+(1,37,2),
+(3,38,2),
+(1,49,0),
+(2,44,0),
+(3,61,2),
+(1,65,2),
+(3,67,1),
+(3,65,2),
+(1,65,2),
+(2,67,2),
+(1,65,2),
+(1,62,2),
+(3,52,2),
+(3,63,2),
+(2,59,2),
+(3,65,2),
+(2,59,0),
+(3,67,2),
+(3,67,2),
+(3,60,2),
+(3,67,2),
+(3,62,2),
+(2,54,2),
+(3,65,2),
+(3,62,2),
+(2,59,2),
+(3,60,2),
+(3,63,2),
+(3,65,2),
+(2,63,1),
+(2,67,2),
+(2,65,2),
+(2,62,2);
+
      2. +
    2. Run the multilogistic regression function. 
      +DROP TABLE IF EXISTS test3_output;
+DROP TABLE IF EXISTS test3_output_summary;
+SELECT madlib.ordinal('test3',
+                       'test3_output',
+                       'cat',
+                       'ARRAY[feat1, feat2]',
+                       '0<1<2',
+                       'logit'
+                       );
+
      3. +
    3. View the regression results. 
      +-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM test3_output;
+
      Result: 
      +-[ RECORD 1 ]------+-------------------------------------------
+coef_threshold     | {4.12831944358935,6.55999442887089}
+std_err_threshold  | {1.3603408170882,1.54843501580999}
+z_stats_threshold  | {3.03476848722806,4.23653195768075}
+p_values_threshold | {0.00240720390579325,2.26998625331282e-05}
+log_likelihood     | -42.1390192418541
+coef_feature       | {0.574822563129293,0.108115645059558}
+std_err_feature    | {0.394064908788145,0.0276025960683975}
+z_stats_feature    | {1.45870020473791,3.91686509456046}
+p_values_feature   | {0.144647639733733,8.9707915817562e-05}
+num_rows_processed | 57
+num_rows_skipped   | 0
+iteration          | 7
+
      4. +
    4. Predicting dependent variable using ordinal model. (This example uses the original data table to perform the prediction. Typically a different test dataset with the same features as the original training dataset would be used for prediction.) 
      +\x off
+-- Add the id column for prediction function
+ALTER TABLE test3 ADD COLUMN id SERIAL;
+-- Predict probabilities for all categories using the original data
+SELECT ordinal_predict('test3_output','test3', 'test3_prd_prob', 'probability');
+-- Display the predicted value
+SELECT * FROM test3_prd_prob;
+
      5. +
    +

    Model Details
    +

    The function ordinal() fit the ordinal response model using a cumulative link model. The ordinal reponse variable, denoted by \( Y_i \), can fall in \( j = 1,.. , J\) categories. Then \( Y_i \) follows a multinomial distribution with parameter \(\pi\) where \(\pi_{ij}\) denote the probability that the \(i\)th observation falls in response category \(j\). We define the cumulative probabilities as

    +\[ \gamma_{ij} = \Pr(Y_i \le j)= \pi_{i1} +...+ \pi_{ij} . \] +

    +

    Next we will consider the logit link for illustration purpose. The logit function is defined as \( \mbox{logit}(\pi) = \log[\pi/(1-\pi)] \) and cumulative logits are defined as:

    +\[ \mbox{logit}(\gamma_{ij})=\mbox{logit}(\Pr(Y_i \le j))=\log \frac{\Pr(Y_i \le j)}{1-\Pr(Y_i\le j)}, j=1,...,J−1 \] +

    +

    so that the cumulative logits are defined for all but the last category.

    +

    A cumulative link model with a logit link, or simply cumulative logit model is a regression model for cumulative logits:

    +\[ \mbox{logit}(\gamma_{ij}) = \theta_j - x^T_i \beta \] +

    +

    where \(x_i\) is a vector of explanatory variables for the \(i\)th observation and \(\beta\) is the corresponding set of regression parameters. The \(\{\theta_j\}\) parameters provide each cumulative logit (for each \(j\)) with its own intercept. A key point is that the regression part \(x^T_i\beta\) is independent of \(j\), so \(\beta\) has the same effect for each of the J − 1 cumulative logits. Note that \(x^T_i\beta\) does not contain an intercept, since the \(\{\theta_j\}\) act as intercepts. For small values of \(x^T_i\beta\) the response is likely to fall in the first category and for large values of \(x^T_i\beta\) the response is likely to fall in the last category. The horizontal displacements of the curves are given by the values of \(\{\theta_j\}\).

    +

    Literature
    +

    A collection of nice write-ups, with valuable pointers into further literature:

    +

    [1] Peter McCullagh: Regression Models for Ordinal Data, Journal of the Royal Statistical Society. Series B (Methodological), Volume 42, Issue 2 (1980), 109-142

    +

    [2] Rune Haubo B Christensen: Analysis of ordinal data with cumulative link models – estimation with the R-package ordinal. cran.r-project.org/web/packages/ordinal/vignettes/clm_intro.pdf

    +

    Related Topics
    +

    File ordinal.sql_in documenting the ordinal regression functions

    +

    Multinomial Regression

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__other__functions.html b/docs/docs/v2.1.0/group__grp__other__functions.html new file mode 100644 index 00000000..6943a6cc --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__other__functions.html @@ -0,0 +1,148 @@ + + + + + + + + +MADlib: Utilities + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
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    + + + +
    +
    + +
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    + +
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    + + +
    + +
    + +
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    +Modules
    +
    +
    Utilities
    +
    +
    +

    Detailed Description

    +

    Useful utilities for data science workflows.

    + + + + + + + + + + + + + + + + + + + + + + + +

    +Modules

     Columns to Vector
     Create a new table with all feature columns inserted into a single column as an array.
     
     Database Functions
     Provides a collection of user-defined functions for performing common tasks in the database.
     
     Linear Solvers
     Methods that implement solutions for systems of consistent linear equations.
     
     Mini-Batch Preprocessor
     Utility that prepares input data for use by models that support mini-batch as an optimization option.
     
     PMML Export
     Implements the PMML XML standard to describe and exchange models produced by data mining and machine learning algorithms.
     
     Term Frequency
     Provides a collection of functions for performing common tasks related to text analytics.
     
     Vector to Columns
     Converts a feature array in a single column of an output table into multiple columns.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__other__functions.js b/docs/docs/v2.1.0/group__grp__other__functions.js new file mode 100644 index 00000000..5d88a128 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__other__functions.js @@ -0,0 +1,10 @@ +var group__grp__other__functions = +[ + [ "Columns to Vector", "group__grp__cols2vec.html", null ], + [ "Database Functions", "group__grp__utilities.html", null ], + [ "Linear Solvers", "group__grp__linear__solver.html", "group__grp__linear__solver" ], + [ "Mini-Batch Preprocessor", "group__grp__minibatch__preprocessing.html", null ], + [ "PMML Export", "group__grp__pmml.html", null ], + [ "Term Frequency", "group__grp__text__utilities.html", null ], + [ "Vector to Columns", "group__grp__vec2cols.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__pagerank.html b/docs/docs/v2.1.0/group__grp__pagerank.html new file mode 100644 index 00000000..b0e71c22 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pagerank.html @@ -0,0 +1,451 @@ + + + + + + + + +MADlib: PageRank + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    +
    PageRank
    Graph
    +
    +
    +
    Contents +

    Given a graph, the PageRank algorithm outputs a probability distribution representing the likelihood that a person randomly traversing the graph will arrive at any particular vertex. This algorithm was originally used by Google to rank websites where the World Wide Web was modeled as a directed graph with the vertices representing the websites. The PageRank algorithm initially proposed by Larry Page and Sergey Brin is implemented here [1].

    +

    We also implement personalized PageRank, in which a notion of importance provides personalization to a query. For example, importance scores can be biased according to a specified set of vertices in the graph that are of interest or special in some way [2].

    +

    PageRank
    +pagerank( vertex_table,
+          vertex_id,
+          edge_table,
+          edge_args,
+          out_table,
+          damping_factor,
+          max_iter,
+          threshold,
+          grouping_cols,
+          personalization_vertices
+        )
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    TEXT, default = 'id'. Name of the column(s) in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous. If multiple columns are used as vertex ids, they are passed in the following format: [<vertex_id1>,<vertex_id2>,...]

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex and destination vertex.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column(s) containing the source vertex ids in the edge table. Default column name is 'src'.
      • +
    • dest (INTEGER or BIGINT): Name of the column(s) containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the result of PageRank. It will contain a row for every vertex from 'vertex_table' with the following columns:

      +
    • vertex_id : The id of a vertex. Will use the input parameter 'vertex_id' for column naming.
      • +
    • pagerank : The vertex's PageRank.
      • +
    • grouping_cols : Grouping column (if any) values associated with the vertex_id.
      • +
    +

    A summary table is also created that contains information regarding the number of iterations required for convergence. It is named by adding the suffix '_summary' to the 'out_table' parameter.

    +

    +
    +
    damping_factor (optional)
    +

    FLOAT8, default 0.85. The probability, at any step, that a user will continue following the links in a random surfer model.

    +

    +
    +
    max_iter (optional)
    +

    INTEGER, default: 100. The maximum number of iterations allowed.

    +

    +
    +
    threshold (optional)
    +

    FLOAT8, default: (1/number of vertices * 1000). If the difference between the PageRank of every vertex of two consecutive iterations is smaller than 'threshold', or the iteration number is larger than 'max_iter', the computation stops. If you set the threshold to zero, then you will force the algorithm to run for the full number of iterations specified in 'max_iter'. It is advisable to set threshold to a value lower than 1/(number of vertices in the graph) since the PageRank value of nodes is initialized to that value.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. A single column or a list of comma-separated columns that divides the input data into discrete groups, resulting in one distribution per group. When this value is NULL, no grouping is used and a single model is generated for all data.
    Note
    Expressions are not currently supported for 'grouping_cols'.
    +
    +
    personalization_vertices (optional)
    +
    INTEGER[] or BIGINT[], default: NULL. A comma separated list of vertices or nodes for personalized PageRank. When this parameter is provided, personalized PageRank will run. In the absence of this parameter, regular PageRank will run. If multiple columns are used for identifying vertices, a 2D array will be required for this parameter.
    +
    +

    Examples
    +

    Download the example sql file here.

    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+    node_id INTEGER
+    );
+CREATE TABLE edge(
+    conn_src INTEGER,
+    conn_dest INTEGER,
+    user_id INTEGER
+);
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6);
+INSERT INTO edge VALUES
+(0, 1, 1),
+(0, 2, 1),
+(0, 4, 1),
+(1, 2, 1),
+(1, 3, 1),
+(2, 3, 1),
+(2, 5, 1),
+(2, 6, 1),
+(3, 0, 1),
+(4, 0, 1),
+(5, 6, 1),
+(6, 3, 1),
+(0, 1, 2),
+(0, 2, 2),
+(0, 4, 2),
+(1, 2, 2),
+(1, 3, 2),
+(2, 3, 2),
+(3, 0, 2),
+(4, 0, 2),
+(5, 6, 2),
+(6, 3, 2);
+
      2. +
    2. Running PageRank with default values for optional parameters: 
      +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;
+SELECT madlib.pagerank(
+                       'vertex',                        -- Vertex table
+                       'node_id',                       -- Vertex id column
+                       'edge',                          -- Edge table
+                       'src=conn_src, dest=conn_dest',  -- Comma delimted string of edge arguments
+                       'pagerank_out');                 -- Output table of PageRank
+SELECT * FROM pagerank_out ORDER BY pagerank DESC;
+
      + node_id |      pagerank
+---------+-------------------
+       0 |  0.28753749341184
+       3 |  0.21016988901855
+       2 |  0.14662683454062
+       4 |  0.10289614384217
+       1 |  0.10289614384217
+       6 |  0.09728637768887
+       5 |  0.05258711765692
+(7 rows)
+
      +SELECT * FROM pagerank_out_summary;
+
      + __iterations__
+ ----------------+
+             16
+(1 row)
+
      3. +
    3. Running PageRank with a damping factor of 0.5 results in different final values: 
      +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;
+SELECT madlib.pagerank(
+                       'vertex',                        -- Vertex table
+                       'node_id',                       -- Vertex id column
+                       'edge',                          -- Edge table
+                       'src=conn_src, dest=conn_dest',  -- Comma delimted string of edge arguments
+                       'pagerank_out',                  -- Output table of PageRank
+                       0.5);                            -- Damping factor
+SELECT * FROM pagerank_out ORDER BY pagerank DESC;
+
      + node_id |      pagerank
+---------+--------------------
+  0      |  0.225477161441199
+  3      |  0.199090328586664
+  2      |  0.136261327206477
+  6      |  0.132691559968224
+  4      |  0.109009291409508
+  1      |  0.109009291409508
+  5      | 0.0884610399788161
+(7 rows)
+
      4. +
    4. Now compute the PageRank of vertices associated with each user using the grouping feature: 
      +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;
+SELECT madlib.pagerank(
+                       'vertex',                        -- Vertex table
+                       'node_id',                       -- Vertex id column
+                       'edge',                          -- Edge table
+                       'src=conn_src, dest=conn_dest',  -- Comma delimted string of edge arguments
+                       'pagerank_out',                  -- Output table of PageRank
+                       NULL,                            -- Default damping factor (0.85)
+                       NULL,                            -- Default max iters (100)
+                       0.00000001,                      -- Threshold
+                       'user_id');                      -- Grouping column name
+SELECT * FROM pagerank_out ORDER BY user_id, pagerank DESC;
+
      + user_id | node_id |      pagerank
+---------+---------+--------------------
+       1 |       0 |  0.27825488388552
+       1 |       3 |  0.20188114667075
+       1 |       2 |  0.14288112346059
+       1 |       6 |  0.11453637832147
+       1 |       1 |  0.10026745615438
+       1 |       4 |  0.10026745615438
+       1 |       5 |  0.06191155535288
+       2 |       0 |  0.31854625004173
+       2 |       3 |  0.23786686773343
+       2 |       2 |  0.15914876489397
+       2 |       1 |  0.11168334437971
+       2 |       4 |  0.11168334437971
+       2 |       6 |  0.03964285714285
+       2 |       5 |  0.02142857142857
+(14 rows)
+
      +SELECT * FROM pagerank_out_summary ORDER BY user_id;
+
      + user_id | __iterations__
+---------+----------------
+       1 |             27
+       2 |             31
+(2 rows)
+
      5. +
    5. Personalized PageRank. Here we specify {2,4} as the personalization vertices. This parameter could be specified as ARRAY[2,4] as well. 
      +DROP TABLE IF EXISTS pagerank_out, pagerank_out_summary;
+SELECT madlib.pagerank(
+                       'vertex',                        -- Vertex table
+                       'node_id',                       -- Vertex id column
+                       'edge',                          -- Edge table
+                       'src=conn_src, dest=conn_dest',  -- Comma delimted string of edge arguments
+                       'pagerank_out',                  -- Output table of PageRank
+                        NULL,                           -- Default damping factor (0.85)
+                        NULL,                           -- Default max iters (100)
+                        NULL,                           -- Default Threshold
+                        NULL,                           -- No Grouping
+                       '{2,4}');                        -- Personalization vertices
+SELECT * FROM pagerank_out ORDER BY pagerank DESC;
+
      + node_id |      pagerank
+---------+--------------------
+  0      |  0.565232961966315
+  2      |  0.378139420991773
+  3      |  0.355003292266017
+  4      |  0.310111215897626
+  1      |  0.160111215897626
+  6      |  0.148615315574136
+  5      | 0.0803403307142321
+(7 rows)
+
      +SELECT * FROM pagerank_out_summary;
+
      + __iterations__
+ ----------------+
+             37
+(1 row)
+
      6. +
    6. Create vertex and edge tables with multiple column ids to represent the graph: 
      +DROP TABLE IF EXISTS vertex_multicol_pagerank, edge_multicol_pagerank;
+CREATE TABLE vertex_multicol_pagerank(
+    node_id_major BIGINT,
+    node_id_minor BIGINT
+);
+CREATE TABLE edge_multicol_pagerank(
+    conn_src_major BIGINT,
+    conn_dest_major BIGINT,
+    user_id_major BIGINT,
+    conn_src_minor BIGINT,
+    conn_dest_minor BIGINT,
+    user_id_minor BIGINT
+);
+INSERT INTO vertex_multicol_pagerank VALUES
+(0, 0),
+(1, 1),
+(2, 2),
+(3, 3),
+(4, 4),
+(5, 5),
+(6, 6);
+INSERT INTO edge_multicol_pagerank VALUES
+(0, 1, 1, 0, 1, 1),
+(0, 2, 1, 0, 2, 1),
+(0, 4, 1, 0, 4, 1),
+(1, 2, 1, 1, 2, 1),
+(1, 3, 1, 1, 3, 1),
+(2, 3, 1, 2, 3, 1),
+(2, 5, 1, 2, 5, 1),
+(2, 6, 1, 2, 6, 1),
+(3, 0, 1, 3, 0, 1),
+(4, 0, 1, 4, 0, 1),
+(5, 6, 1, 5, 6, 1),
+(6, 3, 1, 6, 3, 1),
+(0, 1, 2, 0, 1, 2),
+(0, 2, 2, 0, 2, 2),
+(0, 4, 2, 0, 4, 2),
+(1, 2, 2, 1, 2, 2),
+(1, 3, 2, 1, 3, 2),
+(2, 3, 2, 2, 3, 2),
+(3, 0, 2, 3, 0, 2),
+(4, 0, 2, 4, 0, 2),
+(5, 6, 2, 5, 6, 2),
+(6, 3, 2, 6, 3, 2);
+
      7. +
    7. Personalized PageRank. Here we specify {2,4} as the personalization vertices. This parameter could be specified as ARRAY[2,4] as well. 
      +DROP TABLE IF EXISTS pagerank_multicol_out, pagerank_multicol_out_summary;
+SELECT madlib.pagerank(
+                       'vertex_multicol_pagerank',                                                      -- Vertex table
+                       '[node_id_major,node_id_minor]',                                                 -- Vertex id column
+                       'edge_multicol_pagerank',                                                        -- Edge table
+                       'src=[conn_src_major,conn_src_minor], dest=[conn_dest_major,conn_dest_minor]',   -- Comma delimted string of edge arguments
+                       'pagerank_multicol_out',                                                         -- Output table of PageRank
+                        NULL,                                                                           -- Default damping factor (0.85)
+                        NULL,                                                                           -- Default max iters (100)
+                        NULL,                                                                           -- Default Threshold
+                       'user_id_major,user_id_minor',                                                   -- Grouping Columns
+                       '{{2,2},{4,4}}');                                                                -- Personalization vertices
+SELECT * FROM pagerank_multicol_out ORDER BY pagerank DESC;
+
      + user_id_major | user_id_minor |  id   |      pagerank
+---------------+---------------+-------+--------------------
+             2 |             2 | {0,0} |  0.448826703440932
+             2 |             2 | {3,3} |  0.325943770128465
+             1 |             1 | {0,0} |  0.270635964385879
+             2 |             2 | {2,2} |  0.256179815391031
+             2 |             2 | {4,4} |  0.202149921235622
+             1 |             1 | {2,2} |   0.18423239851445
+             1 |             1 | {3,3} |  0.166801820206414
+             1 |             1 | {4,4} |  0.151661035568349
+             2 |             2 | {1,1} |  0.127149921235622
+             1 |             1 | {6,6} | 0.0965411872854988
+             1 |             1 | {1,1} | 0.0766610355683489
+             2 |             2 | {5,5} |              0.075
+             2 |             2 | {6,6} |            0.06375
+             1 |             1 | {5,5} | 0.0521896024086525
+(7 rows)
+
      +SELECT * FROM pagerank_multicol_out_summary;
+
      + user_id_major | user_id_minor | __iterations__
+---------------+---------------+----------------
+             2 |             2 |             45
+             1 |             1 |             41
+(1 row)
+
      8. +
    +

    Notes
    +
      +
    1. On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance.
      2. +
    +

    Literature
    +

    [1] Brin, S. and Page, L. (1998), "The anatomy of a large-scale hypertextual Web search engine", Computer Networks and ISDN Systems. 30: 107–117, http://infolab.stanford.edu/pub/papers/google.pdf

    +

    [2] Jeh, Glen and Widom, Jennifer. "Scaling Personalized Web Search", Proceedings of the 12th international conference on World Wide Web, Pages 271-279 Budapest, Hungary, May 20-24, 2003, http://ilpubs.stanford.edu:8090/530/1/2002-12.pdf

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__path.html b/docs/docs/v2.1.0/group__grp__path.html new file mode 100644 index 00000000..66c401b0 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__path.html @@ -0,0 +1,472 @@ + + + + + + + + +MADlib: Path + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Path
    Data Types and Transformations
    +
    +
    +
    Contents +

    The goal of the MADlib path function is to perform regular pattern matching over a sequence of rows, and to extract useful information about the pattern matches. The useful information could be a simple count of matches or something more involved like aggregations or window functions.

    +

    Symbols are used to identify particular rows of interest. Then, standard PostgreSQL pattern matching using symbols can be applied to identify patterns across the rows of interest. (This is similar in concept to regular expressions which match patterns within strings of text.)

    +

    For example, a symbol can be defined for purchase events by on-line shoppers. Then, preceding events that led to the purchase can be identified and operated on, perhaps to find the common actions that resulted in a purchase. Or conversely, to find actions that resulted in an exit without a purchase having been made.

    +

    Steps on how to use path functions:

    +
      +
    1. Partition input rows.
      2. +
    2. Order the partitions.
      3. +
    3. Define symbols to match rows of interest.
      4. +
    4. Define regular expression of symbols and operators to define patterns to match in your ordered partitions.
      5. +
    5. Define an aggregate function to compute for each pattern match.
      6. +
    6. If desired, output the pattern matches for inspection or to operate on them with subsequent queries.
      7. +
    +

    Function Syntax
    +path(
+    source_table,
+    output_table,
+    partition_expr,
+    order_expr,
+    symbol,
+    pattern,
+    aggregate_func,
+    persist_rows,
+    overlapping_patterns
+)
+
    +

    Arguments

    +
    source_table
    +

    VARCHAR. Name of the source table, containing data for path analysis.

    +

    +
    +
    output_table
    +

    VARCHAR. Name of the result table.

    +

    +
    +
    partition_expr
    +

    VARCHAR. The 'partition_expr' can be a single column or a list of comma-separated columns/expressions to divide all rows into groups, or partitions. Matching is applied across the rows that fall into the same partition. This can be NULL or '' to indicate the matching is to be applied to the whole table.

    +

    +
    +
    order_expr
    +

    VARCHAR. This expression controls the order in which rows are processed or matched in a partition. For example, time is a common way to order partitions.

    +

    +
    +
    symbol
    +

    VARCHAR. Symbols enable you to express patterns of interest in a simple way (see definition of ‘pattern’ argument below). A symbol identifies a row of a particular type that you’re searching for as part of a pattern match. Symbol definition uses the standard PostgreSQL assignment statement 'identifier := expression;' [1]. A given row can only match one symbol. If a row matches multiple symbols, the symbol that comes first in the symbol definition list will take precedence.

    +

    +
    +
    pattern
    +

    VARCHAR. The 'pattern' clause defines the pattern that the path algorithm searches for. You express the pattern using symbols and operators following regular PostgreSQL pattern matching syntax and rules [2].

    +

    Note
    Symbols defined using more than one (1) character need to be enclosed in parentheses '()' when referenced in the 'pattern' argument. For example:
      +
    • a symbol defined as 'a' in the 'symbol' argument can be used directly in the 'pattern' argument
      • +
    • a symbol defined as 'abc' in the 'symbol' argument must be written as '(abc)' in the 'pattern' argument
      • +
    +
    +

    The following pattern matching metacharacters are supported:

      +
    • +| denotes alternation (either of two alternatives).
      • +
    • +? denotes repetition of the previous item zero or one time.
      • +
    • +* denotes repetition of the previous item zero or more times.
      • +
    • ++ denotes repetition of the previous item one or more times.
      • +
    • +{m} denotes repetition of the previous item exactly m times.
      • +
    • +{m,} denotes repetition of the previous item m or more times.
      • +
    • +{m,n} denotes repetition of the previous item at least m and not more than n times.
      • +
    • +Parentheses () can be used to group items into a single logical item.
      • +
    +

    +
    +
    aggregate_func (optional)
    +

    VARCHAR, default NULL. A comma-separated list of aggregates to be applied to the pattern matches [3]. You can think of this input parameter as being like a SELECT clause. Please note that window functions cannot currently be used in the parameter 'aggregate_func'. If you want to use a window function [4], output the pattern matches and write a SQL query with a window function over the output tuples (see 'persist_rows' parameter below).

    +

    If you just want to output the pattern matched rows and not compute any aggregates, you can put NULL or '' in the 'aggregate_func' parameter.

    +

    +
    +
    persist_rows (optional)
    +

    BOOLEAN, default FALSE. If TRUE the matched rows are persisted in a separate output table. This table is named as <output_table>_tuples (the string "_tuples" is added as suffix to the value of output_table).

    +

    +
    +
    overlapping_patterns (optional)
    +

    BOOLEAN, default FALSE. If TRUE find every occurrence of the pattern in the partition, regardless of whether it might have been part of a previously found match.

    +

    +
    +
    +

    Examples
    +

    The data set describes shopper behavior on a notional web site that sells beer and wine. A beacon fires an event to a log file when the shopper visits different pages on the site: landing page, beer selection page, wine selection page, and checkout. Other pages on the site like help pages show up in the logs as well. Let’s assume that the log has been sessionized.

    +
      +
    1. Create the date table: 
      +DROP TABLE IF EXISTS eventlog;
+CREATE TABLE eventlog (event_timestamp TIMESTAMP,
+            user_id INT,
+            session_id INT,
+            page TEXT,
+            revenue FLOAT);
+INSERT INTO eventlog VALUES
+('04/15/2015 01:03:00', 100821, 100, 'LANDING', 0),
+('04/15/2015 01:04:00', 100821, 100, 'WINE', 0),
+('04/15/2015 01:05:00', 100821, 100, 'CHECKOUT', 39),
+('04/15/2015 02:06:00', 100821, 101, 'WINE', 0),
+('04/15/2015 02:09:00', 100821, 101, 'WINE', 0),
+('04/15/2015 01:15:00', 101121, 102, 'LANDING', 0),
+('04/15/2015 01:16:00', 101121, 102, 'WINE', 0),
+('04/15/2015 01:17:00', 101121, 102, 'CHECKOUT', 15),
+('04/15/2015 01:18:00', 101121, 102, 'LANDING', 0),
+('04/15/2015 01:19:00', 101121, 102, 'HELP', 0),
+('04/15/2015 01:21:00', 101121, 102, 'WINE', 0),
+('04/15/2015 01:22:00', 101121, 102, 'CHECKOUT', 23),
+('04/15/2015 02:15:00', 101331, 103, 'LANDING', 0),
+('04/15/2015 02:16:00', 101331, 103, 'WINE', 0),
+('04/15/2015 02:17:00', 101331, 103, 'HELP', 0),
+('04/15/2015 02:18:00', 101331, 103, 'WINE', 0),
+('04/15/2015 02:19:00', 101331, 103, 'CHECKOUT', 16),
+('04/15/2015 02:22:00', 101443, 104, 'BEER', 0),
+('04/15/2015 02:25:00', 101443, 104, 'CHECKOUT', 12),
+('04/15/2015 02:29:00', 101881, 105, 'LANDING', 0),
+('04/15/2015 02:30:00', 101881, 105, 'BEER', 0),
+('04/15/2015 01:05:00', 102201, 106, 'LANDING', 0),
+('04/15/2015 01:06:00', 102201, 106, 'HELP', 0),
+('04/15/2015 01:09:00', 102201, 106, 'LANDING', 0),
+('04/15/2015 02:15:00', 102201, 107, 'WINE', 0),
+('04/15/2015 02:16:00', 102201, 107, 'BEER', 0),
+('04/15/2015 02:17:00', 102201, 107, 'WINE', 0),
+('04/15/2015 02:18:00', 102871, 108, 'BEER', 0),
+('04/15/2015 02:19:00', 102871, 108, 'WINE', 0),
+('04/15/2015 02:22:00', 102871, 108, 'CHECKOUT', 21),
+('04/15/2015 02:25:00', 102871, 108, 'LANDING', 0),
+('04/15/2015 02:17:00', 103711, 109, 'BEER', 0),
+('04/15/2015 02:18:00', 103711, 109, 'LANDING', 0),
+('04/15/2015 02:19:00', 103711, 109, 'WINE', 0);
+
      2. +
    2. Calculate the revenue by checkout: 
      +DROP TABLE IF EXISTS path_output, path_output_tuples;
+SELECT madlib.path(
+     'eventlog',                -- Name of input table
+     'path_output',             -- Table name to store path results
+     'session_id',              -- Partition input table by session
+     'event_timestamp ASC',     -- Order partitions in input table by time
+     'buy:=page=''CHECKOUT''',  -- Define a symbol for checkout events
+     '(buy)',                   -- Pattern search: purchase
+     'sum(revenue) as checkout_rev',    -- Aggregate:  sum revenue by checkout
+     TRUE                       -- Persist matches
+     );
+SELECT * FROM path_output ORDER BY session_id, match_id;
+
      Result: 
      + session_id | match_id | checkout_rev
+------------+----------+--------------
+        100 |        1 |           39
+        102 |        1 |           15
+        102 |        2 |           23
+        103 |        1 |           16
+        104 |        1 |           12
+        108 |        1 |           21
+(6 rows)
+
      Note that there are 2 checkouts within session 102, which is apparent from the 'match_id' column. This serves to illustrate that the 'aggregate_func' operates on a per pattern match basis, not on a per partition basis. If in fact we wanted revenue by partition ('session_id' in this example), then we could do: 
      +SELECT session_id, sum(checkout_rev) FROM path_output GROUP BY session_id ORDER BY session_id;
+
      Result: 
      + session_id | sum
+------------+-----
+        100 |  39
+        102 |  38
+        103 |  16
+        104 |  12
+        108 |  21
+(5 rows)
+
      Since we set TRUE for 'persist_rows', we can view the associated pattern matches: 
      +SELECT * FROM path_output_tuples ORDER BY session_id ASC, event_timestamp ASC;
+
      Result: 
      +   event_timestamp   | user_id | session_id |   page   | revenue | symbol | match_id
+---------------------+---------+------------+----------+---------+--------+----------
+ 2015-04-15 01:05:00 |  100821 |        100 | CHECKOUT |      39 | buy    |        1
+ 2015-04-15 01:17:00 |  101121 |        102 | CHECKOUT |      15 | buy    |        1
+ 2015-04-15 01:22:00 |  101121 |        102 | CHECKOUT |      23 | buy    |        2
+ 2015-04-15 02:19:00 |  101331 |        103 | CHECKOUT |      16 | buy    |        1
+ 2015-04-15 02:25:00 |  101443 |        104 | CHECKOUT |      12 | buy    |        1
+ 2015-04-15 02:22:00 |  102871 |        108 | CHECKOUT |      21 | buy    |        1
+(6 rows)
+
      Notice that the 'symbol' and 'match_id' columns are added to the right of the matched rows.
      3. +
    3. We are interested in sessions with an order placed within 4 pages of entering the shopping site via the landing page. We represent this by the regular expression: '(land)[^(land)(buy)]{0,2}(buy)'. In other words, visit to the landing page followed by from 0 to 2 non-entry, non-sale pages, followed by a purchase. The SQL is as follows: 
      +DROP TABLE IF EXISTS path_output, path_output_tuples;
+SELECT madlib.path(
+     'eventlog',                -- Name of input table
+     'path_output',             -- Table name to store path results
+     'session_id',              -- Partition input table by session
+     'event_timestamp ASC',     -- Order partitions in input table by time
+     'land:=page=''LANDING'',
+        wine:=page=''WINE'',
+        beer:=page=''BEER'',
+        buy:=page=''CHECKOUT'',
+        other:=page<>''LANDING'' AND page<>''WINE'' AND page<>''BEER'' AND  page<>''CHECKOUT''',    -- Symbols for  page types
+      '(land)[^(land)(buy)]{0,2}(buy)', -- Purchase within 4 pages entering site
+     'sum(revenue) as checkout_rev',    -- Aggregate:  sum revenue by checkout
+     TRUE                       -- Persist matches
+     );
+SELECT * FROM path_output ORDER BY session_id, match_id;
+
      Result: 
      + session_id | match_id | session_rev
+------------+----------+-------------
+        100 |        1 |          39
+        102 |        1 |          15
+        102 |        2 |          23
+(3 rows)
+
      Now view the associated pattern matches: 
      +SELECT * FROM path_output_tuples ORDER BY session_id ASC, event_timestamp ASC;
+
      Result: 
      +   event_timestamp   | user_id | session_id |   page   | revenue | symbol | match_id
+---------------------+---------+------------+----------+---------+--------+----------
+ 2015-04-15 01:03:00 |  100821 |        100 | LANDING  |       0 | land   |        1
+ 2015-04-15 01:04:00 |  100821 |        100 | WINE     |       0 | wine   |        1
+ 2015-04-15 01:05:00 |  100821 |        100 | CHECKOUT |      39 | buy    |        1
+ 2015-04-15 01:15:00 |  101121 |        102 | LANDING  |       0 | land   |        1
+ 2015-04-15 01:16:00 |  101121 |        102 | WINE     |       0 | wine   |        1
+ 2015-04-15 01:17:00 |  101121 |        102 | CHECKOUT |      15 | buy    |        1
+ 2015-04-15 01:18:00 |  101121 |        102 | LANDING  |       0 | land   |        2
+ 2015-04-15 01:19:00 |  101121 |        102 | HELP     |       0 | other  |        2
+ 2015-04-15 01:21:00 |  101121 |        102 | WINE     |       0 | wine   |        2
+ 2015-04-15 01:22:00 |  101121 |        102 | CHECKOUT |      23 | buy    |        2
+(10 rows)
+
      4. +
    4. We may want to use a window function instead of an aggregate. Currently, only aggregates are supported in the core path function in the parameter 'aggregate_func'. However, you can write window functions on the output tuples to achieve the desired result.   Continuing the previous example, let’s say we want to compute average revenue for checkouts within 4 pages of entering the shopping site via the landing page: 
      +SELECT DATE(event_timestamp), user_id, session_id, revenue,
+    avg(revenue) OVER (PARTITION BY DATE(event_timestamp)) as avg_checkout_rev
+    FROM path_output_tuples
+    WHERE page='CHECKOUT'
+    ORDER BY user_id, session_id;
+
      Result: 
      +    date    | user_id | session_id | revenue | avg_checkout_rev
+------------+---------+------------+---------+------------------
+ 2015-04-15 |  100821 |        100 |      39 | 25.6666666666667
+ 2015-04-15 |  101121 |        102 |      15 | 25.6666666666667
+ 2015-04-15 |  101121 |        102 |      23 | 25.6666666666667
+(3 rows)
+
      Here we are partitioning the window function by day because we want daily averages, although our sample data set only has a single day.
      5. +
    5. Now we want to do a golden path analysis to find the most successful shopper paths through the site. Since our data set is small, we decide this means the most frequently viewed page just before a checkout is made: 
      +DROP TABLE IF EXISTS path_output, path_output_tuples;
+SELECT madlib.path(
+     'eventlog',                -- Name of input table
+     'path_output',             -- Table name to store path results
+     'session_id',              -- Partition input table by session
+     'event_timestamp ASC',     -- Order partitions in input table by time
+     'land:=page=''LANDING'',
+        wine:=page=''WINE'',
+        beer:=page=''BEER'',
+        buy:=page=''CHECKOUT'',
+        other:=page<>''LANDING'' AND page<>''WINE'' AND page<>''BEER'' AND  page<>''CHECKOUT''',    -- Symbols for  page types
+      '[^(buy)](buy)',          -- Pattern to match
+     'array_agg(page ORDER BY session_id ASC, event_timestamp ASC) as page_path',    -- Build array with shopper paths
+     FALSE                       -- Don't persist matches
+     );
+
      Now count the common paths and print the most frequent: 
      +SELECT count(*), page_path from
+    (SELECT * FROM path_output) q
+GROUP BY page_path
+ORDER BY count(*) DESC
+LIMIT 10;
+
      Result: 
      + count |    page_path
+-------+-----------------
+     5 | {WINE,CHECKOUT}
+     1 | {BEER,CHECKOUT}
+(2 rows)
+
      There are only 2 different paths. The wine page is viewed more frequently than the beer page just before checkout.
      6. +
    6. To demonstrate the use of 'overlapping_patterns', consider a pattern with at least one page followed by and ending with a checkout: 
      +DROP TABLE IF EXISTS path_output, path_output_tuples;
+SELECT madlib.path(
+     'eventlog',                    -- Name of the table
+     'path_output',                 -- Table name to store the path results
+     'session_id',                  -- Partition by session
+     'event_timestamp ASC',         -- Order partitions in input table by time
+     $$ nobuy:=page<>'CHECKOUT',
+        buy:=page='CHECKOUT'
+     $$,  -- Definition of symbols used in the pattern definition
+     '(nobuy)+(buy)',         -- At least one page followed by and ending with a CHECKOUT.
+     'array_agg(page ORDER BY session_id ASC, event_timestamp ASC) as page_path',
+     FALSE,                        -- Don't persist matches
+     TRUE                          -- Turn on overlapping patterns
+     );
+SELECT * FROM path_output ORDER BY session_id, match_id;
+
      Result with overlap turned on: 
      + session_id | match_id |             page_path
+------------+----------+-----------------------------------
+        100 |        1 | {LANDING,WINE,CHECKOUT}
+        100 |        2 | {WINE,CHECKOUT}
+        102 |        1 | {LANDING,WINE,CHECKOUT}
+        102 |        2 | {WINE,CHECKOUT}
+        102 |        3 | {LANDING,HELP,WINE,CHECKOUT}
+        102 |        4 | {HELP,WINE,CHECKOUT}
+        102 |        5 | {WINE,CHECKOUT}
+        103 |        1 | {LANDING,WINE,HELP,WINE,CHECKOUT}
+        103 |        2 | {WINE,HELP,WINE,CHECKOUT}
+        103 |        3 | {HELP,WINE,CHECKOUT}
+        103 |        4 | {WINE,CHECKOUT}
+        104 |        1 | {BEER,CHECKOUT}
+        108 |        1 | {BEER,WINE,CHECKOUT}
+        108 |        2 | {WINE,CHECKOUT}
+(14 rows)
+
      With overlap turned off, the result would be: 
      + session_id | match_id |             page_path
+------------+----------+-----------------------------------
+        100 |        1 | {LANDING,WINE,CHECKOUT}
+        102 |        1 | {LANDING,WINE,CHECKOUT}
+        102 |        2 | {LANDING,HELP,WINE,CHECKOUT}
+        103 |        1 | {LANDING,WINE,HELP,WINE,CHECKOUT}
+        104 |        1 | {BEER,CHECKOUT}
+        108 |        1 | {BEER,WINE,CHECKOUT}
+(6 rows)
+
      7. +
    +

    Note
    Please note some current limitations of the path algorithm.
      +
    • Window functions cannot currently be used in the parameter 'aggregate_func'. Instead, output the pattern matches and write a SQL query with a window function over the output tuples.
      • +
    • A given row can only match one symbol. If a row matches multiple symbols, the symbol that comes first in the symbol definition list will take precedence.
      • +
    • Maximum number of symbols that can be defined is 35.
      • +
    • The columns 'match_id' and 'symbol' are generated by the path algorithm. If coincidently you have columns in your input data named 'match_id' or 'symbol', the system generated column names will be changed to "__madlib_path_match_id__" and "__madlib_path_symbol__"
      • +
    +
    +

    Nomenclature
    +

    Partition

      +
    • scope of rows to be searched for pattern match
      • +
    • typical examples: user id, session id, portfolio id
      • +
    +

    Order

      +
    • sort order of input rows in partition
      • +
    • typical example: time
      • +
    +

    Symbol

      +
    • a row of a particular type that you’re searching for, that you want to include in a pattern
      • +
    +

    Pattern

      +
    • regular PostgreSQL pattern match expression of symbols and operators that you want to match across rows
      • +
    +

    Pattern match

      +
    • rows that result from a pattern match expression of symbols
      • +
    • can be multiple matches per partition
      • +
    +

    Literature
    +

    NOTE: The following links refer to documentation resources for the current PostgreSQL database version. Depending upon your database platform version, you may need to change "current" references in the links to your database version.

    +

    If your database platform uses the Greenplum Database (or related variants), please check with the project community and/or your database vendor to identify the PostgreSQL version it is based on.

    +

    [1] PostgreSQL basic statements/assignment operator, http://www.postgresql.org/docs/current/static/plpgsql-statements.html

    +

    [2] PostgreSQL pattern matching, http://www.postgresql.org/docs/current/static/functions-matching.html

    +

    [3] PostgreSQL aggregate functions, http://www.postgresql.org/docs/current/static/tutorial-agg.html

    +

    [4] PostgreSQL window functions, http://www.postgresql.org/docs/current/static/tutorial-window.html

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__pca.html b/docs/docs/v2.1.0/group__grp__pca.html new file mode 100644 index 00000000..5385262e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pca.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: Dimensionality Reduction + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Dimensionality Reduction
    Unsupervised Learning
    +
    +
    +

    Detailed Description

    +

    Methods for reducing the number of variables in a dataset to obtain a set of principle variables.

    + + + + + + + + +

    +Modules

     Principal Component Analysis
     Produces a model that transforms a number of (possibly) correlated variables into a (smaller) number of uncorrelated variables called principal components.
     
     Principal Component Projection
     Projects a higher dimensional data point to a lower dimensional subspace spanned by principal components learned through the PCA training procedure.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__pca.js b/docs/docs/v2.1.0/group__grp__pca.js new file mode 100644 index 00000000..2863cf8c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pca.js @@ -0,0 +1,5 @@ +var group__grp__pca = +[ + [ "Principal Component Analysis", "group__grp__pca__train.html", null ], + [ "Principal Component Projection", "group__grp__pca__project.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__pca__project.html b/docs/docs/v2.1.0/group__grp__pca__project.html new file mode 100644 index 00000000..08ba779a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pca__project.html @@ -0,0 +1,490 @@ + + + + + + + + +MADlib: Principal Component Projection + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Principal Component Projection
    Unsupervised Learning » Dimensionality Reduction
    +
    +
    +
    Contents +

    Principal component projection is a mathematical procedure that projects high dimensional data onto a lower dimensional space. This lower dimensional space is defined by the \( k \) principal components with the highest variance in the training data.

    +

    More details on the mathematics of PCA can be found in Principal Component Analysis and some details about principal component projection calculations can be found in the Technical Background.

    +

    Projection Function
    The projection functions are slightly different for dense and sparse matrices. For dense matrices: 
    +madlib.pca_project( source_table,
+                    pc_table,
+                    out_table,
+                    row_id,
+                    residual_table,
+                    result_summary_table
+                  )
+
    For sparse matrices: 
    +madlib.pca_sparse_project( source_table,
+                           pc_table,
+                           out_table,
+                           row_id,
+                           col_id,              -- Sparse matrices only
+                           val_id,              -- Sparse matrices only
+                           row_dim,             -- Sparse matrices only
+                           col_dim,             -- Sparse matrices only
+                           residual_table,
+                           result_summary_table
+                         )
+
    +

    Arguments

    +
    source_table
    +

    TEXT. Source table name. Identical to pca_train, the input data matrix should have \( N \) rows and \( M \) columns, where \( N \) is the number of data points, and \( M \) is the number of features for each data point.

    +

    The input table for pca_project is expected to be in the one of the two standard MADlib dense matrix formats, and the sparse input table for pca_sparse_project should be in the standard MADlib sparse matrix format. These formats are described in the documentation for Principal Component Analysis.

    +

    +
    +
    pc_table
    +

    TEXT. Table name for the table containing principal components.

    +

    +
    +
    out_table
    +

    TEXT. Name of the table that will contain the low-dimensional representation of the input data.

    +

    The out_table encodes a dense matrix with the projection onto the principal components. The table has the following columns:

    + + + + + +
    row_id Row id of the output matrix.
    row_vec A vector containing elements in the row of the matrix.
    +

    +
    +
    row_id
    +

    TEXT. Column name containing the row IDs in the input source table. The column should be of type INT (or a type that can be cast to INT) and should only contain values between 1 and N. For dense matrix format, it should contain all continguous integers from 1 to N describing the full matrix.

    +

    +
    +
    col_id
    +

    TEXT. Column name containing the column IDs in sparse matrix representation. The column should be of type INT (or a type that can be cast to INT) and should only contain values between 1 and M. This parameter applies to sparse matrices only.

    +

    +
    +
    val_id
    +

    TEXT. Name of 'val_id' column in sparse matrix representation defining the values of the nonzero entries. This parameter applies to sparse matrices only.

    +

    +
    +
    row_dim
    +

    INTEGER. The actual number of rows in the matrix. That is, if the matrix was transformed into dense format, this is the number of rows it would have. This parameter applies to sparse matrices only.

    +

    +
    +
    col_dim
    +

    INTEGER. The actual number of columns in the matrix. That is, if the matrix was transformed into dense format, this is the number of columns it would have. This parameter applies to sparse matrices only.

    +
    Note
    The parameters 'row_dim' and 'col_dim' could actually be inferred from the sparse matrix representation, so they will be removed in the future. For now they are maintained for backward compatability so you must enter them. Making 'row_dim' or 'col_dim' larger than the actual matrix has the effect of padding it with zeros, which is probably not useful.
    +
    +
    residual_table (optional)
    +

    TEXT, default: NULL. Name of the optional residual table.

    +

    The residual_table encodes a dense residual matrix. The table has the following columns:

    + + + + + +
    row_id Row id of the output matrix.
    row_vec A vector containing elements in the row of the residual matrix.
    +

    +
    +
    result_summary_table (optional)
    +

    TEXT, default: NULL. Name of the optional summary table.

    +

    The result_summary_table contains information about the performance time of the PCA projection. The table has the following columns:

    + + + + + + +
    exec_time Elapsed time (ms) for execution of the function.
    residual_norm Absolute error of the residuals.
    relative_residual_norm Relative error of the residuals.
    +
    +
    +

    Examples
      +
    1. View online help for the PCA projection function: 
      +SELECT madlib.pca_project();
+
      2. +
    2. Create sample data in dense matrix form: 
      +DROP TABLE IF EXISTS mat;
+CREATE TABLE mat (id integer,
+                  row_vec double precision[]
+                  );
+INSERT INTO mat VALUES
+(1, '{1,2,3}'),
+(2, '{2,1,2}'),
+(3, '{3,2,1}');
+
      3. +
    3. Run the PCA function for a specified number of principal components and view the results: 
      +DROP TABLE IF EXISTS result_table, result_table_mean;
+SELECT madlib.pca_train('mat',             -- Source table
+                        'result_table',    -- Output table
+                        'id',              -- Row id of source table
+                         2);               -- Number of principal components
+SELECT * FROM result_table ORDER BY row_id;
+
      + row_id |                     principal_components                     |      std_dev      |    proportion
+--------+--------------------------------------------------------------+-------------------+-------------------
+      1 | {0.707106781186547,-6.93889390390723e-18,-0.707106781186548} |  1.41421356237309 | 0.857142857142244
+      2 | {0,1,0}                                                      | 0.577350269189626 | 0.142857142857041
+(2 rows)
+
      4. +
    4. Project the original data to a lower dimensional representation and view the result of the projection: 
      +DROP TABLE IF EXISTS residual_table, result_summary_table, out_table;
+SELECT madlib.pca_project( 'mat',
+                           'result_table',
+                           'out_table',
+                           'id',
+                           'residual_table',
+                           'result_summary_table'
+                           );
+SELECT * FROM out_table ORDER BY row_id;
+
      + row_id |               row_vec
+--------+--------------------------------------
+      1 | {-1.41421356237309,-0.33333333333}
+      2 | {2.77555756157677e-17,0.66666666667}
+      3 | {1.41421356237309,-0.33333333333}
+(3 rows)
+
      Check the error in the projection: 
      +SELECT * FROM result_summary_table;
+
      +   exec_time   |   residual_norm   | relative_residual_norm
+---------------+-------------------+------------------------
+ 331.792116165 | 5.89383520611e-16 |      9.68940539229e-17
+(1 row)
+
      Check the residuals: 
      +SELECT * FROM residual_table ORDER BY row_id;
+
      + row_id |                              row_vec
+--------+--------------------------------------------------------------------
+      1 | {-2.22044604925031e-16,-1.11022302462516e-16,3.33066907387547e-16}
+      2 | {-1.12243865646685e-18,0,4.7381731349413e-17}
+      3 | {2.22044604925031e-16,1.11022302462516e-16,-3.33066907387547e-16}
+(3 rows)
+
      5. +
    5. Now we use grouping in dense form to learn different models for different groups. First, we create sample data in dense matrix form with a grouping column. Note we actually have different matrix sizes for the different groups, which is allowed for dense: 
      +DROP TABLE IF EXISTS mat_group;
+CREATE TABLE mat_group (
+    id integer,
+    row_vec double precision[],
+    matrix_id integer
+);
+INSERT INTO mat_group VALUES
+(1, '{1,2,3}', 1),
+(2, '{2,1,2}', 1),
+(3, '{3,2,1}', 1),
+(4, '{1,2,3,4,5}', 2),
+(5, '{2,5,2,4,1}', 2),
+(6, '{5,4,3,2,1}', 2);
+
      6. +
    6. Run the PCA function with grouping for a specified proportion of variance and view the results: 
      +DROP TABLE IF EXISTS result_table_group, result_table_group_mean;
+SELECT madlib.pca_train('mat_group',             -- Source table
+                        'result_table_group',    -- Output table
+                        'id',                    -- Row id of source table
+                         0.8,                    -- Proportion of variance
+                        'matrix_id');            -- Grouping column
+SELECT * FROM result_table_group ORDER BY matrix_id, row_id;
+
      + row_id |                                      principal_components                                      |     std_dev     |    proportion     | matrix_id
+--------+------------------------------------------------------------------------------------------------+-----------------+-------------------+-----------
+      1 | {0.707106781186548,0,-0.707106781186547}                                                       | 1.4142135623731 | 0.857142857142245 |         1
+      1 | {-0.555378486712784,-0.388303582074091,0.0442457354870796,0.255566375612852,0.688115693174023} | 3.2315220311722 | 0.764102534485173 |         2
+      2 | {0.587384101786277,-0.485138064894743,0.311532046315153,-0.449458074050715,0.347212037159181}  |  1.795531127192 | 0.235897465516047 |         2
+(3 rows)
+
      7. +
    7. Run the PCA projection on subsets of an input table based on grouping columns. Note that the parameter 'pc_table' used for projection must be generated in training using the same grouping columns. 
      +DROP TABLE IF EXISTS mat_group_projected;
+SELECT madlib.pca_project('mat_group',
+                          'result_table_group',
+                          'mat_group_projected',
+                          'id');
+SELECT * FROM mat_group_projected ORDER BY matrix_id, row_id;
+
      + row_id |                row_vec                | matrix_id
+--------+---------------------------------------+-----------
+      1 | {1.4142135623731}                     |         1
+      2 | {7.40148683087139e-17}                |         1
+      3 | {-1.4142135623731}                    |         1
+      4 | {-3.59290479201926,0.559694003674779} |         2
+      5 | {0.924092949098971,-2.00871628417505} |         2
+      6 | {2.66881184290186,1.44902228049511}   |         2
+(6 rows)
+
      8. +
    8. Now let's look at sparse matrices. Create sample data in sparse matrix form: 
      +DROP TABLE IF EXISTS mat_sparse;
+CREATE TABLE mat_sparse (
+    row_id integer,
+    col_id integer,
+    value double precision
+);
+INSERT INTO mat_sparse VALUES
+(1, 1, 1.0),
+(2, 2, 2.0),
+(3, 3, 3.0),
+(4, 4, 4.0),
+(1, 5, 5.0),
+(2, 4, 6.0),
+(3, 2, 7.0),
+(4, 3, 8.0);
+
      As an aside, this is what the sparse matrix above looks like when put in dense form: 
      +DROP TABLE IF EXISTS mat_dense;
+SELECT madlib.matrix_densify('mat_sparse',
+                            'row=row_id, col=col_id, val=value',
+                            'mat_dense');
+SELECT * FROM mat_dense ORDER BY row_id;
+
      + row_id |    value
+--------+-------------
+      1 | {1,0,0,0,5}
+      2 | {0,2,0,6,0}
+      3 | {0,7,3,0,0}
+      4 | {0,0,8,4,0}
+(4 rows)
+
      9. +
    9. Run the PCA sparse function for a specified number of principal components and view the results: 
      DROP TABLE IF EXISTS result_table, result_table_mean;
+SELECT madlib.pca_sparse_train( 'mat_sparse',       -- Source table
+                                'result_table',     -- Output table
+                                'row_id',           -- Row id of source table
+                                'col_id',           -- Column id of source table
+                                'value',            -- Value of matrix at row_id, col_id
+                                4,                  -- Actual number of rows in the matrix
+                                5,                  -- Actual number of columns in the matrix
+                                3);                 -- Number of principal components
+SELECT * FROM result_table ORDER BY row_id;
+
      Result (with principal components truncated for readability): 
      + row_id |         principal_components                 |     std_dev      |    proportion
+--------+----------------------------------------------+------------------+-------------------
+      1 | {-0.0876046030186158,-0.0968983772909994,... | 4.21362803829554 | 0.436590030617467
+      2 | {-0.0647272661608605,0.877639526308692,...   | 3.68408023747461 | 0.333748701544697
+      3 | {-0.0780380267884855,0.177956517174911,...   | 3.05606908060098 | 0.229661267837836
+(3 rows)
+
      10. +
    10. Project the original sparse data to low-dimensional representation: 
      +DROP TABLE IF EXISTS mat_sparse_out;
+SELECT madlib.pca_sparse_project(
+                    'mat_sparse',
+                    'result_table',
+                    'mat_sparse_out',
+                    'row_id',
+                    'col_id',
+                    'value',
+                    4,
+                    5
+                    );
+SELECT * FROM mat_sparse_out ORDER BY row_id;
+
      + row_id |                         row_vec
+--------+---------------------------------------------------------
+      1 | {4.66617015032369,-2.63552220635847,2.1865220849604}
+      2 | {0.228360685652383,-1.21616275892926,-4.46864627611561}
+      3 | {0.672067460100428,5.45249627172823,0.56445525585642}
+      4 | {-5.5665982960765,-1.6008113064405,1.71766893529879}
+(4 rows)
+
      11. +
    11. Now we use grouping in sparse form to learn different models for different groups. First, we create sample data in sparse matrix form with a grouping column: 
      +DROP TABLE IF EXISTS mat_sparse_group;
+CREATE TABLE mat_sparse_group (
+    row_id integer,
+    col_id integer,
+    value double precision,
+    matrix_id integer);
+INSERT INTO mat_sparse_group VALUES
+(1, 1, 1.0, 1),
+(2, 2, 2.0, 1),
+(3, 3, 3.0, 1),
+(4, 4, 4.0, 1),
+(1, 5, 5.0, 1),
+(2, 4, 6.0, 2),
+(3, 2, 7.0, 2),
+(4, 3, 8.0, 2);
+
      12. +
    12. Run the PCA function with grouping for a specified proportion of variance and view the results: 
      +DROP TABLE IF EXISTS result_table_group, result_table_group_mean;
+SELECT madlib.pca_sparse_train( 'mat_sparse_group',       -- Source table
+                                'result_table_group',     -- Output table
+                                'row_id',           -- Row id of source table
+                                'col_id',           -- Column id of source table
+                                'value',            -- Value of matrix at row_id, col_id
+                                4,                 -- Actual number of rows in the matrix
+                                5,                 -- Actual number of columns in the matrix
+                                0.8,                 -- Proportion of variance
+                                'matrix_id');
+SELECT * FROM result_table_group ORDER BY matrix_id, row_id;
+
      Result (with principal components truncated for readability): 
      + row_id |           principal_components             |     std_dev      |    proportion     | matrix_id
+--------+--------------------------------------------+------------------+-------------------+-----------
+      1 | {-0.17805696611353,0.0681313257646983,...  | 2.73659933165925 | 0.544652792875481 |         1
+      2 | {-0.0492086814863993,0.149371585357526,... | 2.06058314533194 | 0.308800210823714 |         1
+      1 | {0,-0.479486114660443,...                  | 4.40325305087975 | 0.520500333693473 |         2
+      2 | {0,0.689230898585949,...                   |  3.7435566458567 | 0.376220573442628 |         2
+(4 rows)
+
      13. +
    13. Projection in sparse format with grouping: 
      +DROP TABLE IF EXISTS mat_sparse_group_projected;
+SELECT madlib.pca_sparse_project(
+    'mat_sparse_group',
+    'result_table_group',
+    'mat_sparse_group_projected',
+    'row_id',
+    'col_id',
+    'value',
+    4,
+    5
+    );
+SELECT * FROM mat_sparse_group_projected ORDER BY matrix_id, row_id;
+
      + row_id |                 row_vec                 | matrix_id
+--------+-----------------------------------------+-----------
+      1 | {-4.00039298524261,-0.626820612715982}  |         1
+      2 | {0.765350785238575,0.951348276645455}   |         1
+      3 | {1.04951017256904,2.22388180170356}     |         1
+      4 | {2.185532027435,-2.54840946563303}      |         1
+      1 | {-0.627846810195469,-0.685031603549092} |         2
+      2 | {-1.64754249747757,-4.7662114622896}    |         2
+      3 | {-3.98424961281857,4.13958468655255}    |         2
+      4 | {6.25963892049161,1.31165837928614}     |         2
+(8 rows)
+
      14. +
    +
    +

    Notes
      +
    • This function is intended to operate on the principal component tables generated by pca_train or pca_sparse_train. The MADlib PCA functions generate a table containing the column-means in addition to a table containing the principal components. If this table is not found by the MADlib projection function, it will trigger an error. As long the principal component tables are created with MADlib functions, then the column-means table will be automatically found by the MADlib projection functions.
      • +
    • Because of the centering step in PCA projection (see "Technical Background"), sparse matrices almost always become dense during the projection process. Thus, this implementation automatically densifies sparse matrix input, and there should be no expected performance improvement in using sparse matrix input over dense matrix input.
      • +
    • Table names can be optionally schema qualified (current_schemas() is searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').
      • +
    • If the input table for pca_project (pca_sparse_project) contains grouping columns, the same grouping columns must be used in the training function used to generate the principal components too.
      • +
    +
    +

    Technical Background
    +

    Given a table containing some principal components \( \boldsymbol P \) and some input data \( \boldsymbol X \), the low-dimensional representation \( {\boldsymbol X}' \) is computed as

    +\begin{align*} {\boldsymbol {\hat{X}}} & = {\boldsymbol X} - \vec{e} \hat{x}^T \\ {\boldsymbol X}' & = {\boldsymbol {\hat {X}}} {\boldsymbol P}. \end{align*} +

    +

    where \(\hat{x} \) is the column means of \( \boldsymbol X \) and \( \vec{e} \) is the vector of all ones. This step is equivalent to centering the data around the origin.

    +

    The residual table \( \boldsymbol R \) is a measure of how well the low-dimensional representation approximates the true input data, and is computed as

    +\[ {\boldsymbol R} = {\boldsymbol {\hat{X}}} - {\boldsymbol X}' {\boldsymbol P}^T. \] +

    +

    A residual matrix with entries mostly close to zero indicates a good representation.

    +

    The residual norm \( r \) is simply

    +\[ r = \|{\boldsymbol R}\|_F \] +

    +

    where \( \|\cdot\|_F \) is the Frobenius norm. The relative residual norm \( r' \) is

    +\[ r' = \frac{ \|{\boldsymbol R}\|_F }{\|{\boldsymbol X}\|_F } \] +

    +

    Related Topics
    File pca_project.sql_in documenting the SQL functions
    +

    Principal Component Analysis

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__pca__train.html b/docs/docs/v2.1.0/group__grp__pca__train.html new file mode 100644 index 00000000..88ae7c9e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pca__train.html @@ -0,0 +1,446 @@ + + + + + + + + +MADlib: Principal Component Analysis + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Principal Component Analysis
    Unsupervised Learning » Dimensionality Reduction
    +
    +
    +
    Contents +

    Principal component analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components. This transformation is defined in such a way that the first principal component has the largest possible variance (i.e., accounts for as much of the variability in the data as possible), and each succeeding component in turn has the highest variance possible under the constraint that it be orthogonal to (i.e., uncorrelated with) the preceding components.

    +

    See the Technical Background for an introduction to principal component analysis.

    +

    Training Function
    The training functions are slightly different for dense and sparse matrices. For dense matrices: 
    +pca_train( source_table,
+           out_table,
+           row_id,
+           components_param,
+           grouping_cols,
+           lanczos_iter,
+           use_correlation,
+           result_summary_table
+         )
+
    For sparse matrices: 
    +pca_sparse_train( source_table,
+                  out_table,
+                  row_id,
+                  col_id,           -- Sparse matrices only
+                  val_id,           -- Sparse matrices only
+                  row_dim,          -- Sparse matrices only
+                  col_dim,          -- Sparse matrices only
+                  components_param,
+                  grouping_cols,
+                  lanczos_iter,
+                  use_correlation,
+                  result_summary_table
+                )
+
    +

    Arguments

    +
    source_table
    +

    TEXT. Name of the input table containing the data for PCA training. The input data matrix should have \( N \) rows and \( M \) columns, where \( N \) is the number of data points, and \( M \) is the number of features for each data point.

    +

    A dense input table is expected to be in the one of the two standard MADlib dense matrix formats, and a sparse input table should be in the standard MADlib sparse matrix format.

    +

    The two standard MADlib dense matrix formats are: 

    {TABLE|VIEW} source_table (
+    row_id INTEGER,
+    row_vec FLOAT8[],
+)

    and 

    {TABLE|VIEW} source_table (
+    row_id INTEGER,
+    col1 FLOAT8,
+    col2 FLOAT8,
+    ...
+)

    Note that the column name row_id is taken as an input parameter, and should contain a continguous list of row indices (starting at 1) for the input matrix.

    +

    The input table for sparse PCA is expected to be in the form:

    +
    {TABLE|VIEW} source_table (
+    ...
+    row_id INTEGER,
+    col_id INTEGER,
+    val_id FLOAT8,
+    ...
+)

    The row_id and col_id columns specify which entries in the matrix are nonzero, and the val_id column defines the values of the nonzero entries.

    +

    Please refer to the Matrix Operations documentation for more details on defining matrices.

    +

    +
    +
    out_table
    +

    TEXT. The name of the table that will contain the output. There are three possible output tables as described below.

    +

    The primary output table (out_table) encodes the principal components with the k highest eigenvalues where k is either directly provided by the user or computed according to the proportion of variance. The table has the following columns:

    + + + + + + + + +
    row_id Eigenvalue rank in descending order of the eigenvalue size.
    principal_components Vectors containing elements of the principal components.
    std_dev The standard deviation of each principal component.
    proportion The proportion of variance covered by the principal component.
    +

    The table out_table_mean contains the column means. This table has just one column:

    + + +
    column_mean A vector containing the column means for the input matrix.
    +

    The optional table result_summary_table contains information about the performance of the PCA. The contents of this table are described under the result_summary_table argument.

    +

    +
    +
    row_id
    +

    TEXT. Column name containing the row IDs in the input source table. The column should be of type INT (or a type that can be cast to INT) and should only contain values between 1 and N. For dense matrix format, it should contain all continguous integers from 1 to N describing the full matrix.

    +

    +
    +
    col_id
    +

    TEXT. Column name containing the column IDs in sparse matrix representation. The column should be of type INT (or a type that can be cast to INT) and should only contain values between 1 and M. This parameter applies to sparse matrices only.

    +

    +
    +
    val_id
    +

    TEXT. Name of 'val_id' column in sparse matrix representation defining the values of the nonzero entries. This parameter applies to sparse matrices only.

    +

    +
    +
    row_dim
    +

    INTEGER. The actual number of rows in the matrix. That is, if the matrix was transformed into dense format, this is the number of rows it would have. This parameter applies to sparse matrices only.

    +

    +
    +
    col_dim
    +

    INTEGER. The actual number of columns in the matrix. That is, if the matrix was transformed into dense format, this is the number of columns it would have. This parameter applies to sparse matrices only.

    +
    Note
    The parameters 'row_dim' and 'col_dim' could actually be inferred from the sparse matrix representation, so they will be removed in the future. For now they are maintained for backward compatability so you must enter them. Making 'row_dim' or 'col_dim' larger than the actual matrix has the effect of padding it with zeros, which is probably not useful.
    +
    +
    components_param
    +

    INTEGER or FLOAT. The parameter to control the number of principal components to calculate from the input data. If 'components_param' is INTEGER, it is used to denote the number of principal components (k) to compute. If 'components_param' is FLOAT, the algorithm will return enough principal vectors so that the ratio of the sum of the eigenvalues collected thus far to the sum of all eigenvalues is greater than this parameter (proportion of variance). The value of 'components_param' must be either a positive INTEGER or a FLOAT in the range (0.0,1.0]

    +
    Note
    The difference in interpretation between INTEGER and FLOAT was introduced to maintain backward campatibility after the proportion of variance feature was introduced. A special case to be aware of: 'components_param' = 1 (INTEGER) will return 1 principal component, but 'components_param' = 1.0 (FLOAT) will return all principal components, i.e., proportion of variance of 100%.
    +
    +Also, please note that the number of principal components (k) is global, even in the case where grouping is used (see 'grouping_cols' below). In the case of grouping, proportion of variance might be a better choice; this could result in different numbers of principal components for different groups.
    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. A comma-separated list of column names, with the source data grouped using the combination of all the columns. An independent PCA model will be computed for each combination of the grouping columns.

    +
    Note
    Dense matrices can be different sizes for different groups if desired. Sparse matrices cannot be different sizes for different groups, because the 'row_dim' and 'col_dim' parameters used for sparse matrices are global across all groups.
    +
    +
    lanczos_iter (optional)
    +

    INTEGER, default: minimum of {k+40, smallest matrix dimension} where k is the number of principal components specified in the parameter 'components_param'. This parameter defines the number of Lanczos iterations for the SVD calculation. The Lanczos iteration number roughly corresponds to the accuracy of the SVD calculation, and a higher number of iterations corresponds to greater accuracy but longer computation time. The number of iterations must be at least as large as the value of k, but no larger than the smallest dimension of the matrix. If the number of iterations is set to zero, then the default number of iterations will be used.

    +
    Note
    If both 'lanczos_iter' and proportion of variance (via the 'components_param' parameter) are defined, 'lanczos_iter' will take precedence in determining the number of principal components (i.e. the number of principal components will not be greater than 'lanczos_iter' even if the target proportion had not been reached).
    +
    +
    use_correlation (optional)
    +

    BOOLEAN, default FALSE. Whether to use the correlation matrix for calculating the principal components instead of the covariance matrix. Currently use_correlation is a placeholder for forward compatibility, so this value must be set to false.

    +

    +
    +
    result_summary_table (optional)
    +

    TEXT, default NULL. Name of the optional summary table. When NULL, no summary table is generated.

    +

    This sumary table has the following columns:

    + + + + + + + + + + + + +
    rows_used INTEGER. Number of data points in the input.
    exec_time (ms) FLOAT8. Number of milliseconds for the PCA calculation to run.
    iter INTEGER. Number of iterations used in the SVD calculation.
    recon_error FLOAT8. The absolute error in the SVD approximation.
    relative_recon_error FLOAT8. The relative error in the SVD approximation.
    use_correlation BOOLEAN. Indicates if the correlation matrix was used.
    +
    +
    +

    Examples
    +
      +
    1. View online help for the PCA training functions: 
      +SELECT madlib.pca_train();
+
      or 
      +SELECT madlib.pca_sparse_train();
+
      2. +
    2. Create sample data in dense matrix form: 
      +DROP TABLE IF EXISTS mat;
+CREATE TABLE mat (id integer,
+                  row_vec double precision[]
+                  );
+INSERT INTO mat VALUES
+(1, '{1,2,3}'),
+(2, '{2,1,2}'),
+(3, '{3,2,1}');
+
      3. +
    3. Run the PCA function for a specified number of principal components and view the results: 
      +DROP TABLE IF EXISTS result_table, result_table_mean;
+SELECT madlib.pca_train('mat',             -- Source table
+                        'result_table',    -- Output table
+                        'id',              -- Row id of source table
+                         2);               -- Number of principal components
+SELECT * FROM result_table ORDER BY row_id;
+
      + row_id |                     principal_components                     |      std_dev      |    proportion
+--------+--------------------------------------------------------------+-------------------+-------------------
+      1 | {0.707106781186547,-6.93889390390723e-18,-0.707106781186548} |  1.41421356237309 | 0.857142857142244
+      2 | {0,1,0}                                                      | 0.577350269189626 | 0.142857142857041
+(2 rows)
+
      4. +
    4. Run the PCA function for a specified proportion of variance and view the results: 
      +DROP TABLE IF EXISTS result_table, result_table_mean;
+SELECT madlib.pca_train('mat',             -- Source table
+                        'result_table',    -- Output table
+                        'id',              -- Row id of source table
+                         0.9);             -- Proportion of variance
+SELECT * FROM result_table ORDER BY row_id;
+
      + row_id |                     principal_components                     |      std_dev      |    proportion
+--------+--------------------------------------------------------------+-------------------+-------------------
+      1 | {0.707106781186548,-2.77555756156289e-17,-0.707106781186548} |   1.4142135623731 | 0.857142857142245
+      2 | {-1.11022302462516e-16,-1,0}                                 | 0.577350269189626 | 0.142857142857041
+(2 rows)
+
      5. +
    5. Now we use grouping in dense form to learn different models for different groups. First, we create sample data in dense matrix form with a grouping column. Note we actually have different matrix sizes for the different groups, which is allowed for dense: 
      +DROP TABLE IF EXISTS mat_group;
+CREATE TABLE mat_group (
+    id integer,
+    row_vec double precision[],
+    matrix_id integer
+);
+INSERT INTO mat_group VALUES
+(1, '{1,2,3}', 1),
+(2, '{2,1,2}', 1),
+(3, '{3,2,1}', 1),
+(4, '{1,2,3,4,5}', 2),
+(5, '{2,5,2,4,1}', 2),
+(6, '{5,4,3,2,1}', 2);
+
      6. +
    6. Run the PCA function with grouping for a specified proportion of variance and view the results: 
      +DROP TABLE IF EXISTS result_table_group, result_table_group_mean;
+SELECT madlib.pca_train('mat_group',             -- Source table
+                        'result_table_group',    -- Output table
+                        'id',                    -- Row id of source table
+                         0.8,                    -- Proportion of variance
+                        'matrix_id');            -- Grouping column
+SELECT * FROM result_table_group ORDER BY matrix_id, row_id;
+
      + row_id |                                      principal_components                                      |     std_dev     |    proportion     | matrix_id
+--------+------------------------------------------------------------------------------------------------+-----------------+-------------------+-----------
+      1 | {0.707106781186548,0,-0.707106781186547}                                                       | 1.4142135623731 | 0.857142857142245 |         1
+      1 | {-0.555378486712784,-0.388303582074091,0.0442457354870796,0.255566375612852,0.688115693174023} | 3.2315220311722 | 0.764102534485173 |         2
+      2 | {0.587384101786277,-0.485138064894743,0.311532046315153,-0.449458074050715,0.347212037159181}  |  1.795531127192 | 0.235897465516047 |         2
+(3 rows)
+
      7. +
    7. Now let's look at sparse matrices. Create sample data in sparse matrix form: 
      +DROP TABLE IF EXISTS mat_sparse;
+CREATE TABLE mat_sparse (
+    row_id integer,
+    col_id integer,
+    value double precision
+);
+INSERT INTO mat_sparse VALUES
+(1, 1, 1.0),
+(2, 2, 2.0),
+(3, 3, 3.0),
+(4, 4, 4.0),
+(1, 5, 5.0),
+(2, 4, 6.0),
+(3, 2, 7.0),
+(4, 3, 8.0);
+
      As an aside, this is what the sparse matrix above looks like when put in dense form: 
      +DROP TABLE IF EXISTS mat_dense;
+SELECT madlib.matrix_densify('mat_sparse',
+                            'row=row_id, col=col_id, val=value',
+                            'mat_dense');
+SELECT * FROM mat_dense ORDER BY row_id;
+
      + row_id |    value
+--------+-------------
+      1 | {1,0,0,0,5}
+      2 | {0,2,0,6,0}
+      3 | {0,7,3,0,0}
+      4 | {0,0,8,4,0}
+(4 rows)
+
      8. +
    8. Run the PCA sparse function for a specified number of principal components and view the results: 
      DROP TABLE IF EXISTS result_table, result_table_mean;
+SELECT madlib.pca_sparse_train( 'mat_sparse',       -- Source table
+                                'result_table',     -- Output table
+                                'row_id',           -- Row id of source table
+                                'col_id',           -- Column id of source table
+                                'value',            -- Value of matrix at row_id, col_id
+                                4,                  -- Actual number of rows in the matrix
+                                5,                  -- Actual number of columns in the matrix
+                                3);                 -- Number of principal components
+SELECT * FROM result_table ORDER BY row_id;
+
      Result (with principal components truncated for readability): 
      + row_id |         principal_components                 |     std_dev      |    proportion
+--------+----------------------------------------------+------------------+-------------------
+      1 | {-0.0876046030186158,-0.0968983772909994,... | 4.21362803829554 | 0.436590030617467
+      2 | {-0.0647272661608605,0.877639526308692,...   | 3.68408023747461 | 0.333748701544697
+      3 | {-0.0780380267884855,0.177956517174911,...   | 3.05606908060098 | 0.229661267837836
+(3 rows)
+
      9. +
    9. Now we use grouping in sparse form to learn different models for different groups. First, we create sample data in sparse matrix form with a grouping column: 
      +DROP TABLE IF EXISTS mat_sparse_group;
+CREATE TABLE mat_sparse_group (
+    row_id integer,
+    col_id integer,
+    value double precision,
+    matrix_id integer);
+INSERT INTO mat_sparse_group VALUES
+(1, 1, 1.0, 1),
+(2, 2, 2.0, 1),
+(3, 3, 3.0, 1),
+(4, 4, 4.0, 1),
+(1, 5, 5.0, 1),
+(2, 4, 6.0, 2),
+(3, 2, 7.0, 2),
+(4, 3, 8.0, 2);
+
      10. +
    10. Run the PCA function with grouping for a specified proportion of variance and view the results: 
      +DROP TABLE IF EXISTS result_table_group, result_table_group_mean;
+SELECT madlib.pca_sparse_train( 'mat_sparse_group',   -- Source table
+                                'result_table_group', -- Output table
+                                'row_id',             -- Row id of source table
+                                'col_id',             -- Column id of source table
+                                'value',              -- Value of matrix at row_id, col_id
+                                4,                    -- Actual number of rows in the matrix
+                                5,                    -- Actual number of columns in the matrix
+                                0.8,                  -- Proportion of variance
+                                'matrix_id');
+SELECT * FROM result_table_group ORDER BY matrix_id, row_id;
+
      Result (with principal components truncated for readability): 
      + row_id |           principal_components             |     std_dev      |    proportion     | matrix_id
+--------+--------------------------------------------+------------------+-------------------+-----------
+      1 | {-0.17805696611353,0.0681313257646983,...  | 2.73659933165925 | 0.544652792875481 |         1
+      2 | {-0.0492086814863993,0.149371585357526,... | 2.06058314533194 | 0.308800210823714 |         1
+      1 | {0,-0.479486114660443,...                  | 4.40325305087975 | 0.520500333693473 |         2
+      2 | {0,0.689230898585949,...                   |  3.7435566458567 | 0.376220573442628 |         2
+(4 rows)
+
      11. +
    +

    Notes
    +
      +
    • Table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and all table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').
      • +
    • Because of the centering step in PCA (see Technical Background), sparse matrices almost always become dense during the training process. Since this implementation automatically densifies sparse matrix input, there should be no expected performance improvement in using sparse matrix input over dense matrix input.
      • +
    • For the parameter 'components_param', INTEGER and FLOAT are interpreted differently. A special case to be aware of: 'components_param' = 1 (INTEGER) will return 1 principal component, but 'components_param' = 1.0 (FLOAT) will return all principal components, i.e., proportion of variance of 100%.
      • +
    • If both 'lanczos_iter' and proportion of variance (via the 'components_param' parameter) are defined, 'lanczos_iter' will take precedence in determining the number of principal components (i.e. the number of principal components will not be greater than 'lanczos_iter' even if the target proportion had not been reached).
      • +
    +

    Technical Background
    +

    The PCA implemented here uses a distributed SVD decomposition implementation to recover the principal components (as opposed to the directly computing the eigenvectors of the covariance matrix). Let \( \boldsymbol X \) be the data matrix, and let \( \hat{x} \) be a vector of the column averages of \( \boldsymbol{X}\). PCA computes the matrix \( \hat{\boldsymbol X} \) as

    +\[ \hat{\boldsymbol X} = {\boldsymbol X} - \vec{e} \hat{x}^T \] +

    +

    where \( \vec{e} \) is the vector of all ones.

    +

    PCA then computes the SVD matrix factorization

    +\[ \hat{\boldsymbol X} = {\boldsymbol U}{\boldsymbol \Sigma}{\boldsymbol V}^T \] +

    +

    where \( {\boldsymbol \Sigma} \) is a diagonal matrix. The eigenvalues are recovered as the entries of \( {\boldsymbol \Sigma}/(\sqrt{(N-1)} \), and the principal components are the rows of \( {\boldsymbol V} \). The reasoning behind using N − 1 instead of N to calculate the covariance is Bessel's correction.

    +
    Note
    It is important to note that this PCA implementation assumes that the user will use only the principal components that have non-zero eigenvalues. The SVD calculation is done with the Lanczos method, which does not guarantee correctness for singular vectors with zero-valued eigenvalues. Consequently, principal components with zero-valued eigenvalues are not guaranteed to be correct. Generally, this will not be problem unless the user wants to use the principal components for the entire eigenspectrum.
    +

    Literature
    +

    [1] Principal Component Analysis. http://en.wikipedia.org/wiki/Principal_component_analysis

    +

    [2] Shlens, Jonathon (2009), A Tutorial on Principal Component Analysis

    +

    Related Topics
    +

    File pca.sql_in documenting the SQL functions

    +

    Principal Component Projection

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__pivot.html b/docs/docs/v2.1.0/group__grp__pivot.html new file mode 100644 index 00000000..3aef9802 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pivot.html @@ -0,0 +1,652 @@ + + + + + + + + +MADlib: Pivot + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Pivot
    Data Types and Transformations
    +
    +
    +
    Contents +

    The goal of the MADlib pivot function is to provide a data summarization tool that can do basic OLAP type operations on data stored in one table and output the summarized data to a second table.

    +
    +pivot(
+    source_table,
+    output_table,
+    index,
+    pivot_cols,
+    pivot_values,
+    aggregate_func,
+    fill_value,
+    keep_null,
+    output_col_dictionary,
+    output_type
+    )
+

    Arguments

    +
    source_table
    +

    VARCHAR. Name of the source table (or view) containing data to pivot.

    +

    +
    +
    output_table
    +

    VARCHAR. Name of output table that contains the pivoted data. The output table contains all the columns present in the 'index' column list, plus additional columns for each distinct value in 'pivot_cols'.

    +
    Note
    The names of the columns in the output table are auto-generated. Please see the examples section below to see how this works in practice. The convention used is to concatenate the following strings and separate each by an underscore '_' :
      +
    • name of the value column 'pivot_values'
      • +
    • aggregate function
      • +
    • name of the pivot column 'pivot_cols'
      • +
    • values in the pivot column
      • +
    +
    +
    +
    index
    +

    VARCHAR. Comma-separated columns that will form the index of the output pivot table. By index we mean the values to group by; these are the rows in the output pivot table.

    +

    +
    +
    pivot_cols
    +

    VARCHAR. Comma-separated columns that will form the columns of the output pivot table.

    +

    +
    +
    pivot_values
    +

    VARCHAR. Comma-separated columns that contain the values to be summarized in the output pivot table.

    +

    +
    +
    aggregate_func (optional)
    +

    VARCHAR. default: 'AVG'. A comma-separated list of aggregates to be applied to values. These can be PostgreSQL built-in aggregates [1] or UDAs. It is possible to assign a set of aggregates per value column. Please refer to the examples 12-14 below for syntax details.

    +
    Note
    Only aggregates with strict transition functions are permitted here. A strict transition function means rows with null values are ignored; the function is not called and the previous state value is retained. If you need some other behavior for null inputs, this should be done prior to calling the pivot function. Aggregates with strict transition functions are described in [2,3].
    +
    +
    fill_value (optional)
    +

    VARCHAR. default: NULL. If specified, determines how to fill NULL values resulting from pivot operation. This is a global parameter (not applied per aggregate) and is applied post-aggregation to the output table.

    +

    +
    +
    keep_null (optional)
    +

    BOOLEAN. default: FALSE. If TRUE, then pivot columns are created corresponding to NULL categories. If FALSE, then no pivot columns will be created for NULL categories.

    +

    +
    +
    output_col_dictionary (optional)
    +

    BOOLEAN. default: FALSE. This parameter is used to handle auto-generated column names that exceed the PostgreSQL limit of 63 bytes (could be a common occurrence). If TRUE, column names will be set as numerical IDs and will create a dictionary table called output_table appended with _dictionary. If FALSE, will auto-generate column names in the usual way unless the limit of 63 bytes will be exceeded. In this case, a dictionary output file will be created and a message given to the user.

    +

    +
    +
    output_type (optional)
    +

    VARCHAR. default: 'column'. This parameter controls the output format of the pivoted variables. If 'column', a column is created for each pivot variable. PostgreSQL limits the number of columns in a table (250 - 1600 depending on column types). If the total number of output columns exceeds this limit, then make this parameter either 'array' (to combine the output columns into an array) or 'svec' (to cast the array output to 'madlib.svec' type). If you have an 'aggregate_func' that has an array return type, it cannot be combined with 'output_type'='array' or 'svec'.

    +

    A dictionary will be created (output_col_dictionary=TRUE) when 'output_type' is 'array' or 'svec' to define each index into the array.

    +

    +
    +
    +

    Note
      +
    • NULLs in the index column are treated like any other value.
      • +
    • NULLs in the pivot column are ignored unless keep_null is TRUE.
      • +
    • Only strict transition functions are allowed so NULLs are ignored.
      • +
    • It is not allowed to set the fill_value parameter without setting the aggregate_func parameter due to possible ambiguity. Set aggregate_func to NULL for the default behavior and use fill_value as desired. Please note that full_value must be of the same type as the output of the aggregate_func (or capable of being cast to the same type by PostgreSQL), or else an error will result.
      • +
    • It is not allowed to set the output_col_dictionary parameter without setting the keep_null parameter due to possible ambiguity. Set keep_null to NULL for the default behavior and use output_col_dictionary as desired.
      • +
    • Expressions (instead of column names) are not supported. Create a view with the desired expressions and pass it as the input table (see example 3 below).
      • +
    • It is allowed to pass a partial mapping for the aggregate_func parameter. The missing value columns will be aggregated using the default function (average).
      • +
    +
    +

    Examples
    +
      +
    1. Create a simple dataset to demonstrate a basic pivot: 
      +DROP TABLE IF EXISTS pivset CASCADE; -- View below may depend on table so use CASCADE
+CREATE TABLE pivset(
+                  id INTEGER,
+                  piv INTEGER,
+                  val FLOAT8
+                );
+INSERT INTO pivset VALUES
+    (0, 10, 1),
+    (0, 10, 2),
+    (0, 20, 3),
+    (1, 20, 4),
+    (1, 30, 5),
+    (1, 30, 6),
+    (1, 10, 7),
+    (NULL, 10, 8),
+    (1, NULL, 9),
+    (1, 10, NULL);
+
      2. +
    2. Pivot the table: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset', 'pivout', 'id', 'piv', 'val');
+SELECT * FROM pivout ORDER BY id;
+
      + id | val_avg_piv_10 | val_avg_piv_20 | val_avg_piv_30
+----+----------------+----------------+----------------
+  0 |            1.5 |              3 |
+  1 |              7 |              4 |            5.5
+    |              8 |                |
+
      Here NULL is showing as an empty cell in the output.
      3. +
    3. Now let's add some more columns to our data set and create a view: 
      +DROP VIEW IF EXISTS pivset_ext;
+CREATE VIEW pivset_ext AS
+    SELECT *,
+    COALESCE(id + (val / 3)::integer, 0) AS id2,
+    COALESCE(100*(val / 3)::integer, 0) AS piv2,
+    COALESCE(val + 10, 0) AS val2
+   FROM pivset;
+SELECT id,id2,piv,piv2,val,val2 FROM pivset_ext
+ORDER BY id,id2,piv,piv2,val,val2;
+
      + id | id2 | piv | piv2 | val | val2
+----+-----+-----+------+-----+------
+  0 |   0 |  10 |    0 |   1 |   11
+  0 |   1 |  10 |  100 |   2 |   12
+  0 |   1 |  20 |  100 |   3 |   13
+  1 |   0 |  10 |    0 |     |    0
+  1 |   2 |  20 |  100 |   4 |   14
+  1 |   3 |  10 |  200 |   7 |   17
+  1 |   3 |  30 |  200 |   5 |   15
+  1 |   3 |  30 |  200 |   6 |   16
+  1 |   4 |     |  300 |   9 |   19
+    |   0 |  10 |  300 |   8 |   18
+(10 rows)
+
      4. +
    4. Let's use a different aggregate function on the view we just created: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val', 'sum');
+SELECT * FROM pivout ORDER BY id;
+
      + id | val_sum_piv_10 | val_sum_piv_20 | val_sum_piv_30
+----+----------------+----------------+----------------
+  0 |              3 |              3 |
+  1 |              7 |              4 |             11
+    |              8 |                |
+
      5. +
    5. Now create a custom aggregate. Note that the aggregate must have a strict transition function: 
      +DROP FUNCTION IF EXISTS array_add1 (ANYARRAY, ANYELEMENT) CASCADE;
+CREATE FUNCTION array_add1(ANYARRAY, ANYELEMENT) RETURNS ANYARRAY AS $$
+  SELECT $1 || $2
+$$ LANGUAGE sql STRICT;
+DROP AGGREGATE IF EXISTS array_accum1 (anyelement);
+CREATE AGGREGATE array_accum1 (anyelement) (
+    sfunc = array_add1,
+    stype = anyarray,
+    initcond = '{}'
+);
+DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val', 'array_accum1');
+SELECT * FROM pivout ORDER BY id;
+
      +  id | val_array_accum1_piv_10 | val_array_accum1_piv_20 | val_array_accum1_piv_30
+----+-------------------------+-------------------------+-------------------------
+  0 | {1,2}                   | {3}                     | {}
+  1 | {7}                     | {4}                     | {5,6}
+    | {8}                     | {}                      | {}
+
      6. +
    6. Keep null values in the pivot column: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val', 'sum', True);
+SELECT * FROM pivout ORDER BY id;
+
      + id | val_sum_piv_10 | val_sum_piv_20 | val_sum_piv_30 | val_sum_piv_null
+----+----------------+----------------+----------------+------------------
+  0 |              3 |              3 |                |
+  1 |              7 |              4 |             11 |                9
+    |              8 |                |                |
+
      7. +
    7. Fill null results with a value of interest: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val', 'sum', '111');
+SELECT * FROM pivout ORDER BY id;
+
      + id | val_sum_piv_10 | val_sum_piv_20 | val_sum_piv_30
+----+----------------+----------------+----------------
+  0 |              3 |              3 |            111
+  1 |              7 |              4 |             11
+    |              8 |            111 |            111
+
      8. +
    8. Use multiple index columns: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id,id2', 'piv', 'val');
+SELECT * FROM pivout ORDER BY id,id2;
+
      + id | id2 | val_avg_piv_10 | val_avg_piv_20 | val_avg_piv_30
+----+-----+----------------+----------------+----------------
+  0 |   0 |              1 |                |
+  0 |   1 |              2 |              3 |
+  1 |   0 |                |                |
+  1 |   2 |                |              4 |
+  1 |   3 |              7 |                |            5.5
+  1 |   4 |                |                |
+    |   0 |              8 |                |
+
      9. +
    9. Use multiple pivot columns with columnar output: 
      +\x on
+DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv, piv2', 'val');
+SELECT * FROM pivout ORDER BY id;
+
      +-[ RECORD 1 ]-----------+----
+id                      | 0
+val_avg_piv_10_piv2_0   | 1
+val_avg_piv_10_piv2_100 | 2
+val_avg_piv_10_piv2_200 |
+val_avg_piv_10_piv2_300 |
+val_avg_piv_20_piv2_0   |
+val_avg_piv_20_piv2_100 | 3
+val_avg_piv_20_piv2_200 |
+val_avg_piv_20_piv2_300 |
+val_avg_piv_30_piv2_0   |
+val_avg_piv_30_piv2_100 |
+val_avg_piv_30_piv2_200 |
+val_avg_piv_30_piv2_300 |
+-[ RECORD 2 ]-----------+----
+id                      | 1
+val_avg_piv_10_piv2_0   |
+val_avg_piv_10_piv2_100 |
+val_avg_piv_10_piv2_200 | 7
+val_avg_piv_10_piv2_300 |
+val_avg_piv_20_piv2_0   |
+val_avg_piv_20_piv2_100 | 4
+val_avg_piv_20_piv2_200 |
+val_avg_piv_20_piv2_300 |
+val_avg_piv_30_piv2_0   |
+val_avg_piv_30_piv2_100 |
+val_avg_piv_30_piv2_200 | 5.5
+val_avg_piv_30_piv2_300 |
+...
+
      10. +
    10. Use multiple pivot columns (same as above) with an array output: 
      +DROP TABLE IF EXISTS pivout, pivout_dictionary;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv, piv2', 'val',
+                    NULL, NULL, FALSE, FALSE, 'array');
+\x off
+SELECT * FROM pivout ORDER BY id;
+
      +   id   |                          val_avg
+--------+------------------------------------------------------------
+      0 | {1,2,NULL,NULL,NULL,3,NULL,NULL,NULL,NULL,NULL,NULL}
+      1 | {NULL,NULL,7,NULL,NULL,4,NULL,NULL,NULL,NULL,5.5,NULL}
+ [NULL] | {NULL,NULL,NULL,8,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL}
+
      +-- Use the dictionary to understand what each index of an array corresponds to
+SELECT * FROM pivout_dictionary;
+
      + __pivot_cid__ | pval | agg | piv | piv2 |         col_name
+---------------+------+-----+-----+------+---------------------------
+ 1             | val  | avg |  10 |    0 | "val_avg_piv_10_piv2_0"
+ 2             | val  | avg |  10 |  100 | "val_avg_piv_10_piv2_100"
+ 3             | val  | avg |  10 |  200 | "val_avg_piv_10_piv2_200"
+ 4             | val  | avg |  10 |  300 | "val_avg_piv_10_piv2_300"
+ 5             | val  | avg |  20 |    0 | "val_avg_piv_20_piv2_0"
+ 6             | val  | avg |  20 |  100 | "val_avg_piv_20_piv2_100"
+ 7             | val  | avg |  20 |  200 | "val_avg_piv_20_piv2_200"
+ 8             | val  | avg |  20 |  300 | "val_avg_piv_20_piv2_300"
+ 9             | val  | avg |  30 |    0 | "val_avg_piv_30_piv2_0"
+ 10            | val  | avg |  30 |  100 | "val_avg_piv_30_piv2_100"
+ 11            | val  | avg |  30 |  200 | "val_avg_piv_30_piv2_200"
+ 12            | val  | avg |  30 |  300 | "val_avg_piv_30_piv2_300"
+
      11. +
    11. Use multiple value columns: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val, val2');
+\x on
+SELECT * FROM pivout ORDER BY id;
+
      +-[ RECORD 1 ]---+-----
+id              | 0
+val_avg_piv_10  | 1.5
+val_avg_piv_20  | 3
+val_avg_piv_30  |
+val2_avg_piv_10 | 11.5
+val2_avg_piv_20 | 13
+val2_avg_piv_30 |
+-[ RECORD 2 ]---+-----
+id              | 1
+val_avg_piv_10  | 7
+val_avg_piv_20  | 4
+val_avg_piv_30  | 5.5
+val2_avg_piv_10 | 8.5
+val2_avg_piv_20 | 14
+val2_avg_piv_30 | 15.5
+...
+
      12. +
    12. Use multiple aggregate functions on the same value column (cross product): 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val', 'avg, sum');
+\x on
+SELECT * FROM pivout ORDER BY id;
+
      +-[ RECORD 1 ]--+----
+id             | 0
+val_avg_piv_10 | 1.5
+val_avg_piv_20 | 3
+val_avg_piv_30 |
+val_sum_piv_10 | 3
+val_sum_piv_20 | 3
+val_sum_piv_30 |
+-[ RECORD 2 ]--+----
+id             | 1
+val_avg_piv_10 | 7
+val_avg_piv_20 | 4
+val_avg_piv_30 | 5.5
+val_sum_piv_10 | 7
+val_sum_piv_20 | 4
+val_sum_piv_30 | 11
+...
+
      13. +
    13. Use different aggregate functions for different value columns: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val, val2',
+    'val=avg, val2=sum');
+\x on
+SELECT * FROM pivout ORDER BY id;
+
      +-[ RECORD 1 ]---+----
+id              | 0
+val_avg_piv_10  | 1.5
+val_avg_piv_20  | 3
+val_avg_piv_30  |
+val2_sum_piv_10 | 23
+val2_sum_piv_20 | 13
+val2_sum_piv_30 |
+-[ RECORD 2 ]---+----
+id              | 1
+val_avg_piv_10  | 7
+val_avg_piv_20  | 4
+val_avg_piv_30  | 5.5
+val2_sum_piv_10 | 17
+val2_sum_piv_20 | 14
+val2_sum_piv_30 | 31
+...
+
      14. +
    14. Use multiple aggregate functions for different value columns: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id', 'piv', 'val, val2',
+    'val=avg, val2=[avg,sum]');
+\x on
+SELECT * FROM pivout ORDER BY id;
+
      +-[ RECORD 1 ]---+-----
+id              | 0
+val_avg_piv_10  | 1.5
+val_avg_piv_20  | 3
+val_avg_piv_30  |
+val2_avg_piv_10 | 11.5
+val2_avg_piv_20 | 13
+val2_avg_piv_30 |
+val2_sum_piv_10 | 23
+val2_sum_piv_20 | 13
+val2_sum_piv_30 |
+-[ RECORD 2 ]---+-----
+id              | 1
+val_avg_piv_10  | 7
+val_avg_piv_20  | 4
+val_avg_piv_30  | 5.5
+val2_avg_piv_10 | 8.5
+val2_avg_piv_20 | 14
+val2_avg_piv_30 | 15.5
+val2_sum_piv_10 | 17
+val2_sum_piv_20 | 14
+val2_sum_piv_30 | 31
+...
+
      15. +
    15. Combine all of the options: 
      +DROP TABLE IF EXISTS pivout;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id, id2', 'piv, piv2', 'val, val2',
+    'val=avg, val2=[avg,sum]', '111', True);
+\x on
+SELECT * FROM pivout ORDER BY id,id2;
+
      +-[ RECORD 1 ]--------------+-----
+id                         | 0
+id2                        | 0
+val_avg_piv_null_piv2_0    | 111
+val_avg_piv_null_piv2_100  | 111
+val_avg_piv_null_piv2_200  | 111
+val_avg_piv_null_piv2_300  | 111
+val_avg_piv_10_piv2_0      | 1
+val_avg_piv_10_piv2_100    | 111
+val_avg_piv_10_piv2_200    | 111
+val_avg_piv_10_piv2_300    | 111
+val_avg_piv_20_piv2_0      | 111
+val_avg_piv_20_piv2_100    | 111
+val_avg_piv_20_piv2_200    | 111
+val_avg_piv_20_piv2_300    | 111
+val_avg_piv_30_piv2_0      | 111
+val_avg_piv_30_piv2_100    | 111
+val_avg_piv_30_piv2_200    | 111
+val_avg_piv_30_piv2_300    | 111
+val2_avg_piv_null_piv2_0   | 111
+val2_avg_piv_null_piv2_100 | 111
+val2_avg_piv_null_piv2_200 | 111
+val2_avg_piv_null_piv2_300 | 111
+val2_avg_piv_10_piv2_0     | 11
+val2_avg_piv_10_piv2_100   | 111
+...
+-[ RECORD 2 ]--------------+-----
+id                         | 0
+id2                        | 1
+val_avg_piv_null_piv2_0    | 111
+val_avg_piv_null_piv2_100  | 111
+val_avg_piv_null_piv2_200  | 111
+val_avg_piv_null_piv2_300  | 111
+val_avg_piv_10_piv2_0      | 111
+val_avg_piv_10_piv2_100    | 2
+val_avg_piv_10_piv2_200    | 111
+val_avg_piv_10_piv2_300    | 111
+val_avg_piv_20_piv2_0      | 111
+val_avg_piv_20_piv2_100    | 3
+val_avg_piv_20_piv2_200    | 111
+val_avg_piv_20_piv2_300    | 111
+val_avg_piv_30_piv2_0      | 111
+val_avg_piv_30_piv2_100    | 111
+val_avg_piv_30_piv2_200    | 111
+val_avg_piv_30_piv2_300    | 111
+val2_avg_piv_null_piv2_0   | 111
+val2_avg_piv_null_piv2_100 | 111
+val2_avg_piv_null_piv2_200 | 111
+val2_avg_piv_null_piv2_300 | 111
+...
+
      16. +
    16. Create a dictionary for output column names: 
      +DROP TABLE IF EXISTS pivout, pivout_dictionary;
+SELECT madlib.pivot('pivset_ext', 'pivout', 'id, id2', 'piv, piv2', 'val, val2',
+    'val=avg, val2=[avg,sum]', '111', True, True);
+\x off
+SELECT * FROM pivout_dictionary order by __pivot_cid__;
+
      +__pivot_cid__ | pval | agg |  piv   | piv2 |           col_name
+---------------+------+-----+--------+------+------------------------------
+ __p_1__       | val  | avg | [NULL] |    0 | "val_avg_piv_null_piv2_0"
+ __p_2__       | val  | avg | [NULL] |  100 | "val_avg_piv_null_piv2_100"
+ __p_3__       | val  | avg | [NULL] |  200 | "val_avg_piv_null_piv2_200"
+ __p_4__       | val  | avg | [NULL] |  300 | "val_avg_piv_null_piv2_300"
+ __p_5__       | val  | avg |     10 |    0 | "val_avg_piv_10_piv2_0"
+ __p_6__       | val  | avg |     10 |  100 | "val_avg_piv_10_piv2_100"
+ __p_7__       | val  | avg |     10 |  200 | "val_avg_piv_10_piv2_200"
+ __p_8__       | val  | avg |     10 |  300 | "val_avg_piv_10_piv2_300"
+ __p_9__       | val  | avg |     20 |    0 | "val_avg_piv_20_piv2_0"
+ __p_10__      | val  | avg |     20 |  100 | "val_avg_piv_20_piv2_100"
+ __p_11__      | val  | avg |     20 |  200 | "val_avg_piv_20_piv2_200"
+ __p_12__      | val  | avg |     20 |  300 | "val_avg_piv_20_piv2_300"
+ __p_13__      | val  | avg |     30 |    0 | "val_avg_piv_30_piv2_0"
+ __p_14__      | val  | avg |     30 |  100 | "val_avg_piv_30_piv2_100"
+ __p_15__      | val  | avg |     30 |  200 | "val_avg_piv_30_piv2_200"
+ __p_16__      | val  | avg |     30 |  300 | "val_avg_piv_30_piv2_300"
+ __p_17__      | val2 | avg | [NULL] |    0 | "val2_avg_piv_null_piv2_0"
+ __p_18__      | val2 | avg | [NULL] |  100 | "val2_avg_piv_null_piv2_100"
+ __p_19__      | val2 | avg | [NULL] |  200 | "val2_avg_piv_null_piv2_200"
+ __p_20__      | val2 | avg | [NULL] |  300 | "val2_avg_piv_null_piv2_300"
+ __p_21__      | val2 | avg |     10 |    0 | "val2_avg_piv_10_piv2_0"
+...
+(48 rows)
+
      +\x on
+SELECT * FROM pivout ORDER BY id,id2;
+
      +-[ RECORD 1 ]----
+id       | 0
+id2      | 0
+__p_1__  | 111
+__p_2__  | 111
+__p_3__  | 111
+__p_4__  | 111
+__p_5__  | 1
+__p_6__  | 111
+__p_7__  | 111
+__p_8__  | 111
+__p_9__  | 111
+__p_10__ | 111
+__p_11__ | 111
+__p_12__ | 111
+__p_13__ | 111
+...
+-[ RECORD 2 ]----
+id       | 0
+id2      | 1
+__p_1__  | 111
+__p_2__  | 111
+__p_3__  | 111
+__p_4__  | 111
+__p_5__  | 111
+__p_6__  | 2
+__p_7__  | 111
+__p_8__  | 111
+__p_9__  | 111
+__p_10__ | 3
+__p_11__ | 111
+__p_12__ | 111
+__p_13__ | 111
+...
+-[ RECORD 3 ]----
+id       | 1
+id2      | 0
+__p_1__  | 111
+__p_2__  | 111
+__p_3__  | 111
+__p_4__  | 111
+__p_5__  | 111
+__p_6__  | 111
+__p_7__  | 111
+__p_8__  | 111
+__p_9__  | 111
+__p_10__ | 111
+__p_11__ | 111
+__p_12__ | 111
+__p_13__ | 111
+...
+
      17. +
    +

    Literature
    +

    NOTE: The following links refer to documentation resources for the current PostgreSQL database version. Depending upon your database platform version, you may need to change "current" references in the links to your database version.

    +

    If your database platform uses the Greenplum Database (or related variants), please check with the project community and/or your database vendor to identify the PostgreSQL version it is based on.

    +

    [1] https://www.postgresql.org/docs/current/static/functions-aggregate.html

    +

    [2] https://www.postgresql.org/docs/current/static/sql-createaggregate.html

    +

    [3] https://www.postgresql.org/docs/current/static/xaggr.html

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__pmml.html b/docs/docs/v2.1.0/group__grp__pmml.html new file mode 100644 index 00000000..8e68924f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pmml.html @@ -0,0 +1,323 @@ + + + + + + + + +MADlib: PMML Export + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    PMML Export
    Utilities
    +
    +
    +
    Contents +

    PMML Export Function
    The PMML export function in MADlib has the following syntax: 
    +pmml ( model_table,
+       name_spec
+     )
+
    Arguments
    +
    model_table
    +

    VARCHAR. The name of the table containing the model.

    +

    +
    +
    name_spec (optional)
    +
    VARCHAR or VARCHAR[]. Names to be used in the Data Dictionary of the PMML. See pmml() for detailed explanation.
    +
    +
    +

    Output XML. The output of this function is a standard PMML document, some examples of which are covered in the next section.

    +
    Note
    In PostgreSQL, users may be required to install their database with XML support in order to use this function.
    +

    Usually the user wants to export the resulting PMML contents into a PMML file so that external softwares can use it. The following method can be used (Note: the user needs to use unaligned table output mode for psql with '-A' flag. And inside psql client, both '\t' and '\o' should be used):

    +
    +> # under bash
+> psql -A my_database
+# -- in psql now
+# \t
+# \o test.pmml -- export to a file
+# select madlib.pmml('tree_out');
+# \o
+# \t
+

    Examples
      +
    1. Create the training data table. 
      +CREATE TABLE patients( id integer NOT NULL,
+                       second_attack integer,
+                       treatment integer,
+                       trait_anxiety integer);
+INSERT INTO patients(id, second_attack, treatment, trait_anxiety) VALUES
+( 1, 1, 1, 70),
+( 3, 1, 1, 50),
+( 5, 1, 0, 40),
+( 7, 1, 0, 75),
+( 9, 1, 0, 70),
+(11, 0, 1, 65),
+(13, 0, 1, 45),
+(15, 0, 1, 40),
+(17, 0, 0, 55),
+(19, 0, 0, 50),
+( 2, 1, 1, 80),
+( 4, 1, 0, 60),
+( 6, 1, 0, 65),
+( 8, 1, 0, 80),
+(10, 1, 0, 60),
+(12, 0, 1, 50),
+(14, 0, 1, 35),
+(16, 0, 1, 50),
+(18, 0, 0, 45),
+(20, 0, 0, 60);
+
      2. +
    2. Train a regression model using logregr_train(). 
      +SELECT madlib.logregr_train(
+        'patients',
+        'patients_logregr',
+        'second_attack',
+        'ARRAY[1, treatment, trait_anxiety]');
+
      3. +
    3. View the PMML export for this model. 
      +SELECT madlib.pmml('patients_logregr');
+
      Result: 
      +<?xml version="1.0" standalone="yes"?>
+<PMML version="4.1" xmlns="http://www.dmg.org/pmml-v4-1.html">
+  <Header copyright="redacted for this example">
+    <Extension extender="MADlib" name="user" value="gpadmin">
+    <Application name="MADlib" version="1.7">
+    <Timestamp>
+      2014-06-13 17:30:14.527899 PDT
+    </Timestamp>
+  </Header>
+  <DataDictionary numberoffields="4">
+    <DataField datatype="boolean" name="second_attack_pmml_prediction" optype="categorical">
+    <DataField datatype="double" name="1" optype="continuous">
+    <DataField datatype="double" name="treatment" optype="continuous">
+    <DataField datatype="double" name="trait_anxiety" optype="continuous">
+  </DataDictionary>
+  <RegressionModel functionname="classification" normalizationmethod="softmax">
+    <MiningSchema>
+      <MiningField name="second_attack_pmml_prediction" usagetype="predicted">
+      <MiningField name="1">
+      <MiningField name="treatment">
+      <MiningField name="trait_anxiety">
+    </MiningSchema>
+    <RegressionTable intercept="0.0" targetcategory="True">
+      <NumericPredictor coefficient="-6.36346994178" name="1">
+      <NumericPredictor coefficient="-1.02410605239" name="treatment">
+      <NumericPredictor coefficient="0.119044916669" name="trait_anxiety">
+    </RegressionTable>
+    <RegressionTable intercept="0.0" targetcategory="False">
+  </RegressionModel>
+</PMML>
+
      4. +
    +
    +

    Alternatively, the above can also be invoked as below if custom names are needed for fields in the Data Dictionary: 

    +SELECT madlib.pmml('patients_logregr',
+                   'out_attack~1+in_trait_anxiety+in_treatment');
+

    Note: If the second argument of 'pmml' function is not specified, a default suffix "_pmml_prediction" will be automatically append to the column name to be predicted. This can help avoid name conflicts.

    +

    The following example demonstrates grouping columns in the model table for the same dataset as the previous example.

    +
      +
    1. Train a different regression model with 'treatment' as the grouping column. 
      +SELECT madlib.logregr_train(
+        'patients',
+        'patients_logregr_grouping',
+        'second_attack',
+        'ARRAY[1, trait_anxiety]',
+        'treatment');
+
      2. +
    2. View the PMML export for this model. 
      +SELECT madlib.pmml('patients_logregr_grouping',
+                   ARRAY['second_attack','1','in_trait_anxiety']);
+
      Result: 
      +<?xml version="1.0" standalone="yes"?>
+ <PMML version="4.1" xmlns="http://www.dmg.org/pmml-v4-1.html">
+   <Header copyright="redacted for this example">
+     <Extension extender="MADlib" name="user" value="gpadmin">
+     <Application name="MADlib" version="1.7">
+     <Timestamp>
+       2014-06-13 17:37:55.786307 PDT
+     </Timestamp>
+   </Header>
+   <DataDictionary numberoffields="4">
+     <DataField datatype="boolean" name="second_attack" optype="categorical">
+     <DataField datatype="double" name="1" optype="continuous">
+     <DataField datatype="double" name="in_trait_anxiety" optype="continuous">
+     <DataField datatype="string" name="treatment" optype="categorical">
+   </DataDictionary>
+   <MiningModel functionname="classification">
+     <MiningSchema>
+       <MiningField name="second_attack" usagetype="predicted">
+       <MiningField name="1">
+       <MiningField name="in_trait_anxiety">
+       <MiningField name="treatment">
+     </MiningSchema>
+     <Segmentation multiplemodelmethod="selectFirst">
+       <Segment>
+         <SimplePredicate field="treatment" operator="equal" value="1">
+         <RegressionModel functionname="classification" normalizationmethod="softmax">
+           <MiningSchema>
+             <MiningField name="second_attack" usagetype="predicted">
+             <MiningField name="1">
+             <MiningField name="in_trait_anxiety">
+           </MiningSchema>
+           <RegressionTable intercept="0.0" targetcategory="True">
+             <NumericPredictor coefficient="-8.02068430057" name="1">
+             <NumericPredictor coefficient="0.130090428526" name="in_trait_anxiety">
+           </RegressionTable>
+           <RegressionTable intercept="0.0" targetcategory="False">
+         </RegressionModel>
+       </Segment>
+       <Segment>
+         <SimplePredicate field="treatment" operator="equal" value="0">
+         <RegressionModel functionname="classification" normalizationmethod="softmax">
+           <MiningSchema>
+             <MiningField name="second_attack" usagetype="predicted">
+             <MiningField name="1">
+             <MiningField name="in_trait_anxiety">
+           </MiningSchema>
+           <RegressionTable intercept="0.0" targetcategory="True">
+             <NumericPredictor coefficient="-5.75043192191" name="1">
+             <NumericPredictor coefficient="0.108282446319" name="in_trait_anxiety">
+           </RegressionTable>
+           <RegressionTable intercept="0.0" targetcategory="False">
+         </RegressionModel>
+       </Segment>
+     </Segmentation>
+   </MiningModel>
+ </PMML>
+
      3. +
    +

    Note: MADlib currently supports PMML export for Linear Regression, Logistic Regression, Generalized Linear Regression Model, Multinomial Logistic Regression, Ordinal Linear Regression, Decision Tree and Random Forests.

    +

    In Ordinal Regression, the signs of feature coefficients will be different in PMML export and in the default output model table from ordinal(). This is due to the difference of model settings.

    +

    Background
    The Predictive Model Markup Language (PMML) is an XML-based file format that provides a way for applications to describe and exchange models produced by data mining and machine learning algorithms. A PMML file comprises the following components:
      +
    • Header: Contains general information of the model, such as copyright information and model description.
      • +
    • Data Dictionary: Contains definitions of fields used in the model.
      • +
    • Data Transformations: Contains transformations for mapping user data into a form that can be used by the mining model.
      • +
    • Model: Contains definitions of the data mining model, which includes attributes such as the model name, function name, and algorithm name.
      • +
    • Mining Schema: Contains specific information for the fields used in the model, which includes the name and usage type.
      • +
    • Targets: Allows for post-processing of the predicted value.
      • +
    • Output: Allows for naming of output fields expected from the model.
      • +
    +
    +

    MADlib follows the PMML v4.1 standard. For more details about PMML, see http://www.dmg.org/v4-1/GeneralStructure.html.

    +

    Related Topics
    +

    File table_to_pmml.sql_in documenting the PMML export functions.

    +

    Linear Regression

    +

    Logistic Regression

    +

    Generalized Linear Models

    +

    Ordinal Regression

    +

    Multinomial Regression

    +

    Decision Tree

    +

    Random Forest

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__pred.html b/docs/docs/v2.1.0/group__grp__pred.html new file mode 100644 index 00000000..9b36b1e8 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__pred.html @@ -0,0 +1,357 @@ + + + + + + + + +MADlib: Prediction Metrics + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Prediction Metrics
    Model Selection
    +
    +
    +
    Contents +

    This module provides a set of metrics to evaluate the quality of predictions of a model. A typical function will take a set of "prediction" and "observation" values and use them to calculate the desired metric, unless noted otherwise. Grouping is supported for all functions (except confusion matrix).

    +

    Prediction Metrics Functions
    + + + + + + + + + + + + + + + + + + +
    mean_abs_error(table_in, table_out, prediction_col, observed_col, grouping_cols)Mean absolute error
    mean_abs_perc_error(table_in, table_out, prediction_col, observed_col, grouping_cols)Mean absolute percentage error
    mean_perc_error(table_in, table_out, prediction_col, observed_col, grouping_cols)Mean percentage error
    mean_squared_error(table_in, table_out, prediction_col, observed_col, grouping_cols)Mean squared error
    r2_score(table_in, table_out, prediction_col, observed_col, grouping_cols)R-squared
    adjusted_r2_score(table_in, table_out, prediction_col, observed_col, num_predictors, training_size, grouping_cols)Adjusted R-squared
    binary_classifier(table_in, table_out, prediction_col, observed_col, grouping_cols)Collection of prediction metrics related to binary classification
    area_under_roc(table_in, table_out, prediction_col, observed_col, grouping_cols)Area under the ROC curve (in binary classification)
    confusion_matrix(table_in, table_out, prediction_col, observed_col, grouping_cols)Confusion matrix for a multi-class classifier
    +
    +

    Arguments

    +
    table_in
    +
    TEXT. Name of the input table.
    +
    table_out
    +
    TEXT. Name of the output table. For consistency, a table is created for all metric outputs even when grouping is not used, which may mean there is only a single value in the output table in some cases.
    +
    prediction_col
    +
    TEXT. Name of the column of predicted values from input table.
    +
    observed_col
    +
    TEXT. Name of the column of observed values from input table.
    +
    num_predictors (for adjusted R-squared score only)
    +
    INTEGER. The number of parameters in the predicting model, not counting the constant term.
    +
    training_size (for adjusted R-squared score only)
    +
    INTEGER. The number of rows used for training, excluding any NULL rows.
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. Name of the column of grouping values from input table.
    +
    +

    Function Specific Details
    +

    R-squared Score

    +

    This function returns the coefficient of determination (R2) between the predicted and observed values. An R2 of 1 indicates that the regression line perfectly fits the data, while an R2 of 0 indicates that the line does not fit the data at all. Negative values of R2 may occur when fitting non-linear functions to data. Please refer to reference [1] for more details.

    +

    Adjusted R-squared Score

    +

    This function returns the adjusted R2 score in addition to the R-squared score described above. Adjusted R2 score is used to counter the problem of the R2 automatically increasing when extra explanatory variables are added to the model. It takes two additional parameters describing the degrees of freedom of the model (num_predictors) and the size of the training set over which it was developed (training_size):

    +
      +
    • num_predictors: Indicates the number of parameters the model has other than the constant term. For example, if it is set to '3' the model may take the following form as an example: 7 + 5x + 39y + 0.91z.
      • +
    • training_size: Indicates the number of rows in the training set (excluding any NULL rows).
      • +
    +

    Neither of these arguments can be deduced from the predicted values and the test data alone which is why they are explicit inputs. Please refer to reference [1] for more details.

    +

    Binary Classification

    +

    This function returns an output table with a number of metrics commonly used in binary classification.

    +

    The definitions of the various metrics are as follows:

    +
      +
    • \(\textit{tp}\) is the count of correctly-classified positives.
      • +
    • \(\textit{tn}\) is the count of correctly-classified negatives.
      • +
    • \(\textit{fp}\) is the count of misclassified negatives.
      • +
    • \(\textit{fn}\) is the count of misclassified positives.
      • +
    • \(\textit{tpr}=\textit{tp}/(\textit{tp}+\textit{fn})\).
      • +
    • \(\textit{tnr}=\textit{tn}/(\textit{fp}+\textit{tn})\).
      • +
    • \(\textit{ppv}=\textit{tp}/(\textit{tp}+\textit{fp})\).
      • +
    • \(\textit{npv}=\textit{tn}/(\textit{tn}+\textit{fn})\).
      • +
    • \(\textit{fpr}=\textit{fp}/(\textit{fp}+\textit{tn})\).
      • +
    • \(\textit{fdr}=1-\textit{ppv}\).
      • +
    • \(\textit{fnr}=\textit{fn}/(\textit{fn}+\textit{tp})\).
      • +
    • \(\textit{acc}=(\textit{tp}+\textit{tn})/(\textit{tp}+\textit{tn}+\textit{fp} +\textit{fn})\).
      • +
    • \(\textit{f1}=2*\textit{tp}/(2*\textit{tp}+\textit{fp}+\textit{fn})\).
      • +
    +

    Area Under ROC Curve

    +

    This function returns the area under the Receiver Operating Characteristic curve for binary classification (the AUC). The ROC curve is the curve relating the classifier's TPR and FPR metrics. (See Binary Classification above for a definition of these metrics). Please refer to reference [2] for more details. Note that the binary classification function can be used to obtain the data (TPR and FPR values) required for drawing the ROC curve.

    +
    Note
    For 'binary_classifier' and 'area_under_roc' functions:
      +
    • The 'observed_col' column is assumed to be a numeric column with two values: 0 and 1, or a Boolean column. For the purposes of the metric calculation, 0 is considered to be negative and 1 to be positive.
      • +
    • The 'pred_col' column is expected to contain numeric values corresponding to likelihood/probability. A larger value corresponds to greater certainty that the observed value will be '1', and a lower value corresponds to a greater certainty that it will be '0'.
      • +
    +
    +

    Confusion Matrix

    +

    This function returns the confusion matrix of a multi-class classification. Each column of the matrix represents the instances in a predicted class while each row represents the instances in an actual class. This allows more detailed analysis than mere proportion of correct guesses (accuracy). Please refer to the reference [3] for more details. Please note that grouping is not supported for the confusion matrix.

    +

    Examples
    +
      +
    1. Create the sample data: 
      +DROP TABLE IF EXISTS test_set;
+CREATE TABLE test_set(
+                  pred FLOAT8,
+                  obs FLOAT8
+                );
+INSERT INTO test_set VALUES
+  (37.5,53.1), (12.3,34.2), (74.2,65.4), (91.1,82.1);
+
      2. +
    2. Run the Mean Absolute Error function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.mean_abs_error( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out;
+
      Result 
      + mean_abs_error
+ ----------------
+         13.825
+
      3. +
    3. Run the Mean Absolute Percentage Error function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.mean_abs_perc_error( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out;
+
      Result 
      + mean_abs_perc_error
+ ---------------------
+   0.294578793636013
+
      4. +
    4. Run the Mean Percentage Error function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.mean_perc_error( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out;
+
      Result 
      + mean_perc_error
+ -------------------
+   -0.17248930032771
+
      5. +
    5. Run the Mean Squared Error function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.mean_squared_error( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out;
+
      Result 
      + mean_squared_error
+ --------------------
+   220.3525
+
      6. +
    6. Run the R2 Score function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.r2_score( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out;
+
      Result 
      + r2_score
+ ------------------------
+   0.27992908844337695865
+
      7. +
    7. Run the Adjusted R2 Score function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.adjusted_r2_score( 'test_set', 'table_out', 'pred', 'obs', 3, 100);
+SELECT * FROM table_out;
+
      Result 
      +       r2_score      | adjusted_r2_score
+ --------------------+------------------
+   0.279929088443375 | 0.257426872457231
+
      8. +
    8. Create the sample data for binary classifier metrics: 
      +DROP TABLE IF EXISTS test_set;
+CREATE TABLE test_set AS
+    SELECT ((a*8)::integer)/8.0 pred,
+        ((a*0.5+random()*0.5)>0.5) obs
+    FROM (select random() as a from generate_series(1,100)) x;
+
      9. +
    9. Run the Binary Classifier metrics function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.binary_classifier( 'test_set', 'table_out', 'pred', 'obs');
+
      10. +
    10. View the True Positive Rate and the False Positive Rate: 
      +SELECT threshold, tpr, fpr FROM table_out ORDER BY threshold;
+
      Result (your results for this and other functions below will look different due to the presence of the random function in sample data generator): 
      +       threshold        |          tpr           |          fpr
+------------------------+------------------------+------------------------
+ 0.00000000000000000000 | 1.00000000000000000000 | 1.00000000000000000000
+ 0.12500000000000000000 | 1.00000000000000000000 | 0.94915254237288135593
+ 0.25000000000000000000 | 0.92682926829268292683 | 0.64406779661016949153
+ 0.37500000000000000000 | 0.80487804878048780488 | 0.47457627118644067797
+ 0.50000000000000000000 | 0.70731707317073170732 | 0.35593220338983050847
+ 0.62500000000000000000 | 0.63414634146341463415 | 0.25423728813559322034
+ 0.75000000000000000000 | 0.48780487804878048780 | 0.06779661016949152542
+ 0.87500000000000000000 | 0.29268292682926829268 | 0.03389830508474576271
+ 1.00000000000000000000 | 0.12195121951219512195 | 0.00000000000000000000
+
      11. +
    11. View all metrics at a given threshold value: 
      +-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM table_out WHERE threshold=0.5;
+
      Result 
      +-[ RECORD 1 ]---------------------
+threshold | 0.50000000000000000000
+tp        | 29
+fp        | 21
+fn        | 12
+tn        | 38
+tpr       | 0.70731707317073170732
+tnr       | 0.64406779661016949153
+ppv       | 0.58000000000000000000
+npv       | 0.76000000000000000000
+fpr       | 0.35593220338983050847
+fdr       | 0.42000000000000000000
+fnr       | 0.29268292682926829268
+acc       | 0.67000000000000000000
+f1        | 0.63736263736263736264
+
      12. +
    12. Run the Area Under ROC curve function: 
      +\x off
+DROP TABLE IF EXISTS table_out;
+SELECT madlib.area_under_roc( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out;
+
      Result 
      + area_under_roc
+ ---------------------------------------------
+0.77428689541132699462698842496899545266640
+
      13. +
    13. Create the sample data for confusion matrix. 
      +DROP TABLE IF EXISTS test_set;
+CREATE TABLE test_set AS
+    SELECT (x+y)%5+1 AS pred,
+        (x*y)%5 AS obs
+    FROM generate_series(1,5) x,
+        generate_series(1,5) y;
+
      14. +
    14. Run the confusion matrix function: 
      +DROP TABLE IF EXISTS table_out;
+SELECT madlib.confusion_matrix( 'test_set', 'table_out', 'pred', 'obs');
+SELECT * FROM table_out ORDER BY class;
+
      Result 
      + row_id | class | confusion_arr
+--------+-------+---------------
+      1 |     0 | {0,1,2,2,2,2}
+      2 |     1 | {0,2,0,1,1,0}
+      3 |     2 | {0,0,0,2,2,0}
+      4 |     3 | {0,0,2,0,0,2}
+      5 |     4 | {0,2,1,0,0,1}
+      6 |     5 | {0,0,0,0,0,0}
+
      15. +
    +

    Literature
    +

    [1] https://en.wikipedia.org/wiki/Coefficient_of_determination

    +

    [2] https://en.wikipedia.org/wiki/Receiver_operating_characteristic

    +

    [3] https://en.wikipedia.org/wiki/Confusion_matrix

    +

    Related Topics
    +

    File pred_metrics.sql_in for list of functions and usage.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__prob.html b/docs/docs/v2.1.0/group__grp__prob.html new file mode 100644 index 00000000..46c0e06e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__prob.html @@ -0,0 +1,155 @@ + + + + + + + + +MADlib: Probability Functions + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Probability Functions
    Statistics
    +
    +
    +
    Contents +

    The Probability Functions module provides cumulative distribution, density/mass, and quantile functions for a wide range of probability distributions.

    +

    Unless otherwise documented, all of these functions are wrappers around functionality provided by the boost C++ library [1, “Statistical Distributions and Functions”].

    +

    For convenience, all cumulative distribution and density/mass functions (CDFs and PDF/PMFs in short) are defined over the range of all floating-point numbers including infinity. Inputs that are NULL or NaN (not a number) will always produce a NULL or NaN result, respectively. Inputs that are plus or minus infinity will return the respective limits.

    +

    A quantile function for a probability distrution with CDF \( F \) takes a probability argument \( p \in [0,1] \) and returns the value \( x \) so that \( F(x) = p \), provided such an \( x \) exists and it is unique. If it does not, the result will be \( \sup \{ x \in D \mid F(x) \leq p \} \) (interpreted as 0 if the supremum is over an empty set) if \( p < 0.5 \), and \( \inf \{ x \in D \mid F(x) \geq p \} \) if \( p \geq 0.5 \). Here \( D \) denotes the domain of the distribution, which is the set of reals \( \mathbb R \) for continuous and the set of nonnegative integers \( \mathbb N_0 \) for discrete distributions.

    +

    Intuitively, the formulas in the previous paragraph deal with the following special cases. The 0-quantile will always be the “left end” of the support, and the 1-quantile will be the “right end” of the support of the distribution. For discrete distributions, most values of \( p \in [0,1] \) do not admit an \( x \) with \( F(x) = p \). Instead, there is an \( x \in \mathbb N_0 \) so that \( F(x) < p < F(x + 1) \). The above formulas mean that the value returned as \( p \)-quantile is \( x \) if \( p < 0.5 \), and it is \( x + 1 \) if \( p \geq 0.5 \). (As a special case, in order to ensure that quantiles are always within the support, the \( p \)-quantile will be 0 if \( p < F(0) \)).

    +

    The rationale for choosing this behavior is that \(p\)-quantiles for \( p < 0.5 \) are typically requested when interested in the value \( x \) such that with confidence level at least \( 1 - p \) a random variable will be \( > x \) (or equivalently, with probability at most \( p \), it will be \( \leq x \)). Likewise, \(p\)-quantiles for \( p \geq 0.5 \) are typically requested when interested in the value \( x \) such that with confidence level at least \( p \) a random variable will be \( \leq x \). See also [1, “Understanding Quantiles of Discrete Distributions”].

    +

    Function Syntax
    +

    Cumulative distribution functions:

    +
    distribution_cdf(random variate[, parameter1 [, parameter2 [, parameter3] ] ])

    Probability density/mass functions: 

    distribution_{pdf|pmf}(random variate[, parameter1 [, parameter2 [, parameter3] ] ])

    Quantile functions: 

    distribution_quantile(probability[, parameter1 [, parameter2 [, parameter3] ] ])

    For concrete function signatures, see prob.sql_in.

    +

    Examples
    +
    +SELECT madlib.normal_cdf(0);
+

    Result: 

    + normal_cdf
+ -----------
+        0.5
+
    +SELECT madlib.normal_quantile(0.5, 0, 1);
+

    Result: 

    + normal_quantile
+ ----------------
+               0
+(1 row)
+

    Literature
    +

    [1] John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg: Boost Math Toolkit, Version 1.49, available at: http://www.boost.org/doc/libs/1_49_0/libs/math/doc/sf_and_dist/html/index.html

    +
    Related Topics
    File prob.sql_in documenting the SQL functions.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__random__forest.html b/docs/docs/v2.1.0/group__grp__random__forest.html new file mode 100644 index 00000000..98c17b5f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__random__forest.html @@ -0,0 +1,1165 @@ + + + + + + + + +MADlib: Random Forest + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Random Forest
    Supervised Learning » Tree Methods
    +
    +
    +
    Contents +

    Random forest builds an ensemble of classifiers, each of which is a tree model constructed using bootstrapped samples from the input data. The results of these models are then combined to yield a single prediction, which, at the expense of some loss in interpretation, can be highly accurate. Refer to Breiman et al. [1][2][3] for details on the implementation used here.

    +

    Also refer to the decision tree user documentation since many parameters and examples are similar to random forest.

    +

    Training Function
    Random forest training function has the following format: 
    +forest_train(training_table_name,
+             output_table_name,
+             id_col_name,
+             dependent_variable,
+             list_of_features,
+             list_of_features_to_exclude,
+             grouping_cols,
+             num_trees,
+             num_random_features,
+             importance,
+             num_permutations,
+             max_tree_depth,
+             min_split,
+             min_bucket,
+             num_splits,
+             null_handling_params,
+             verbose,
+             sample_ratio
+             )
+
    +

    Arguments

    +
    training_table_name
    +

    text. Name of the table containing the training data.

    +

    +
    +
    output_table_name
    +

    TEXT. Name of the generated table containing the model. If a table with the same name already exists, an error will be returned. A summary table named <output_table_name>_summary and a grouping table named <output_table_name>_group are also created. These are described later on this page.

    +

    +
    +
    id_col_name
    +

    TEXT. Name of the column containing id information in the training data. This is a mandatory argument and is used for prediction and other purposes. The values are expected to be unique for each row.

    +

    +
    +
    dependent_variable
    +

    TEXT. Name of the column that contains the output (response) for training. Boolean, integer and text types are considered to be classification outputs, while double precision values are considered to be regression outputs. The response variable for a classification tree can be multinomial, but the time and space complexity of the training function increases linearly as the number of response classes increases.

    +

    +
    +
    list_of_features
    +

    TEXT. Comma-separated string of column names or expressions to use as predictors. Can also be a '*' implying all columns are to be used as predictors (except for the ones included in the next argument that lists exclusions). The types of the features can be mixed: boolean, integer, and text columns are considered categorical and double precision columns are considered continuous. Categorical variables are not encoded and used as is in the training.

    +

    Array columns can also be included in the list, where the array is expanded to treat each element of the array as a feature.

    +

    Note that not every combination of the levels of a categorical variable is checked when evaluating a split. The levels of the non-integer categorical variable are ordered by the entropy of the variable in predicting the response. The split at each node is evaluated between these ordered levels. Integer categorical variables, however, are simply ordered by their value.

    +

    +
    +
    list_of_features_to_exclude
    +

    TEXT. Comma-separated string of column names to exclude from the predictors list. If the dependent_variable is an expression (including cast of a column name), then this list should include the columns present in the dependent_variable expression, otherwise those columns will be included in the features (resulting in meaningless trees). The names in this parameter should be identical to the names used in the table and quoted appropriately.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. Comma-separated list of column names to group the data by. This will produce multiple random forests, one for each group.

    +

    +
    +
    num_trees (optional)
    +

    INTEGER, default: 100. Maximum number of trees to grow in the random forest model. Actual number of trees grown may be different, depending on the data.

    +

    +
    +
    num_random_features (optional)
    +

    INTEGER, default: sqrt(n) for classification, n/3 for regression, where n is the number of features. This parameter is the number of features to randomly select at each split.

    +

    +
    +
    importance (optional)
    +

    BOOLEAN, default: true. Whether or not to calculate variable importance. If set to true, out-of-bag variable importance and impurity variable importance for categorical and continuous features will be output to the group table <model_table>_group. Note that total runtime will increase when variable importance is turned on. Refer to [1][2][3] for more information on variable importance.

    +

    +
    +
    num_permutations (optional)
    +

    INTEGER, default: 1. Number of times to permute each feature value while calculating the out-of-bag variable importance. Only applies when the 'importance' parameter is set to true.

    +
    Note
    Variable importance for a feature is determined by permuting the variable and computing the drop in predictive accuracy using out-of-bag samples [1]. Setting this greater than 1 performs an average over multiple importance calculations, but increases total run time. In most cases, the default value of 1 is sufficient to compute the importance. Due to nature of permutation, the importance value can end up being negative if the number of levels for a categorical variable is small and is unbalanced. In such a scenario, the importance values are shifted to ensure that the lowest importance value is 0. To see importance values normalized to sum to 100 across all variables, use the importance display helper function described later on this page.
    +

    +
    +
    max_tree_depth (optional)
    +

    INTEGER, default: 7. Maximum depth of any node of a tree, with the root node counted as depth 0. A deeper tree can lead to better prediction but will also result in longer processing time and higher memory usage. Current allowed maximum is 15. Note that since random forest is an ensemble method, individual trees typically do not need to be deep.

    +

    +
    +
    min_split (optional)
    +

    INTEGER, default: 20. Minimum number of observations that must exist in a node for a split to be attempted.

    +

    +
    +
    min_bucket (optional)
    +

    INTEGER, default: min_split/3. Minimum number of observations in any terminal node. If only one of min_bucket or min_split is specified, min_split is set to min_bucket*3 or min_bucket to min_split/3, as appropriate.

    +

    +
    +
    num_splits (optional)
    +

    INTEGER, default: 20. Continuous-valued features are binned into discrete quantiles to compute split boundaries. This global parameter is used to compute the resolution of splits for continuous features. Higher number of bins will lead to better prediction, but will also result in longer processing time and higher memory usage.

    +

    +
    +
    null_handling_params (optional)
    +

    TEXT. Comma-separated string of key-value pairs controlling the behavior of various features handling missing values. One of the following can be used if desired (not both):

    + + + + +
    max_surrogates Default: 0. Number of surrogates to store for each node. One approach to handling NULLs is to use surrogate splits for each node. A surrogate variable enables you to make better use of the data by using another predictor variable that is associated (correlated) with the primary split variable. The surrogate variable comes into use when the primary predictior value is NULL. Surrogate rules implemented here are based on reference [1].
    null_as_category

    Default: FALSE. Whether to treat NULL as a valid level for categorical features. FALSE means that NULL is not a valid level, which is probably the most common sitation.

    +

    If set to TRUE, NULL values are considered a categorical value and placed at the end of the ordering of categorical levels. Placing at the end ensures that NULL is never used as a value to split a node on. One reason to make NULL a category is that it allows you to predict on categorical levels that were not in the training data by lumping them into an "other bucket."

    +

    This parameter is ignored for continuous-valued features.

    +
    +

    +
    +
    verbose (optional)
    +

    BOOLEAN, default: FALSE. Provides verbose output of the results of training.

    +

    +
    +
    sample_ratio (optional)
    +
    DOUBLE PRECISION, in the range of (0, 1], default: 1. If 'sample_ratio' is less than 1, a bootstrap sample size smaller than the data table is used for training each tree in the forest. A ratio that is close to 0 may result in trees with only the root node. This sample parameter allows users to quickly experiment with the random forest function since it reduces run time by using only some of the data.
    +
    +

    Output

    +
    +

    The model table produced by the training function contains the following columns:

    + + + + + + + +
    gid INTEGER. Group id that uniquely identifies a set of grouping column values.
    sample_id INTEGER. The id of the bootstrap sample that this tree is a part of.
    tree BYTEA8. Trained tree model stored in binary format (not human readable).
    +

    A summary table named <model_table>_summary is also created at the same time, which contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    method

    'forest_train'

    +

    +
    is_classification

    BOOLEAN. True if it is a classification model, false if for regression.

    +

    +
    source_table

    TEXT. Data source table name.

    +

    +
    model_table

    TEXT. Model table name.

    +

    +
    id_col_name

    TEXT. The ID column name.

    +

    +
    dependent_varname

    TEXT. Dependent variable.

    +

    +
    independent_varnames

    TEXT. Independent variables

    +

    +
    cat_features

    TEXT. List of categorical features as a comma-separated string.

    +

    +
    con_features

    TEXT. List of continuous feature as a comma-separated string.

    +

    +
    grouping_cols

    INTEGER. Names of grouping columns.

    +

    +
    num_trees

    INTEGER. Number of trees grown by the model.

    +

    +
    num_random_features

    INTEGER. Number of features randomly selected for each split.

    +

    +
    max_tree_depth

    INTEGER. Maximum depth of any tree in the random forest model_table.

    +

    +
    min_split

    INTEGER. Minimum number of observations in a node for it to be split.

    +

    +
    min_bucket

    INTEGER. Minimum number of observations in any terminal node.

    +

    +
    num_splits

    INTEGER. Number of buckets for continuous variables.

    +

    +
    verbose

    BOOLEAN. Whether or not to display debug info.

    +

    +
    importance

    BOOLEAN. Whether or not to calculate variable importance.

    +

    +
    num_permutations

    INTEGER. Number of times feature values are permuted while calculating out-of-bag variable importance.

    +

    +
    num_all_groups

    INTEGER. Number of groups during forest training.

    +

    +
    num_failed_groups

    INTEGER. Number of failed groups during forest training.

    +

    +
    total_rows_processed

    BIGINT. Total numbers of rows processed in all groups.

    +

    +
    total_rows_skipped

    BIGINT. Total numbers of rows skipped in all groups due to missing values or failures.

    +

    +
    dependent_var_levels

    TEXT. For classification, the distinct levels of the dependent variable.

    +

    +
    dependent_var_type

    TEXT. The type of dependent variable.

    +

    +
    independent_var_types

    TEXT. A comma separated string for the types of independent variables.

    +

    +
    null_proxy TEXT. Describes how NULLs are handled. If NULL is not treated as a separate categorical variable, this will be NULL. If NULL is treated as a separate categorical value, this will be set to "__NULL__"
    +

    A table named <model_table>_group is also created at the same time, even if no grouping is specified. It contains the following columns:

    + + + + + + + + + + + + + + + + +
    gid

    integer. Group id that uniquely identifies a set of grouping column values. If grouping is not used, this will always be 1.

    +

    +
    <...>

    Same type as in the training data table 'grouping_cols'. This could be multiple columns depending on the 'grouping_cols' input.

    +

    +
    success

    BOOLEAN. Indicator of the success of the group.

    +

    +
    cat_levels_in_text

    TEXT[]. Ordered levels (values) of categorical variables corresponding to the categorical features in the 'list_of_features' argument above. Used to help interpret the trained tree. For example, if the categorical features specified are weather_outlook and windy in that order, then 'cat_levels_in_text' might be [overcast, rain, sunny, False, True].

    +

    +
    cat_n_levels

    INTEGER[]. Number of levels for each categorical variable. Used to help interpret the trained tree. In the example from above, 'cat_n_levels' would be [3, 2] since there are 3 levels for weather_outlook and 2 levels windy.

    +

    +
    oob_error

    DOUBLE PRECISION. Out-of-bag error for the random forest model.

    +

    +
    oob_var_importance

    DOUBLE PRECISION[]. Out-of-bag variable importance for both categorical and continuous features. The order corresponds to the order of the variables in 'independent_varnames' in <model_table>_summary.

    +

    +
    impurity_var_importance

    DOUBLE PRECISION[]. Impurity variable importance for both categorial and continuous features. The order corresponds to the order of the variables in 'independent_varnames' in <model_table>_summary.

    +

    +
    +

    Run-time and Memory Usage
    +

    The number of features and the number of class values per categorical feature have a direct impact on run-time and memory. In addition, here is a summary of the main parameters in the training function that affect run-time and memory:

    + + + + + + + + + + + + + + + + + + + +
    Parameter Run-time Memory Notes
    'num_trees' High No or little effect. Linear with number of trees. Notes that trees train sequentially one after another, though each tree is trained in parallel.
    'importance' Moderate No or little effect. Depends on number of features and 'num_permutations' parameter.
    'num_permutations' Moderate No or little effect. Depends on number of features.
    'max_tree_depth' High High Deeper trees can take longer to run and use more memory.
    'min_split' No or little effect, unless very small. No or little effect, unless very small. If too small, can impact run-time by building trees that are very thick.
    'min_bucket' No or little effect, unless very small. No or little effect, unless very small. If too small, can impact run-time by building trees that are very thick.
    'num_splits' High High Depends on number of continuous variables. Effectively adds more features as the binning becomes more granular.
    'sample_ratio' High High Reduces run time by using only some of the data.
    +

    If you experience long run-times or are hitting memory limits, consider reducing one or more of these parameters. One approach when building a random forest model is to start with a small number of trees and a low maximum depth value, and use suggested defaults for other parameters. This will give you a sense of run-time and test set accuracy. Then you can change number of trees and maximum depth in a systematic way as required to improve accuracy.

    +

    Prediction Function
    The prediction function estimates the conditional mean given a new predictor. It has the following syntax: 
    +forest_predict(random_forest_model,
+               new_data_table,
+               output_table,
+               type)
+
    +

    Arguments

    +
    forest_model
    +

    text. Name of the table containing the random forest model from training.

    +

    +
    +
    new_data_table
    +

    TEXT. Name of the table containing prediction data. This table is expected to contain the same features that were used during training. The table should also contain id_col_name used for identifying each row.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table to output prediction results. If this table already exists, an error is returned. The table contains the id_col_name column giving the 'id' for each prediction and the prediction columns for the dependent variable.

    +

    If type = 'response', then the table has a single additional column with the prediction value of the response. The type of this column depends on the type of the response variable used during training.

    +

    If type = 'prob', then the table has multiple additional columns, one for each possible value of the response variable. The columns are labeled as 'estimated_prob_dep_value', where dep_value represents each value of the response variable.

    +

    +
    +
    type (optional)
    +
    TEXT, optional, default: 'response'. For regression trees, the output is always the predicted value of the dependent variable. For classification trees, the type variable can be 'response', giving the classification prediction as output, or 'prob', giving the class probabilities as output. For each value of the dependent variable, a column with the probabilities is added to the output table.
    +
    +

    Tree Display
    The display function outputs a graph representation of a single tree of the random forest. The output can either be in the popular 'dot' format that can be visualized using various programs including those in the GraphViz package, or in a simple text format. The details of the text format are output with the tree. 
    +get_tree(forest_model_table,
+         gid,
+         sample_id,
+         dot_format,
+         verbose)
+
    +

    An additional display function is provided to output the surrogate splits chosen for each internal node: 

    +get_tree_surr(forest_model_table,
+              gid,
+              sample_id)
+

    This output contains the list of surrogate splits for each internal node. The nodes are sorted in ascending order by id. This is equivalent to viewing the tree in a breadth-first manner. For each surrogate, we output the surrogate split (variable and threshold) and also give the number of rows that were common between the primary split and the surrogate split. Finally, the number of rows present in the majority branch of the primary split is also shown. Only surrogates that perform better than this majority branch are included in the surrogate list. When the primary variable has a NULL value the surrogate variables are used in order to compute the split for that node. If all surrogates variables are NULL, then the majority branch is used to compute the split for a tuple.

    +

    Arguments

    +
    forest_model_table
    +

    TEXT. Name of the table containing the random forest model.

    +

    +
    +
    gid
    +

    INTEGER. Id of the group that this tree is part of.

    +

    +
    +
    sample_id
    +

    INTEGER. Id of the bootstrap sample that this tree is part of.

    +

    +
    +
    dot_format (optional)
    +

    BOOLEAN, default = TRUE. Output can either be in a dot format or a text format. If TRUE, the result is in the dot format, else output is in text format.

    +

    +
    +
    verbose (optional)
    +
    BOOLEAN, default = FALSE. If true, the dot format output will contain additional information (impurity, sample size, number of weighted rows for each response variable, classification or prediction if the tree was pruned at this level)
    +
    +

    The output is always returned as a 'TEXT'. For the dot format, the output can be redirected to a file on the client side and then rendered using visualization programs.

    +

    To export the dot format result to an external file, use the method below. Please note that you should use unaligned table output mode for psql with '-A' flag, or else you may get an error when you try to convert the dot file to another format for viewing (e.g., PDF). And inside the psql client, both '\t' and '\o' should be used:

    +
    +> # under bash
+> psql -A my_database
+# -- in psql now
+# \t
+# \o test.dot -- export to a file
+# select madlib.tree_display('tree_out');
+# \o
+# \t
+

    After the dot file has been generated, use third-party plotting software to plot the trees in a nice format: 

    +> # under bash, convert the dot file into a PDF file
+> dot -Tpdf test.dot > test.pdf
+> xpdf test.pdf&
+

    Please see the decision tree user documentation for more details on working with tree output formats.

    +

    Importance Display
    This is a helper function that creates a table to more easily view out-of-bag and impurity variable importance values for a given model table. This function rescales the importance values to represent them as percentages i.e. importance values are scaled to sum to 100.
    +
    +get_var_importance(model_table, output_table)
+

    Arguments

    +
    model_table
    +
    TEXT. Name of the table containing the random forest model.
    +
    output_table
    +
    TEXT. Name of the table to create for importance values.
    +
    +

    The summary and group tables generated by the forest_train function are required for this function to work.

    +

    Examples
    +
    Note
      +
    • Not all random forest parameters are demonstrated in the examples below. Some are shown in the decision tree user documentation since usage is similar.
      • +
    • Your results may look different than those below due the random nature of random forests.
      • +
    +
    +

    Random Forest Classification Example

    +
      +
    1. Load input data set related to whether to play golf or not: 
      +DROP TABLE IF EXISTS rf_golf CASCADE;
+CREATE TABLE rf_golf (
+    id integer NOT NULL,
+    "OUTLOOK" text,
+    temperature double precision,
+    humidity double precision,
+    "Temp_Humidity" double precision[],
+    clouds_airquality text[],
+    windy boolean,
+    class text
+);
+INSERT INTO rf_golf VALUES
+(1,'sunny', 85, 85, ARRAY[85, 85],ARRAY['none', 'unhealthy'], 'false','Don''t Play'),
+(2, 'sunny', 80, 90, ARRAY[80, 90], ARRAY['none', 'moderate'], 'true', 'Don''t Play'),
+(3, 'overcast', 83, 78, ARRAY[83, 78], ARRAY['low', 'moderate'], 'false', 'Play'),
+(4, 'rain', 70, 96, ARRAY[70, 96], ARRAY['low', 'moderate'], 'false', 'Play'),
+(5, 'rain', 68, 80, ARRAY[68, 80], ARRAY['medium', 'good'], 'false', 'Play'),
+(6, 'rain', 65, 70, ARRAY[65, 70], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play'),
+(7, 'overcast', 64, 65, ARRAY[64, 65], ARRAY['medium', 'moderate'], 'true', 'Play'),
+(8, 'sunny', 72, 95, ARRAY[72, 95], ARRAY['high', 'unhealthy'], 'false', 'Don''t Play'),
+(9, 'sunny', 69, 70, ARRAY[69, 70], ARRAY['high', 'good'], 'false', 'Play'),
+(10, 'rain', 75, 80, ARRAY[75, 80], ARRAY['medium', 'good'], 'false', 'Play'),
+(11, 'sunny', 75, 70, ARRAY[75, 70], ARRAY['none', 'good'], 'true', 'Play'),
+(12, 'overcast', 72, 90, ARRAY[72, 90], ARRAY['medium', 'moderate'], 'true', 'Play'),
+(13, 'overcast', 81, 75, ARRAY[81, 75], ARRAY['medium', 'moderate'], 'false', 'Play'),
+(14, 'rain', 71, 80, ARRAY[71, 80], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play');
+
      2. +
    2. Train random forest and view the summary table: 
      +DROP TABLE IF EXISTS train_output, train_output_group, train_output_summary;
+SELECT madlib.forest_train('rf_golf',         -- source table
+                           'train_output',    -- output model table
+                           'id',              -- id column
+                           'class',           -- response
+                           '"OUTLOOK", temperature, humidity, windy',   -- features
+                           NULL,              -- exclude columns
+                           NULL,              -- grouping columns
+                           20::integer,       -- number of trees
+                           2::integer,        -- number of random features
+                           TRUE::boolean,     -- variable importance
+                           1::integer,        -- num_permutations
+                           8::integer,        -- max depth
+                           3::integer,        -- min split
+                           1::integer,        -- min bucket
+                           10::integer        -- number of splits per continuous variable
+                           );
+\x on
+SELECT * FROM train_output_summary;
+
      +-[ RECORD 1 ]---------+--------------------------------------------------
+method                | forest_train
+is_classification     | t
+source_table          | rf_golf
+model_table           | train_output
+id_col_name           | id
+dependent_varname     | class
+independent_varnames  | "OUTLOOK",windy,temperature,humidity
+cat_features          | "OUTLOOK",windy
+con_features          | temperature,humidity
+grouping_cols         |
+num_trees             | 20
+num_random_features   | 2
+max_tree_depth        | 8
+min_split             | 3
+min_bucket            | 1
+num_splits            | 10
+verbose               | f
+importance            | t
+num_permutations      | 1
+num_all_groups        | 1
+num_failed_groups     | 0
+total_rows_processed  | 14
+total_rows_skipped    | 0
+dependent_var_levels  | "Don't Play","Play"
+dependent_var_type    | text
+independent_var_types | text, boolean, double precision, double precision
+null_proxy            | None
+
      View the group table output: 
      +SELECT * FROM train_output_group;
+
      +-[ RECORD 1 ]-----------+----------------------------------------------------------------------
+gid                     | 1
+success                 | t
+cat_n_levels            | {3,2}
+cat_levels_in_text      | {overcast,sunny,rain,False,True}
+oob_error               | 0.64285714285714285714
+oob_var_importance      | {0.0525595238095238,0,0.0138095238095238,0.0276190476190476}
+impurity_var_importance | {0.254133481284938,0.0837130966399198,0.258520599370744,0.173196167388586}
+
      The 'cat_levels_in_text' array shows the levels of the categorical variables "OUTLOOK" and windy, which have 3 and 2 levels respectively. Out-of-bag and impurity variable importance arrays are ordered according to the order of the variables in 'independent_varnames' in <model_table>_summary. A higher value means higher importance for the variable. We can use the helper function to get a normalized view of variable importance: 
      +\x off
+DROP TABLE IF EXISTS imp_output;
+SELECT madlib.get_var_importance('train_output','imp_output');
+SELECT * FROM imp_output ORDER BY oob_var_importance DESC;
+
      +   feature   | oob_var_importance | impurity_var_importance
+-------------+--------------------+-------------------------
+ "OUTLOOK"   |   55.9214692843572 |        33.0230751036133
+ humidity    |   29.3856871437619 |        22.5057714332356
+ temperature |    14.692843571881 |        33.5931539822541
+ windy       |                  0 |         10.877999480897
+(4 rows)
+
      3. +
    3. Predict output categories. For the purpose of this example, we use the same data that was used for training: 
      +\x off
+DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.forest_predict('train_output',        -- tree model
+                             'rf_golf',             -- new data table
+                             'prediction_results',  -- output table
+                             'response');           -- show response
+SELECT g.id, class, estimated_class FROM prediction_results p,
+rf_golf g WHERE p.id = g.id ORDER BY g.id;
+
      + id |   class    | estimated_class
+----+------------+-----------------
+  1 | Don't Play | Don't Play
+  2 | Don't Play | Don't Play
+  3 | Play       | Play
+  4 | Play       | Play
+  5 | Play       | Play
+  6 | Don't Play | Don't Play
+  7 | Play       | Play
+  8 | Don't Play | Don't Play
+  9 | Play       | Play
+ 10 | Play       | Play
+ 11 | Play       | Play
+ 12 | Play       | Play
+ 13 | Play       | Play
+ 14 | Don't Play | Don't Play
+(14 rows)
+
      To display the probabilities associated with each value of the dependent variable, set the 'type' parameter to 'prob': 
      +DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.forest_predict('train_output',        -- tree model
+                             'rf_golf',             -- new data table
+                             'prediction_results',  -- output table
+                             'prob');               -- show probability
+SELECT g.id, class, "estimated_prob_Don't Play",  "estimated_prob_Play"
+FROM prediction_results p, rf_golf g WHERE p.id = g.id ORDER BY g.id;
+
      + id |   class    | estimated_prob_Don't Play | estimated_prob_Play
+----+------------+---------------------------+---------------------
+  1 | Don't Play |                       0.9 |                 0.1
+  2 | Don't Play |                      0.85 |                0.15
+  3 | Play       |                         0 |                   1
+  4 | Play       |                      0.35 |                0.65
+  5 | Play       |                      0.05 |                0.95
+  6 | Don't Play |                      0.85 |                0.15
+  7 | Play       |                      0.25 |                0.75
+  8 | Don't Play |                      0.85 |                0.15
+  9 | Play       |                      0.15 |                0.85
+ 10 | Play       |                      0.15 |                0.85
+ 11 | Play       |                      0.35 |                0.65
+ 12 | Play       |                       0.1 |                 0.9
+ 13 | Play       |                         0 |                   1
+ 14 | Don't Play |                       0.8 |                 0.2
+(14 rows)
+
      4. +
    4. View a single tree in text format within the forest identified by 'gid' and 'sample_id', out of the several that were created: 
      +SELECT madlib.get_tree('train_output',1,7, FALSE);
+
      + -------------------------------------
+ - Each node represented by 'id' inside ().
+ - Leaf nodes have a * while internal nodes have the split condition at the end.
+ - For each internal node (i), it's children will be at (2i+1) and (2i+2).
+ - For each split the first indented child (2i+1) is the 'True' node and
+second indented child (2i+2) is the 'False' node.
+ - Number of (weighted) rows for each response variable inside [].
+ - Order of values = ['"Don\'t Play"', '"Play"']
+ -------------------------------------
+ (0)[ 5 10]  windy in {False}
+    (1)[2 8]  "OUTLOOK" in {overcast,sunny}
+       (3)[2 1]  humidity <= 75
+          (7)[0 1]  * --> "Play"
+          (8)[2 0]  * --> "Don't Play"
+       (4)[0 7]  * --> "Play"
+    (2)[3 2]  temperature <= 75
+       (5)[1 2]  humidity <= 70
+          (11)[1 1]  * --> "Don't Play"
+          (12)[0 1]  * --> "Play"
+       (6)[2 0]  * --> "Don't Play"
+ -------------------------------------
+
      Please see the decision tree user documentation for an explanation on how to interpret the tree display above.
      5. +
    5. View tree in dot format: 
      +SELECT madlib.get_tree('train_output',1,7);
+
      + ----------------------------------------------------
+ digraph "Classification tree for rf_golf" {
+ "0" [label="windy <= False", shape=ellipse];
+ "0" -> "1"[label="yes"];
+ "0" -> "2"[label="no"];
+ "1" [label="\"OUTLOOK" <= sunny", shape=ellipse];
+ "1" -> "3"[label="yes"];
+ "1" -> "4"[label="no"];
+ "4" [label=""Play"",shape=box];
+ "2" [label="temperature <= 75", shape=ellipse];
+ "2" -> "5"[label="yes"];
+ "2" -> "6"[label="no"];
+ "6" [label=""Don't Play"",shape=box];
+ "3" [label="humidity <= 75", shape=ellipse];
+ "3" -> "7"[label="yes"];
+ "7" [label=""Play"",shape=box];
+ "3" -> "8"[label="no"];
+ "8" [label=""Don't Play"",shape=box];
+ "5" [label="humidity <= 70", shape=ellipse];
+ "5" -> "11"[label="yes"];
+ "11" [label=""Don't Play"",shape=box];
+ "5" -> "12"[label="no"];
+ "12" [label=""Play"",shape=box];
+ } //---end of digraph---------
+
      6. +
    6. View tree in dot format with additional information: 
      +SELECT madlib.get_tree('train_output',1,7, TRUE, TRUE);
+
      + ---------------------------------------------------------------------------------------------------------------------------
+ digraph "Classification tree for rf_golf" {
+ "0" [label="windy <= False\\n impurity = 0.444444\\n samples = 15\\n value = [ 5 10]\\n class = \"Play"", shape=ellipse];
+ "0" -> "1"[label="yes"];
+ "0" -> "2"[label="no"];
+ "1" [label=""OUTLOOK" <= sunny\n impurity = 0.32\n samples = 10\n value = [2 8]\n class = "Play"", shape=ellipse];
+ "1" -> "3"[label="yes"];
+ "1" -> "4"[label="no"];
+ "4" [label=""Play"\n impurity = 0\n samples = 7\n value = [0 7]",shape=box];
+ "2" [label="temperature <= 75\n impurity = 0.48\n samples = 5\n value = [3 2]\n class = "Don't Play"", shape=ellipse];
+ "2" -> "5"[label="yes"];
+ "2" -> "6"[label="no"];
+ "6" [label=""Don't Play"\n impurity = 0\n samples = 2\n value = [2 0]",shape=box];
+ "3" [label="humidity <= 75\n impurity = 0.444444\n samples = 3\n value = [2 1]\n class = "Don't Play"", shape=ellipse];
+ "3" -> "7"[label="yes"];
+ "7" [label=""Play"\n impurity = 0\n samples = 1\n value = [0 1]",shape=box];
+ "3" -> "8"[label="no"];
+ "8" [label=""Don't Play"\n impurity = 0\n samples = 2\n value = [2 0]",shape=box];
+ "5" [label="humidity <= 70\n impurity = 0.444444\n samples = 3\n value = [1 2]\n class = "Play"", shape=ellipse];
+ "5" -> "11"[label="yes"];
+ "11" [label=""Don't Play"\n impurity = 0.5\n samples = 2\n value = [1 1]",shape=box];
+ "5" -> "12"[label="no"];
+ "12" [label=""Play"\n impurity = 0\n samples = 1\n value = [0 1]",shape=box];
+ } //---end of digraph---------
+
      7. +
    7. Arrays of features. Categorical and continuous features can be array columns, in which case the array is expanded to treat each element of the array as a feature: 
      +DROP TABLE IF EXISTS train_output, train_output_group, train_output_summary;
+SELECT madlib.forest_train('rf_golf',         -- source table
+                           'train_output',    -- output model table
+                           'id',              -- id column
+                           'class',           -- response
+                           '"Temp_Humidity", clouds_airquality',   -- features
+                           NULL,              -- exclude columns
+                           NULL,              -- grouping columns
+                           20::integer,       -- number of trees
+                           2::integer,        -- number of random features
+                           TRUE::boolean,     -- variable importance
+                           1::integer,        -- num_permutations
+                           8::integer,        -- max depth
+                           3::integer,        -- min split
+                           1::integer,        -- min bucket
+                           10::integer        -- number of splits per continuous variable
+                           );
+\x on
+SELECT * FROM train_output_summary;
+
      +-[ RECORD 1 ]---------+----------------------------------------------------------------------------------------
+method                | forest_train
+is_classification     | t
+source_table          | rf_golf
+model_table           | train_output
+id_col_name           | id
+dependent_varname     | class
+independent_varnames  | (clouds_airquality)[1],(clouds_airquality)[2],("Temp_Humidity")[1],("Temp_Humidity")[2]
+cat_features          | (clouds_airquality)[1],(clouds_airquality)[2]
+con_features          | ("Temp_Humidity")[1],("Temp_Humidity")[2]
+grouping_cols         |
+num_trees             | 20
+num_random_features   | 2
+max_tree_depth        | 8
+min_split             | 3
+min_bucket            | 1
+num_splits            | 10
+verbose               | f
+importance            | t
+num_permutations      | 1
+num_all_groups        | 1
+num_failed_groups     | 0
+total_rows_processed  | 14
+total_rows_skipped    | 0
+dependent_var_levels  | "Don't Play","Play"
+dependent_var_type    | text
+independent_var_types | text, text, double precision, double precision
+null_proxy            | None
+
      8. +
    8. Sample ratio. Use the sample ratio parameter to train on a subset of the data: 
      +DROP TABLE IF EXISTS train_output, train_output_group, train_output_summary;
+SELECT madlib.forest_train('rf_golf',         -- source table
+                           'train_output',    -- output model table
+                           'id',              -- id column
+                           'class',           -- response
+                           '"OUTLOOK", temperature, humidity, windy',   -- features
+                           NULL,              -- exclude columns
+                           NULL,              -- grouping columns
+                           20::integer,       -- number of trees
+                           2::integer,        -- number of random features
+                           TRUE::boolean,     -- variable importance
+                           1::integer,        -- num_permutations
+                           8::integer,        -- max depth
+                           3::integer,        -- min split
+                           1::integer,        -- min bucket
+                           10::integer,       -- number of splits per continuous variable
+                           NULL,              -- NULL handling
+                           FALSE,             -- Verbose
+                           0.5                -- Sample ratio
+                           );
+SELECT * FROM train_output_group;
+
      +-[ RECORD 1 ]-----------+--------------------------------------------------------------------
+gid                     | 1
+success                 | t
+cat_n_levels            | {3,2}
+cat_levels_in_text      | {overcast,rain,sunny,False,True}
+oob_error               | 0.57142857142857142857
+oob_var_importance      | {0,0.0166666666666667,0.0166666666666667,0.0166666666666667}
+impurity_var_importance | {0.143759266026582,0.0342777777777778,0.157507369614512,0.0554953231292517}
+
      9. +
    +

    Random Forest Regression Example

    +
      +
    1. Load input data related to fuel consumption and 10 aspects of automobile design and performance for 32 automobiles (1973–74 models). Data was extracted from the 1974 Motor Trend US magazine. 
      +DROP TABLE IF EXISTS mt_cars;
+CREATE TABLE mt_cars (
+    id integer NOT NULL,
+    mpg double precision,
+    cyl integer,
+    disp double precision,
+    hp integer,
+    drat double precision,
+    wt double precision,
+    qsec double precision,
+    vs integer,
+    am integer,
+    gear integer,
+    carb integer
+);
+INSERT INTO mt_cars VALUES
+(1,18.7,8,360,175,3.15,3.44,17.02,0,0,3,2),
+(2,21,6,160,110,3.9,2.62,16.46,0,1,4,4),
+(3,24.4,4,146.7,62,3.69,3.19,20,1,0,4,2),
+(4,21,6,160,110,3.9,2.875,17.02,0,1,4,4),
+(5,17.8,6,167.6,123,3.92,3.44,18.9,1,0,4,4),
+(6,16.4,8,275.8,180,3.078,4.07,17.4,0,0,3,3),
+(7,22.8,4,108,93,3.85,2.32,18.61,1,1,4,1),
+(8,17.3,8,275.8,180,3.078,3.73,17.6,0,0,3,3),
+(9,21.4,null,258,110,3.08,3.215,19.44,1,0,3,1),
+(10,15.2,8,275.8,180,3.078,3.78,18,0,0,3,3),
+(11,18.1,6,225,105,2.768,3.46,20.22,1,0,3,1),
+(12,32.4,4,78.7,66,4.08,2.20,19.47,1,1,4,1),
+(13,14.3,8,360,245,3.21,3.578,15.84,0,0,3,4),
+(14,22.8,4,140.8,95,3.92,3.15,22.9,1,0,4,2),
+(15,30.4,4,75.7,52,4.93,1.615,18.52,1,1,4,2),
+(16,19.2,6,167.6,123,3.92,3.44,18.3,1,0,4,4),
+(17,33.9,4,71.14,65,4.22,1.835,19.9,1,1,4,1),
+(18,15.2,null,304,150,3.15,3.435,17.3,0,0,3,2),
+(19,10.4,8,472,205,2.93,5.25,17.98,0,0,3,4),
+(20,27.3,4,79,66,4.08,1.935,18.9,1,1,4,1),
+(21,10.4,8,460,215,3,5.424,17.82,0,0,3,4),
+(22,26,4,120.3,91,4.43,2.14,16.7,0,1,5,2),
+(23,14.7,8,440,230,3.23,5.345,17.42,0,0,3,4),
+(24,30.4,4,95.14,113,3.77,1.513,16.9,1,1,5,2),
+(25,21.5,4,120.1,97,3.70,2.465,20.01,1,0,3,1),
+(26,15.8,8,351,264,4.22,3.17,14.5,0,1,5,4),
+(27,15.5,8,318,150,2.768,3.52,16.87,0,0,3,2),
+(28,15,8,301,335,3.54,3.578,14.6,0,1,5,8),
+(29,13.3,8,350,245,3.73,3.84,15.41,0,0,3,4),
+(30,19.2,8,400,175,3.08,3.845,17.05,0,0,3,2),
+(31,19.7,6,145,175,3.62,2.77,15.5,0,1,5,6),
+(32,21.4,4,121,109,4.11,2.78,18.6,1,1,4,2);
+
      2. +
    2. We train a regression random forest tree with grouping on transmission type (0 = automatic, 1 = manual) and use surrogates for NULL handling: 
      +DROP TABLE IF EXISTS mt_cars_output, mt_cars_output_group, mt_cars_output_summary;
+SELECT madlib.forest_train('mt_cars',         -- source table
+                           'mt_cars_output',  -- output model table
+                           'id',              -- id column
+                           'mpg',             -- response
+                           '*',               -- features
+                           'id, hp, drat, am, gear, carb',  -- exclude columns
+                           'am',              -- grouping columns
+                           10::integer,       -- number of trees
+                           2::integer,        -- number of random features
+                           TRUE::boolean,     -- variable importance
+                           1,                 -- num_permutations
+                           10,                -- max depth
+                           8,                 -- min split
+                           3,                 -- min bucket
+                           10,                -- number of splits per continuous variable
+                           'max_surrogates=2' -- NULL handling
+                           );
+\x on
+SELECT * FROM mt_cars_output_summary;
+
      +-[ RECORD 1 ]---------+-----------------------------------------------------------------------
+method                | forest_train
+is_classification     | f
+source_table          | mt_cars
+model_table           | mt_cars_output
+id_col_name           | id
+dependent_varname     | mpg
+independent_varnames  | vs,cyl,disp,qsec,wt
+cat_features          | vs,cyl
+con_features          | disp,qsec,wt
+grouping_cols         | am
+num_trees             | 10
+num_random_features   | 2
+max_tree_depth        | 10
+min_split             | 8
+min_bucket            | 3
+num_splits            | 10
+verbose               | f
+importance            | t
+num_permutations      | 1
+num_all_groups        | 2
+num_failed_groups     | 0
+total_rows_processed  | 32
+total_rows_skipped    | 0
+dependent_var_levels  |
+dependent_var_type    | double precision
+independent_var_types | integer, integer, double precision, double precision, double precision
+null_proxy            | None
+
      Review the group table to see variable importance by group: 
      +SELECT * FROM mt_cars_output_group ORDER BY gid;
+
      +-[ RECORD 1 ]-----------+----------------------------------------------------------------------------------------
+gid                     | 1
+am                      | 0
+success                 | t
+cat_n_levels            | {2,3}
+cat_levels_in_text      | {0,1,4,6,8}
+oob_error               | 8.64500988190963
+oob_var_importance      | {3.91269987042436,0,2.28278236607143,0.0994074074074073,3.42585277187264}
+impurity_var_importance | {5.07135586863621,3.72145581490929,5.06700415274492,0.594942174008333,8.10909642389614}
+-[ RECORD 2 ]-----------+----------------------------------------------------------------------------------------
+gid                     | 2
+am                      | 1
+success                 | t
+cat_n_levels            | {2,3}
+cat_levels_in_text      | {0,1,4,6,8}
+oob_error               | 16.5197718747446
+oob_var_importance      | {5.22711111111111,10.0872041666667,9.6875362244898,3.97782,2.99447839506173}
+impurity_var_importance | {5.1269704861111,7.04765974920884,20.9817274159476,4.02800949238769,10.5539079705215}
+
      Use the helper function to display normalized variable importance: 
      +\x off
+DROP TABLE IF EXISTS mt_imp_output;
+SELECT madlib.get_var_importance('mt_cars_output','mt_imp_output');
+SELECT * FROM mt_imp_output ORDER BY am, oob_var_importance DESC;
+
      + am | feature | oob_var_importance | impurity_var_importance
+----+---------+--------------------+-------------------------
+  0 | vs      |   40.2510395098467 |        22.4755743014842
+  0 | wt      |   35.2427070417256 |        35.9384361725319
+  0 | disp    |   23.4836216045257 |        22.4562880757909
+  0 | qsec    |   1.02263184390195 |        2.63670453886068
+  0 | cyl     |                  0 |        16.4929969113323
+  1 | cyl     |   31.5479979891794 |        14.7631219023997
+  1 | disp    |   30.2980259228064 |        43.9515825943964
+  1 | vs      |   16.3479283355324 |        10.7397480823277
+  1 | qsec    |   12.4407373230344 |         8.4376938269215
+  1 | wt      |    9.3653104294474 |        22.1078535939547
+
      3. +
    3. Predict regression output for the same data and compare with original: 
      +\x off
+DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.forest_predict('mt_cars_output',
+                             'mt_cars',
+                             'prediction_results',
+                             'response');
+SELECT s.am, s.id, mpg, estimated_mpg, mpg-estimated_mpg as delta
+FROM prediction_results p, mt_cars s WHERE s.id = p.id ORDER BY s.am, s.id;
+
      +  am | id | mpg  |  estimated_mpg   |        delta
+----+----+------+------------------+----------------------
+  0 |  1 | 18.7 | 16.5055222816399 |     2.19447771836007
+  0 |  3 | 24.4 | 21.8437857142857 |     2.55621428571428
+  0 |  5 | 17.8 | 19.2085504201681 |    -1.40855042016807
+  0 |  6 | 16.4 | 15.7340778371955 |    0.665922162804513
+  0 |  8 | 17.3 | 15.7340778371955 |     1.56592216280452
+  0 |  9 | 21.4 | 18.2305980392157 |     3.16940196078431
+  0 | 10 | 15.2 | 15.2640778371955 |  -0.0640778371954838
+  0 | 11 | 18.1 | 18.9192647058824 |    -0.81926470588235
+  0 | 13 | 14.3 | 15.0690909090909 |   -0.769090909090908
+  0 | 14 | 22.8 | 21.8437857142857 |    0.956214285714289
+  0 | 16 | 19.2 | 19.2085504201681 | -0.00855042016807062
+  0 | 18 | 15.2 | 16.0805222816399 |    -0.88052228163993
+  0 | 19 | 10.4 | 14.7914111705288 |    -4.39141117052882
+  0 | 21 | 10.4 | 14.7914111705288 |    -4.39141117052882
+  0 | 23 | 14.7 | 15.0525222816399 |    -0.35252228163993
+  0 | 25 | 21.5 | 21.8437857142857 |   -0.343785714285712
+  0 | 27 | 15.5 | 15.4775222816399 |   0.0224777183600704
+  0 | 29 | 13.3 | 15.0690909090909 |    -1.76909090909091
+  0 | 30 | 19.2 | 15.4775222816399 |     3.72247771836007
+  1 |  2 |   21 |         19.53275 |              1.46725
+  1 |  4 |   21 | 20.3594166666667 |    0.640583333333332
+  1 |  7 | 22.8 | 23.0550833333333 |   -0.255083333333335
+  1 | 12 | 32.4 | 27.1501666666667 |     5.24983333333333
+  1 | 15 | 30.4 | 28.9628333333333 |     1.43716666666667
+  1 | 17 | 33.9 | 28.0211666666667 |     5.87883333333333
+  1 | 20 | 27.3 | 27.7138333333333 |   -0.413833333333333
+  1 | 22 |   26 | 26.8808333333333 |   -0.880833333333335
+  1 | 24 | 30.4 |          27.8225 |               2.5775
+  1 | 26 | 15.8 | 17.2924166666667 |    -1.49241666666666
+  1 | 28 |   15 | 17.2924166666667 |    -2.29241666666667
+  1 | 31 | 19.7 |         19.53275 |    0.167249999999999
+  1 | 32 | 21.4 | 23.0550833333333 |    -1.65508333333334
+(32 rows)
+
      4. +
    4. Display a single tree of the random forest in dot format: 
      +SELECT madlib.get_tree('mt_cars_output',1,7);
+
      + digraph "Regression tree for mt_cars" {
+ "0" [label="disp <= 258", shape=ellipse];
+ "0" -> "1"[label="yes"];
+ "1" [label="20.35",shape=box];
+ "0" -> "2"[label="no"];
+ "2" [label="qsec <= 17.6", shape=ellipse];
+ "2" -> "5"[label="yes"];
+ "5" [label="15.8",shape=box];
+ "2" -> "6"[label="no"];
+ "6" [label="12.8",shape=box];
+ } //---end of digraph---------
+
      Display the surrogate variables that are used to compute the split for each node when the primary variable is NULL: 
      +SELECT madlib.get_tree_surr('mt_cars_output',1,7);
+
      +    -------------------------------------
+       Surrogates for internal nodes
+    -------------------------------------
+ (0) disp <= 258
+      1: wt <= 3.46    [common rows = 12]
+      2: cyl in {4,6}    [common rows = 11]
+      [Majority branch = 6 ]
+ (2) qsec <= 17.6
+      1: wt <= 3.435    [common rows = 6]
+      2: disp > 275.8    [common rows = 5]
+      [Majority branch = 4 ]
+
      5. +
    +

    NULL Handling Example

    +
      +
    1. Create toy example to illustrate 'null-as-category' handling for categorical features: 
      +DROP TABLE IF EXISTS null_handling_example;
+CREATE TABLE null_handling_example (
+    id integer,
+    country text,
+    city text,
+    weather text,
+    response text
+);
+INSERT INTO null_handling_example VALUES
+(1,null,null,null,'a'),
+(2,'US',null,null,'b'),
+(3,'US','NY',null,'c'),
+(4,'US','NY','rainy','d');
+
      2. +
    2. Train random forest tree. Note that 'NULL' is set as a valid level for the categorical features country, weather and city: 
      +DROP TABLE IF EXISTS train_output, train_output_group, train_output_summary;
+SELECT madlib.forest_train('null_handling_example',  -- source table
+                           'train_output',    -- output model table
+                           'id',              -- id column
+                           'response',        -- response
+                           'country, weather, city',   -- features
+                           NULL,              -- exclude columns
+                           NULL,              -- grouping columns
+                           10::integer,        -- number of trees
+                           2::integer,        -- number of random features
+                           TRUE::boolean,     -- variable importance
+                           1::integer,        -- num_permutations
+                           3::integer,        -- max depth
+                           2::integer,        -- min split
+                           1::integer,        -- min bucket
+                           3::integer,        -- number of splits per continuous variable
+                           'null_as_category=TRUE'
+                           );
+\x on
+SELECT * FROM train_output_summary;
+
      +-[ RECORD 1 ]---------+----------------------
+method                | forest_train
+is_classification     | t
+source_table          | null_handling_example
+model_table           | train_output
+id_col_name           | id
+dependent_varname     | response
+independent_varnames  | country,weather,city
+cat_features          | country,weather,city
+con_features          |
+grouping_cols         |
+num_trees             | 10
+num_random_features   | 2
+max_tree_depth        | 3
+min_split             | 2
+min_bucket            | 1
+num_splits            | 3
+verbose               | f
+importance            | t
+num_permutations      | 1
+num_all_groups        | 1
+num_failed_groups     | 0
+total_rows_processed  | 4
+total_rows_skipped    | 0
+dependent_var_levels  | "a","b","c","d"
+dependent_var_type    | text
+independent_var_types | text, text, text
+null_proxy            | __NULL__
+
      View the summary table: 
      +SELECT * FROM train_output_group;
+
      +-[ RECORD 1 ]-----------+-----------------------------------------
+gid                     | 1
+success                 | t
+cat_n_levels            | {2,2,2}
+cat_levels_in_text      | {US,__NULL__,rainy,__NULL__,NY,__NULL__}
+oob_error               | 1.00000000000000000000
+oob_var_importance      | {0,0,0}
+impurity_var_importance | {0.125,0.0944444444444,0.1836666666667}
+
      3. +
    3. Predict for data not previously seen by assuming NULL value as the default: 
      +\x off
+DROP TABLE IF EXISTS table_test;
+CREATE TABLE table_test (
+    id integer,
+    country text,
+    city text,
+    weather text,
+    expected_response text
+);
+INSERT INTO table_test VALUES
+(1,'IN','MUM','cloudy','a'),
+(2,'US','HOU','humid','b'),
+(3,'US','NY','sunny','c'),
+(4,'US','NY','rainy','d');
+DROP TABLE IF EXISTS prediction_results;
+SELECT madlib.forest_predict('train_output',
+                             'table_test',
+                             'prediction_results',
+                             'response');
+SELECT s.id, expected_response, estimated_response
+FROM prediction_results p, table_test s
+WHERE s.id = p.id ORDER BY id;
+
      + id | expected_response | estimated_response
+----+-------------------+--------------------
+  1 | a                 | a
+  2 | b                 | b
+  3 | c                 | c
+  4 | d                 | d
+(4 rows)
+
      There is only training data for country 'US' so the response for country 'IN' is 'a', corresponding to a NULL (not 'US') country level. Likewise, any city in the 'US' that is not 'NY' will predict response 'b', corresponding to a NULL (not 'NY') city level.
      4. +
    +

    Literature
    [1] L. Breiman and A. Cutler. Random Forests. http://www.stat.berkeley.edu/~breiman/RandomForests
    +

    [2] L. Breiman, A. Cutler, A. Liaw, and M. Wiener. randomForest: Breiman and Cutler's Random Forests for Classification and Regression. http://cran.r-project.org/web/packages/randomForest/index.html

    +

    [3] L. Breiman, J. Friedman, R. Olshen, C. Stone. "Classification and Regression Trees", Chapman & Hall, 1984.

    +

    Related Topics
    +

    File random_forest.sql_in documenting the training function

    +

    Decision Tree

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__regml.html b/docs/docs/v2.1.0/group__grp__regml.html new file mode 100644 index 00000000..44a9890c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__regml.html @@ -0,0 +1,157 @@ + + + + + + + + +MADlib: Regression Models + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
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    +Modules
    +
    +
    Regression Models
    Supervised Learning
    +
    +
    +

    Detailed Description

    +

    A collection of methods for modeling conditional expectation of a response variable.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Modules

     Clustered Variance
     Calculates clustered variance for linear, logistic, and multinomial logistic regression models, and Cox proportional hazards models.
     
     Cox-Proportional Hazards Regression
     Models the relationship between one or more independent predictor variables and the amount of time before an event occurs.
     
     Elastic Net Regularization
     Generates a regularized regression model for variable selection in linear and logistic regression problems, combining the L1 and L2 penalties of the lasso and ridge methods.
     
     Generalized Linear Models
     Estimate generalized linear model (GLM). GLM is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
     
     Linear Regression
     Also called Ordinary Least Squares Regression, models linear relationship between a dependent variable and one or more independent variables.
     
     Logistic Regression
     Models the relationship between one or more predictor variables and a binary categorical dependent variable by predicting the probability of the dependent variable using a logistic function.
     
     Marginal Effects
     Calculates marginal effects for the coefficients in regression problems.
     
     Multinomial Regression
     Multinomial regression is to model the conditional distribution of the multinomial response variable using a linear combination of predictors.
     
     Ordinal Regression
     Regression to model data with ordinal response variable.
     
     Robust Variance
     Calculates Huber-White variance estimates for linear, logistic, and multinomial regression models, and for Cox proportional hazards models.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__regml.js b/docs/docs/v2.1.0/group__grp__regml.js new file mode 100644 index 00000000..76e3c69b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__regml.js @@ -0,0 +1,13 @@ +var group__grp__regml = +[ + [ "Clustered Variance", "group__grp__clustered__errors.html", null ], + [ "Cox-Proportional Hazards Regression", "group__grp__cox__prop__hazards.html", null ], + [ "Elastic Net Regularization", "group__grp__elasticnet.html", null ], + [ "Generalized Linear Models", "group__grp__glm.html", null ], + [ "Linear Regression", "group__grp__linreg.html", null ], + [ "Logistic Regression", "group__grp__logreg.html", null ], + [ "Marginal Effects", "group__grp__marginal.html", null ], + [ "Multinomial Regression", "group__grp__multinom.html", null ], + [ "Ordinal Regression", "group__grp__ordinal.html", null ], + [ "Robust Variance", "group__grp__robust.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__robust.html b/docs/docs/v2.1.0/group__grp__robust.html new file mode 100644 index 00000000..922cc223 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__robust.html @@ -0,0 +1,431 @@ + + + + + + + + +MADlib: Robust Variance + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
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    +
    Robust Variance
    Supervised Learning » Regression Models
    +
    +
    +
    Contents +

    The functions in this module calculate robust variance (Huber-White estimates) for linear regression, logistic regression, multinomial logistic regression, and Cox proportional hazards. They are useful in calculating variances in a dataset with potentially noisy outliers. The Huber-White implemented here is identical to the "HC0" sandwich operator in the R module "sandwich".

    +

    The interfaces for robust linear, logistic, and multinomial logistic regression are similar. Each regression type has its own training function. The regression results are saved in an output table with small differences, depending on the regression type.

    +
    Warning
    Please note that the interface for Cox proportional hazards, unlike the interface of other regression methods, accepts an output model table produced by coxph_train() function.
    +

    Robust Linear Regression Training Function
    +

    The robust_variance_linregr() function has the following syntax: 

    +robust_variance_linregr( source_table,
+                         out_table,
+                         dependent_varname,
+                         independent_varname,
+                         grouping_cols
+                       )
+
    +
    source_table
    +
    VARCHAR. The name of the table containing the training data.
    +
    out_table
    +

    VARCHAR. Name of the generated table containing the output model. The output table contains the following columns.

    + + + + + + + + +
    coef DOUBLE PRECISION[]. Vector of the coefficients of the regression.
    std_err DOUBLE PRECISION[]. Vector of the standard error of the coefficients.
    t_stats DOUBLE PRECISION[]. Vector of the t-stats of the coefficients.
    p_values DOUBLE PRECISION[]. Vector of the p-values of the coefficients.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by linregr_train function. Please refer to the documentation for linear regression for details.

    +
    +
    dependent_varname
    +
    VARCHAR. The name of the column containing the dependent variable.
    +
    independent_varname
    +
    VARCHAR. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list.
    +
    grouping_cols (optional)
    +
    VARCHAR, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single result model is generated. Default value: NULL.
    +
    +

    Robust Logistic Regression Training Function
    +

    The robust_variance_logregr() function has the following syntax: 

    +robust_variance_logregr( source_table,
+                         out_table,
+                         dependent_varname,
+                         independent_varname,
+                         grouping_cols,
+                         max_iter,
+                         optimizer,
+                         tolerance,
+                         verbose_mode
+                       )
+
    +
    source_table
    +
    VARCHAR. The name of the table containing the training data.
    +
    out_table
    +

    VARCHAR. Name of the generated table containing the output model. The output table has the following columns:

    + + + + + + + + +
    coef Vector of the coefficients of the regression.
    std_err Vector of the standard error of the coefficients.
    z_stats Vector of the z-stats of the coefficients.
    p_values Vector of the p-values of the coefficients.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by logregr_train function. Please refer to the documentation for logistic regression for details.

    +
    +
    dependent_varname
    +
    VARCHAR. The name of the column containing the independent variable.
    +
    independent_varname
    +
    VARCHAR. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list.
    +
    grouping_cols (optional)
    +
    VARCHAR, default: NULL. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single result model is generated.
    +
    max_iter (optional)
    +
    INTEGER, default: 20. The maximum number of iterations that are allowed.
    +
    optimizer
    +
    VARCHAR, default: 'fista'. Name of optimizer, either 'fista' or 'igd'.
    +
    tolerance (optional)
    +
    DOUBLE PRECISION, default: 1e-6. The criteria to end iterations. Both the 'fista' and 'igd' optimizers compute the average difference between the coefficients of two consecutive iterations, and when the difference is smaller than tolerance or the iteration number is larger than max_iter, the computation stops.
    +
    verbose_mode (optional)
    +
    BOOLEAN, default: FALSE. Whether the regression fit should print any warning messages.
    +
    +

    Robust Multinomial Logistic Regression Function
    +

    The robust_variance_mlogregr() function has the following syntax: 

    +robust_variance_mlogregr( source_table,
+                          out_table,
+                          dependent_varname,
+                          independent_varname,
+                          ref_category,
+                          grouping_cols,
+                          optimizer_params,
+                          verbose_mode
+                        )
+
    +
    source_table
    +
    VARCHAR. The name of the table containing training data, properly qualified.
    +
    out_table
    +

    VARCHAR. The name of the table where the regression model will be stored. The output table has the following columns:

    + + + + + + + + + + + + +
    category The category.
    ref_category The refererence category used for modeling.
    coef Vector of the coefficients of the regression.
    std_err Vector of the standard error of the coefficients.
    z_stats Vector of the z-stats of the coefficients.
    p_values Vector of the p-values of the coefficients.
    +

    A summary table named <out_table>_summary is also created, which is the same as the summary table created by mlogregr_train function. Please refer to the documentation for multinomial logistic regression for details.

    +
    +
    dependent_varname
    +
    VARCHAR. The name of the column containing the dependent variable.
    +
    independent_varname
    +
    VARCHAR. Expression list to evaluate for the independent variables. An intercept variable is not assumed. It is common to provide an explicit intercept term by including a single constant 1 term in the independent variable list. The independent_varname can be the name of a column that contains an array of numeric values. It can also be a string with the format 'ARRAY[1, x1, x2, x3]', where x1, x2 and x3 are each column names.
    +
    ref_category (optional)
    +
    INTEGER, default: 0. The reference category.
    +
    grouping_cols (optional)
    +
    VARCHAR, default: NULL. Not currently implemented. Any non-NULL value is ignored. An expression list used to group the input dataset into discrete groups, running one regression per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single result model is generated.
    +
    optimizer_params (optional)
    +
    TEXT, default: NULL, which uses the default values of optimizer parameters: max_iter=20, optimizer='newton', tolerance=1e-4. It should be a string that contains pairs of 'key=value' separated by commas.
    +
    verbose_mode (optional)
    +
    BOOLEAN, default FALSE. Not currently implemented. TRUE if the regression fit should print warning messages.
    +
    +

    Robust Variance Function For Cox Proportional Hazards
    +

    The robust_variance_coxph() function has the following syntax: 

    +robust_variance_coxph(model_table, output_table)
+

    Arguments

    +
    model_table
    +
    TEXT. The name of the model table, which is exactaly the same as the 'output_table' parameter of coxph_train() function.
    +
    output_table
    +
    TEXT. The name of the table where the output is saved. It has the following columns: + + + + + + + + + + + + + + +
    coef FLOAT8[]. Vector of the coefficients.
    loglikelihood FLOAT8. Log-likelihood value of the MLE estimate.
    std_err FLOAT8[]. Vector of the standard error of the coefficients.
    robust_se FLOAT8[]. Vector of the robust standard errors of the coefficients.
    robust_z FLOAT8[]. Vector of the robust z-stats of the coefficients.
    robust_p FLOAT8[]. Vector of the robust p-values of the coefficients.
    hessian FLOAT8[]. The Hessian matrix.
    +
    +
    +

    Examples
    +

    Logistic Regression Example

      +
    1. View online help for the logistic regression training function. 
      +SELECT madlib.robust_variance_logregr();
+
      2. +
    2. Create the training data table. 
      +DROP TABLE IF EXISTS patients;
+CREATE TABLE patients (id INTEGER NOT NULL, second_attack INTEGER,
+    treatment INTEGER, trait_anxiety INTEGER);
+COPY patients FROM STDIN WITH DELIMITER '|';
+  1 |             1 |         1 |            70
+  3 |             1 |         1 |            50
+  5 |             1 |         0 |            40
+  7 |             1 |         0 |            75
+  9 |             1 |         0 |            70
+ 11 |             0 |         1 |            65
+ 13 |             0 |         1 |            45
+ 15 |             0 |         1 |            40
+ 17 |             0 |         0 |            55
+ 19 |             0 |         0 |            50
+  2 |             1 |         1 |            80
+  4 |             1 |         0 |            60
+  6 |             1 |         0 |            65
+  8 |             1 |         0 |            80
+ 10 |             1 |         0 |            60
+ 12 |             0 |         1 |            50
+ 14 |             0 |         1 |            35
+ 16 |             0 |         1 |            50
+ 18 |             0 |         0 |            45
+ 20 |             0 |         0 |            60
+\.
+
      3. +
    3. Run the logistic regression training function and compute the robust logistic variance of the regression: 
      +DROP TABLE IF EXISTS patients_logregr, patients_logregr_summary;
+SELECT madlib.robust_variance_logregr( 'patients',
+                                       'patients_logregr',
+                                       'second_attack',
+                                       'ARRAY[1, treatment, trait_anxiety]'
+                                     );
+
      4. +
    4. View the regression results. 
      +\x on
+SELECT * FROM patients_logregr;
+
      Result: 
      + -[ RECORD 1 ]-------------------------------------------------------
+ coef     | {-6.36346994178179,-1.02410605239327,0.119044916668605}
+ std_err  | {3.45872062333648,1.1716192578234,0.0534328864185018}
+ z_stats  | {-1.83983346294192,-0.874094587943036,2.22793348156809}
+ p_values | {0.0657926909738889,0.382066744585541,0.0258849510757339}
+
      Alternatively, unnest the arrays in the results for easier reading of output. 
      +\x off
+SELECT unnest(array['intercept', 'treatment', 'trait_anxiety' ]) as attribute,
+       unnest(coef) as coefficient,
+       unnest(std_err) as standard_error,
+       unnest(z_stats) as z_stat,
+       unnest(p_values) as pvalue
+FROM patients_logregr;
+
      5. +
    +

    Cox Proportional Hazards Example

      +
    1. View online help for the robust Cox Proportional hazards training method. 
      +SELECT madlib.robust_variance_coxph();
+
      2. +
    2. Create an input data set. 
      +DROP TABLE IF EXISTS sample_data;
+CREATE TABLE sample_data (
+    id INTEGER NOT NULL,
+    grp DOUBLE PRECISION,
+    wbc DOUBLE PRECISION,
+    timedeath INTEGER,
+    status BOOLEAN
+);
+COPY sample_data FROM STDIN DELIMITER '|';
+  0 |   0 | 1.45 |        35 | t
+  1 |   0 | 1.47 |        34 | t
+  3 |   0 |  2.2 |        32 | t
+  4 |   0 | 1.78 |        25 | t
+  5 |   0 | 2.57 |        23 | t
+  6 |   0 | 2.32 |        22 | t
+  7 |   0 | 2.01 |        20 | t
+  8 |   0 | 2.05 |        19 | t
+  9 |   0 | 2.16 |        17 | t
+ 10 |   0 |  3.6 |        16 | t
+ 11 |   1 |  2.3 |        15 | t
+ 12 |   0 | 2.88 |        13 | t
+ 13 |   1 |  1.5 |        12 | t
+ 14 |   0 |  2.6 |        11 | t
+ 15 |   0 |  2.7 |        10 | t
+ 16 |   0 |  2.8 |         9 | t
+ 17 |   1 | 2.32 |         8 | t
+ 18 |   0 | 4.43 |         7 | t
+ 19 |   0 | 2.31 |         6 | t
+ 20 |   1 | 3.49 |         5 | t
+ 21 |   1 | 2.42 |         4 | t
+ 22 |   1 | 4.01 |         3 | t
+ 23 |   1 | 4.91 |         2 | t
+ 24 |   1 |    5 |         1 | t
+\.
+
      3. +
    3. Run the Cox regression function. 
      +DROP TABLE IF EXISTS sample_cox, sample_cox_summary;
+SELECT madlib.coxph_train( 'sample_data',
+                           'sample_cox',
+                           'timedeath',
+                           'ARRAY[grp,wbc]',
+                           'status'
+                         );
+
      4. +
    4. Run the Robust Cox regression function. 
      +SELECT madlib.robust_variance_coxph( 'sample_cox',
+                           'sample_robust_cox'
+                         );
+
      5. +
    5. View the results of the robust Cox regression. 
      +\x on
+SELECT * FROM sample_robust_cox;
+
      Results: 
      +-[ RECORD 1 ]-+----------------------------------------------------------------------------
+coef          | {2.54407073265105,1.67172094780081}
+loglikelihood | -37.8532498733452
+std_err       | {0.677180599295459,0.387195514577754}
+robust_se     | {0.621095581073685,0.274773521439328}
+robust_z      | {4.09610180811965,6.08399579058399}
+robust_p      | {4.2016521208424e-05,1.17223683104729e-09}
+hessian       | {{2.78043065745405,-2.25848560642669},{-2.25848560642669,8.50472838284265}}
+
      6. +
    +

    Technical Background
    +

    When doing regression analysis, we are sometimes interested in the variance of the computed coefficients \( \boldsymbol c \). While the built-in regression functions provide variance estimates, we may prefer a robust variance estimate.

    +

    The robust variance calculation can be expressed in a sandwich formation, which is the form

    +\[ S( \boldsymbol c) = B( \boldsymbol c) M( \boldsymbol c) B( \boldsymbol c) \] +

    +

    where \( B( \boldsymbol c)\) and \( M( \boldsymbol c)\) are matrices. The \( B( \boldsymbol c) \) matrix, also known as the bread, is relatively straight forward, and can be computed as

    +\[ B( \boldsymbol c) = n\left(\sum_i^n -H(y_i, x_i, \boldsymbol c) \right)^{-1} \] +

    +

    where \( H \) is the hessian matrix.

    +

    The \( M( \boldsymbol c)\) matrix has several variations, each with different robustness properties. The form implemented here is the Huber-White sandwich operator, which takes the form

    +\[ M_{H} =\frac{1}{n} \sum_i^n \psi(y_i,x_i, \boldsymbol c)^T \psi(y_i,x_i, \boldsymbol c). \] +

    +

    The above method for calculating robust variance (Huber-White estimates) is implemented for linear regression, logistic regression, and multinomial logistic regression. It is useful in calculating variances in a dataset with potentially noisy outliers. The Huber-White implemented here is identical to the "HC0" sandwich operator in the R module "sandwich".

    +

    When multinomial logistic regression is computed before the multinomial robust regression, it uses a default reference category of zero and the regression coefficients are included in the output table. The regression coefficients in the output are in the same order as the multinomial logistic regression function, which is described below. For a problem with \( K \) dependent variables \( (1, ..., K) \) and \( J \) categories \( (0, ..., J-1) \), let \( {m_{k,j}} \) denote the coefficient for dependent variable \( k \) and category \( j \) . The output is \( {m_{k_1, j_0}, m_{k_1, j_1} \ldots m_{k_1, j_{J-1}}, m_{k_2, j_0}, m_{k_2, j_1} \ldots m_{k_K, j_{J-1}}} \). The order is NOT CONSISTENT with the multinomial regression marginal effect calculation with function marginal_mlogregr. This is deliberate because the interfaces of all multinomial regressions (robust, clustered, ...) will be moved to match that used in marginal.

    +

    The robust variance of Cox proportional hazards is more complex because coeeficients are trained by maximizing a partial log-likelihood. Therefore, one cannot directly use the formula for \( M( \boldsymbol c) \) as in Huber-White robust estimator. Extra terms are needed. See [4] for details.

    +

    Literature
    +

    [1] vce(cluster) function in STATA: http://www.stata.com/help.cgi?vce_option

    +

    [2] clustered estimators in R: http://people.su.se/~ma/clustering.pdf

    +

    [3] Achim Zeileis: Object-oriented Computation of Sandwich Estimators. Research Report Series / Department of Statistics and Mathematics, 37. Department of Statistics and Mathematics, WU Vienna University of Economics and Business, Vienna. http://cran.r-project.org/web/packages/sandwich/vignettes/sandwich-OOP.pdf

    +

    [4] D. Y. Lin and L . J. Wei, The Robust Inference for the Cox Proportional Hazards Model, Journal of the American Statistical Association, Vol. 84, No. 408, p.1074 (1989).

    +

    Related Topics
    File robust.sql_in documenting the SQL functions File robust_variance_coxph.sql_in documenting more the SQL functions
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__sample.html b/docs/docs/v2.1.0/group__grp__sample.html new file mode 100644 index 00000000..e647794f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sample.html @@ -0,0 +1,141 @@ + + + + + + + + +MADlib: Random Sampling + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Random Sampling
    Early Stage Development
    +
    +
    +
    Contents +
    Warning
    This MADlib method is still in early stage development. Interface and implementation are subject to change.
    +

    The random sampling module consists of useful utility functions for sampling operations. These functions can be used while implementing new algorithms.

    +

    Functions
    +

    Sample a single row according to weights. 

    +weighted_sample( value,
+                 weight
+               )
+

    Arguments

    +
    value
    +
    BIGINT or FLOAT8[]. Value of row. Uniqueness is not enforced. If a value occurs multiple times, the probability of sampling this value is proportional to the sum of its weights.
    +
    weight
    +
    FLOAT8. Weight for row. A negative value here is treated has zero weight.
    +
    +

    Refer to the file for documentation on each of the utility functions.

    +

    Related Topics
    +
    See also
    File sample.sql_in documenting the SQL functions.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__sampling.html b/docs/docs/v2.1.0/group__grp__sampling.html new file mode 100644 index 00000000..697e819a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sampling.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: Sampling + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Sampling
    +
    +
    +

    Detailed Description

    +

    A collection of methods for sampling from a population.

    + + + + + + + + +

    +Modules

     Balanced Sampling
     A method to independently sample classes to produce a balanced data set. This is commonly used when classes are imbalanced, to ensure that subclasses are adequately represented in the sample.
     
     Stratified Sampling
     A method for independently sampling subpopulations (strata).
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__sampling.js b/docs/docs/v2.1.0/group__grp__sampling.js new file mode 100644 index 00000000..719fc9d7 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sampling.js @@ -0,0 +1,5 @@ +var group__grp__sampling = +[ + [ "Balanced Sampling", "group__grp__balance__sampling.html", null ], + [ "Stratified Sampling", "group__grp__strs.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__sessionize.html b/docs/docs/v2.1.0/group__grp__sessionize.html new file mode 100644 index 00000000..2e58bc95 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sessionize.html @@ -0,0 +1,267 @@ + + + + + + + + +MADlib: Sessionize + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Sessionize
    Data Types and Transformations
    +
    +
    +
    Contents +

    The MADlib sessionize function performs time-oriented session reconstruction on a data set comprising a sequence of events. A defined period of inactivity indicates the end of one session and beginning of the next session. Sessions can be useful in many domains including web analytics [1], network security, manufacturing, finance, and operational analytics.

    +

    Function Syntax
    +sessionize(
+   source_table,
+   output_table,
+   partition_expr,
+   time_stamp,
+   max_time,
+   output_cols,
+   create_view
+)
+
    +

    Arguments

    +
    source_table
    +

    VARCHAR. Name of the source table that contains the data to be sessionized.

    +

    +
    +
    output_table
    +

    VARCHAR. Name of the output view or table. (The parameter create_view described below defines whether the output is actually a view or a table.) In addition to the columns in the source_table, the output also contains a new column called session_id:

      +
    • +session_id=1,2,...n where n is the number of the session in the partition.
      • +
    +

    +
    +
    partition_expr
    +

    VARCHAR. The 'partition_expr' is a single column or a list of comma-separated columns/expressions to divide all rows into groups, or partitions. Sessionization is applied across the rows that fall into the same partition. This parameter can be set to NULL or '' to indicate the sessionization operation is to be applied to the whole input table.

    +

    +
    +
    time_stamp
    +

    VARCHAR. The time stamp column name that is used for sessionization calculation. Note that the time_stamp column will be sorted in ascending order before the session reconstruction is done within a partition.

    +

    +
    +
    max_time
    +

    INTERVAL. Maximum delta time (i.e., time out) between subsequent events that define a session. If the elapsed time between subsequent events is longer than max_time, a new session is created.

    +

    Note
    Note that max_time is of time type INTERVAL which is a PostgreSQL way of describing elapsed time. For more information on INTERVAL please refer to reference [2].
    +
    +
    output_cols (optional)
    +

    VARCHAR. An optional comma separated list of columns to be written to the output_table. Must be a valid SELECT expression. This is set to '*' by default, which means all columns in the input table will be written to the output_table plus the session_id column. Note that this parameter could include a list containing the partition_expr or any other expressions of interest. E.g., '*, expr1, expr2, etc.' where this means output all columns from the input table plus the expressions listed plus the session_id column.

    +

    +
    +
    create_view (optional)
    +
    BOOLEAN default: TRUE. Determines whether to create a view or materialize the output as a table. If you only need session info once, creating a view could be significantly faster than materializing as a table. Please note that if you set create_view to NULL (allowed by PostgreSQL) it will get set to the default value of TRUE.
    +
    +

    Examples
    +

    The data set describes shopper behavior on a notional web site that sells beer and wine. A beacon fires an event to a log file when the shopper visits different pages on the site: landing page, beer selection page, wine selection page, and checkout. Each user is identified by a a user id, and every time a page is visited, the page and time stamp are logged.

    +

    Create the data table:

    +
    +DROP TABLE IF EXISTS eventlog CASCADE;  -- Using CASCADE in case you are running through this example more than once (views used below)
+CREATE TABLE eventlog (event_timestamp TIMESTAMP,
+            user_id INT,
+            page TEXT,
+            revenue FLOAT);
+INSERT INTO eventlog VALUES
+('04/15/2015 02:19:00', 101331, 'CHECKOUT', 16),
+('04/15/2015 02:17:00', 202201, 'WINE', 0),
+('04/15/2015 03:18:00', 202201, 'BEER', 0),
+('04/15/2015 01:03:00', 100821, 'LANDING', 0),
+('04/15/2015 01:04:00', 100821, 'WINE', 0),
+('04/15/2015 01:05:00', 100821, 'CHECKOUT', 39),
+('04/15/2015 02:06:00', 100821, 'WINE', 0),
+('04/15/2015 02:09:00', 100821, 'WINE', 0),
+('04/15/2015 02:15:00', 101331, 'LANDING', 0),
+('04/15/2015 02:16:00', 101331, 'WINE', 0),
+('04/15/2015 02:17:00', 101331, 'HELP', 0),
+('04/15/2015 02:18:00', 101331, 'WINE', 0),
+('04/15/2015 02:29:00', 201881, 'LANDING', 0),
+('04/15/2015 02:30:00', 201881, 'BEER', 0),
+('04/15/2015 01:05:00', 202201, 'LANDING', 0),
+('04/15/2015 01:06:00', 202201, 'HELP', 0),
+('04/15/2015 01:09:00', 202201, 'LANDING', 0),
+('04/15/2015 02:15:00', 202201, 'WINE', 0),
+('04/15/2015 02:16:00', 202201, 'BEER', 0),
+('04/15/2015 03:19:00', 202201, 'WINE', 0),
+('04/15/2015 03:22:00', 202201, 'CHECKOUT', 21);
+

    Sessionize the table by each user_id: 

    + DROP VIEW IF EXISTS sessionize_output_view;
+ SELECT madlib.sessionize(
+     'eventlog',             -- Name of input table
+     'sessionize_output_view',   -- View to store sessionize results
+     'user_id',             -- Partition input table by user id
+     'event_timestamp',      -- Time column used to compute sessions
+     '0:30:0'                -- Use 30 minute time out to define sessions
+    );
+SELECT * FROM sessionize_output_view ORDER BY user_id, event_timestamp;
+

    Result: 

    +   event_timestamp   | user_id |   page   | revenue | session_id
+---------------------+---------+----------+---------+------------
+ 2015-04-15 01:03:00 |  100821 | LANDING  |       0 |          1
+ 2015-04-15 01:04:00 |  100821 | WINE     |       0 |          1
+ 2015-04-15 01:05:00 |  100821 | CHECKOUT |      39 |          1
+ 2015-04-15 02:06:00 |  100821 | WINE     |       0 |          2
+ 2015-04-15 02:09:00 |  100821 | WINE     |       0 |          2
+ 2015-04-15 02:15:00 |  101331 | LANDING  |       0 |          1
+ 2015-04-15 02:16:00 |  101331 | WINE     |       0 |          1
+ 2015-04-15 02:17:00 |  101331 | HELP     |       0 |          1
+ 2015-04-15 02:18:00 |  101331 | WINE     |       0 |          1
+ 2015-04-15 02:19:00 |  101331 | CHECKOUT |      16 |          1
+ 2015-04-15 02:29:00 |  201881 | LANDING  |       0 |          1
+ 2015-04-15 02:30:00 |  201881 | BEER     |       0 |          1
+ 2015-04-15 01:05:00 |  202201 | LANDING  |       0 |          1
+ 2015-04-15 01:06:00 |  202201 | HELP     |       0 |          1
+ 2015-04-15 01:09:00 |  202201 | LANDING  |       0 |          1
+ 2015-04-15 02:15:00 |  202201 | WINE     |       0 |          2
+ 2015-04-15 02:16:00 |  202201 | BEER     |       0 |          2
+ 2015-04-15 02:17:00 |  202201 | WINE     |       0 |          2
+ 2015-04-15 03:18:00 |  202201 | BEER     |       0 |          3
+ 2015-04-15 03:19:00 |  202201 | WINE     |       0 |          3
+ 2015-04-15 03:22:00 |  202201 | CHECKOUT |      21 |          3
+(21 rows)
+

    Now let's say we want to see 3 minute sessions by a group of users with a certain range of user IDs. To do this, we need to sessionize the table based on a partition expression. Also, we want to persist a table output with a reduced set of columns in the table. 

    + DROP TABLE IF EXISTS sessionize_output_table;
+ SELECT madlib.sessionize(
+     'eventlog',                    -- Name of input table
+     'sessionize_output_table',     -- Table to store sessionize results
+     'user_id < 200000',            -- Partition input table by subset of users
+     'event_timestamp',             -- Order partitions in input table by time
+     '180',                         -- Use 180 second time out to define sessions (same as '0:03:0')
+     'event_timestamp, user_id, user_id < 200000 AS "Department-A1"',    -- Select only user_id and event_timestamp columns, along with the session id as output
+     'f'                            -- create a table
+     );
+ SELECT * FROM sessionize_output_table WHERE "Department-A1"='TRUE' ORDER BY event_timestamp;
+

    Result showing 2 users and 3 total sessions across the group: 

    +   event_timestamp   | user_id | Department-A1 | session_id
+---------------------+---------+---------------+------------
+ 2015-04-15 01:03:00 |  100821 | t             |          1
+ 2015-04-15 01:04:00 |  100821 | t             |          1
+ 2015-04-15 01:05:00 |  100821 | t             |          1
+ 2015-04-15 02:06:00 |  100821 | t             |          2
+ 2015-04-15 02:09:00 |  100821 | t             |          2
+ 2015-04-15 02:15:00 |  101331 | t             |          3
+ 2015-04-15 02:16:00 |  101331 | t             |          3
+ 2015-04-15 02:17:00 |  101331 | t             |          3
+ 2015-04-15 02:18:00 |  101331 | t             |          3
+ 2015-04-15 02:19:00 |  101331 | t             |          3
+(10 rows)
+

    Literature
    +

    NOTE: The following PostgreSQL link refers to documentation resources for the current PostgreSQL database version. Depending upon your database platform version, you may need to change "current" reference in the link to your database version.

    +

    If your database platform uses the Greenplum Database (or related variants), please check with the project community and/or your database vendor to identify the PostgreSQL version it is based on.

    +

    [1] Sesssions in web analytics https://en.wikipedia.org/wiki/Session_(web_analytics)

    +

    [2] PostgreSQL date/time types https://www.postgresql.org/docs/current/static/datatype-datetime.html

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__sketches.html b/docs/docs/v2.1.0/group__grp__sketches.html new file mode 100644 index 00000000..6b83e75a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sketches.html @@ -0,0 +1,151 @@ + + + + + + + + +MADlib: Cardinality Estimators + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Cardinality Estimators
    Statistics » Descriptive Statistics
    +
    +
    +

    Detailed Description

    +

    A collection of methods to estimate the number of unique values contained in the data.

    +

    Sketches (sometimes called "synopsis data structures") are small randomized in-memory data structures that capture statistical properties of a large set of values (e.g., a column of a table). Sketches can be formed in a single pass of the data, and used to approximate a variety of descriptive statistics.

    +

    We implement sketches as SQL User-Defined Aggregates (UDAs). Because they are single-pass, small-space and parallelized, a single query can use many sketches to gather summary statistics on many columns of a table efficiently.

    +

    This module currently implements user-defined aggregates based on three main sketch methods:

      +
    • Count-Min (CM) sketches, which can be used to approximate a number of descriptive statistics including
        +
      • COUNT of rows whose column value matches a given value in a set
        • +
      • COUNT of rows whose column value falls in a range (*)
        • +
      • order statistics including median and centiles (*)
        • +
      • histograms: both equi-width and equi-depth (*)
        • +
      +
      • +
    • Flajolet-Martin (FM) sketches for approximating COUNT(DISTINCT).
      • +
    • Most Frequent Value (MFV) sketches, which output the most frequently-occuring values in a column, along with their associated counts.
      • +
    +

    Note: Features marked with a star (*) only work for discrete types that can be cast to int8.

    +

    The sketch methods consist of a number of SQL UDAs (user-defined aggregates) and UDFs (user-defined functions), to be used directly in SQL queries.

    + + + + + + + + + + + +

    +Modules

     CountMin (Cormode-Muthukrishnan)
     Implements Cormode-Mathukrishnan CountMin sketches on integer values as a user-defined aggregate.
     
     FM (Flajolet-Martin)
     Implements Flajolet-Martin's distinct count estimation as a user-defined aggregate.
     
     MFV (Most Frequent Values)
     Implements the most frequent values variant of the CountMin sketch as a user-defined aggregate.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__sketches.js b/docs/docs/v2.1.0/group__grp__sketches.js new file mode 100644 index 00000000..1e443dd9 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sketches.js @@ -0,0 +1,6 @@ +var group__grp__sketches = +[ + [ "CountMin (Cormode-Muthukrishnan)", "group__grp__countmin.html", null ], + [ "FM (Flajolet-Martin)", "group__grp__fmsketch.html", null ], + [ "MFV (Most Frequent Values)", "group__grp__mfvsketch.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__sparse__linear__solver.html b/docs/docs/v2.1.0/group__grp__sparse__linear__solver.html new file mode 100644 index 00000000..0acdae91 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sparse__linear__solver.html @@ -0,0 +1,345 @@ + + + + + + + + +MADlib: Sparse Linear Systems + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Sparse Linear Systems
    Utilities » Linear Solvers
    +
    +
    +
    Contents +

    The sparse linear systems module implements solution methods for systems of consistent linear equations. Systems of linear equations take the form:

    +\[ Ax = b \] +

    +

    where \(x \in \mathbb{R}^{n}\), \(A \in \mathbb{R}^{m \times n} \) and \(b \in \mathbb{R}^{m}\). This module accepts sparse matrix input formats for \(A\) and \(b\). We assume that there are no rows of \(A\) where all elements are zero.

    +
    Note
    Algorithms with fail if there is an row of the input matrix containing all zeros.
    +

    The algorithms implemented in this module can handle large sparse square linear systems. Currently, the algorithms implemented in this module solve the linear system using direct or iterative methods.

    +

    Sparse Linear Systems Solution Function
    +
    +linear_solver_sparse( tbl_source_lhs,
+                      tbl_source_rhs,
+                      tbl_result,
+                      lhs_row_id,
+                      lhs_col_id,
+                      lhs_value,
+                      rhs_row_id,
+                      rhs_value,
+                      grouping_cols := NULL,
+                      optimizer := 'direct',
+                      optimizer_params :=
+                      'algorithm = llt'
+                    )
+

    Arguments

    +
    tbl_source_lhs
    +

    The name of the table containing the left hand side matrix. For the LHS matrix, the input data is expected to be of the following form: 

    +{TABLE|VIEW} sourceName (
+    ...
+    row_id FLOAT8,
+    col_id FLOAT8,
+    value FLOAT8,
+    ...
+)

    Each row represents a single equation. The rhs columns refer to the right hand side of the equations and the lhs columns refer to the multipliers on the variables on the left hand side of the same equations.

    +

    +
    +
    tbl_source_rhs
    +

    TEXT. The name of the table containing the right hand side vector. For the RHS matrix, the input data is expected to be of the following form: 

    {TABLE|VIEW} <em>sourceName</em> (
+    ...
+    <em>row_id</em> FLOAT8,
+    <em>value</em> FLOAT8
+    ...
+)

    Each row represents a single equation. The rhs columns refer to the right hand side of the equations while the lhs columns refers to the multipliers on the variables on the left hand side of the same equations.

    +

    +
    +
    tbl_result
    +

    TEXT. The name of the table where the output is saved. Output is stored in the tabled named by the tbl_result argument. The table contains the following columns. The output contains the following columns:

    + + + + + + +
    solution FLOAT8[]. The solution is an array with the variables in the same order as that provided as input in the 'left_hand_side' column name of the 'source_table'
    residual_norm FLOAT8. Scaled residual norm, defined as \( \frac{|Ax - b|}{|b|} \). This value is an indication of the accuracy of the solution.
    iters INTEGER. Number of iterations required by the algorithm (only applicable for iterative algorithms) . The output is NULL for 'direct' methods.
    +

    +
    +
    lhs_row_id
    +
    TEXT. The name of the column storing the 'row id' of the equations.
    Note
    For a system with N equations, the row_id's must be a continuous range of integers from \( 0 \ldots n-1 \).
    +
    +
    lhs_col_id
    +

    TEXT. The name of the column (in tbl_source_lhs) storing the 'col id' of the equations.

    +

    +
    +
    lhs_value
    +

    TEXT. The name of the column (in tbl_source_lhs) storing the 'value' of the equations.

    +

    +
    +
    rhs_row_id
    +

    TEXT. The name of the column (in tbl_source_rhs) storing the 'col id' of the equations.

    +

    +
    +
    rhs_value
    +

    TEXT. The name of the column (in tbl_source_rhs) storing the 'value' of the equations.

    +

    +
    +
    num_vars
    +

    INTEGER. The number of variables in the linear system equations.

    +

    +
    +
    grouping_col (optional)
    +
    TEXT, default: NULL. Group by column names.
    Note
    The grouping feature is currently not implemented and this parameter is only a placeholder.
    +
    +
    optimizer (optional)
    +

    TEXT, default: 'direct'. Type of optimizer.

    +

    +
    +
    optimizer_params (optional)
    +
    TEXT, default: NULL. Optimizer specific parameters.
    +
    +

    Optimizer Parameters
    +

    For each optimizer, there are specific parameters that can be tuned for better performance.

    +
    +
    algorithm (default: ldlt)
    +

    +

    There are several algorithms that can be classified as 'direct' methods of solving linear systems. Madlib functions provide various algorithmic options available for users.

    +

    The following table provides a guideline on the choice of algorithm based on conditions on the A matrix, speed of the algorithms and numerical stability.

    +
        Algorithm          | Conditions on A  | Speed | Memory
+    ----------------------------------------------------------
+    llt                | Sym. Pos Def     |  ++   |  ---
+    ldlt               | Sym. Pos Def     |  ++   |  ---
+
+    For speed '++' is faster than '+', which is faster than '-'.
+    For accuracy '+++' is better than '++'.
+    For memory, '-' uses less memory than '--'.
+
+    Note: ldlt is often preferred over llt
+

    There are several algorithms that can be classified as 'iterative' methods of solving linear systems. Madlib functions provide various algorithmic options available for users.

    +

    The following table provides a guideline on the choice of algorithm based on conditions on the A matrix, speed of the algorithms and numerical stability.

    +
        Algorithm            | Conditions on A  | Speed | Memory | Convergence
+    ----------------------------------------------------------------------
+    cg-mem               | Sym. Pos Def     |  +++  |   -    |    ++
+    bicgstab-mem         | Square           |  ++   |   -    |    +
+    precond-cg-mem       | Sym. Pos Def     |  ++   |   -    |    +++
+    precond-bicgstab-mem | Square           |  +    |   -    |    ++
+
+    For memory, '-' uses less memory than '--'.
+    For speed, '++' is faster than '+'.
+

    Algorithm Details:

    + + + + + + + + +
    cg-memIn memory conjugate gradient with diagonal preconditioners.
    bicgstab-memBi-conjugate gradient (equivalent to performing CG on the least squares formulation of Ax=b) with incomplete LU preconditioners.
    precond-cg-memIn memory conjugate gradient with diagonal preconditioners.
    bicgstab-memBi-conjugate gradient (equivalent to performing CG on the least squares formulation of Ax=b) with incomplete LU preconditioners.
    +

    +
    +
    toler (default: 1e-5)
    +

    Termination tolerance (applicable only for iterative methods) which determines the stopping criterion (with respect to residual norm) for iterative methods.

    +

    +
    +
    +

    Examples
    +
      +
    1. View online help for the sparse linear systems solver function. 
      +SELECT madlib.linear_solver_sparse();
+
      2. +
    2. Create the sample data set. 
      +DROP TABLE IF EXISTS sparse_linear_systems_lhs;
+CREATE TABLE sparse_linear_systems_lhs (
+    rid INTEGER NOT NULL,
+    cid  INTEGER,
+    val DOUBLE PRECISION
+);
+DROP TABLE IF EXISTS sparse_linear_systems_rhs;
+CREATE TABLE sparse_linear_systems_rhs (
+    rid INTEGER NOT NULL,
+    val DOUBLE PRECISION
+);
+INSERT INTO sparse_linear_systems_lhs(rid, cid, val) VALUES
+(0, 0, 1),
+(1, 1, 1),
+(2, 2, 1),
+(3, 3, 1);
+INSERT INTO sparse_linear_systems_rhs(rid, val) VALUES
+(0, 10),
+(1, 20),
+(2, 30);
+
      3. +
    3. Solve the linear systems with default parameters. 
      +SELECT madlib.linear_solver_sparse( 'sparse_linear_systems_lhs',
+                                    'sparse_linear_systems_rhs',
+                                    'output_table',
+                                    'rid',
+                                    'cid',
+                                    'val',
+                                    'rid',
+                                    'val',
+                                    4
+                                  );
+
      4. +
    4. View the contents of the output table. 
      +\x on
+SELECT * FROM output_table;
+
      Result: 
      +--------------------+-------------------------------------
+solution            | {10,20,30,0}
+residual_norm       | 0
+iters               | NULL
+
      5. +
    5. Choose a different algorithm than the default algorithm. 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.linear_solver_sparse( 'sparse_linear_systems_lhs',
+                                    'sparse_linear_systems_rhs',
+                                    'output_table',
+                                    'rid',
+                                    'cid',
+                                    'val',
+                                    'rid',
+                                    'val',
+                                    4,
+                                    NULL,
+                                    'direct',
+                                    'algorithm=llt'
+                                  );
+
      6. +
    6. Choose a different algorithm than the default algorithm. 
      +DROP TABLE IF EXISTS output_table;
+SELECT madlib.linear_solver_sparse(
+                                    'sparse_linear_systems_lhs',
+                                    'sparse_linear_systems_rhs',
+                                    'output_table',
+                                    'rid',
+                                    'cid',
+                                    'val',
+                                    'rid',
+                                    'val',
+                                    4,
+                                    NULL,
+                                    'iterative',
+                                    'algorithm=cg-mem, toler=1e-5'
+                                  );
+
      7. +
    +

    Related Topics
    File sparse_linear_sytems.sql_in documenting the SQL functions.
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__sssp.html b/docs/docs/v2.1.0/group__grp__sssp.html new file mode 100644 index 00000000..2bf0d072 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__sssp.html @@ -0,0 +1,357 @@ + + + + + + + + +MADlib: Single Source Shortest Path + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Single Source Shortest Path
    Graph
    +
    +
    +
    Contents +

    Given a graph and a source vertex, the single source shortest path (SSSP) algorithm finds a path from the source vertex to every other vertex in the graph, such that the sum of the weights of the path edges is minimized.

    +

    SSSP
    +graph_sssp( vertex_table,
+            vertex_id,
+            edge_table,
+            edge_args,
+            source_vertex,
+            out_table,
+            grouping_cols
+          )
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    +
    +
    vertex_id
    +

    TEXT, default = 'id'. Name of the column in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous.

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex, destination vertex and edge weight. Column naming convention is described below in the 'edge_args' parameter.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column containing the source vertex ids in the edge table. Default column name is 'src'.
      • +
    • dest (INTEGER or BIGINT): Name of the column containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    • weight (FLOAT8): Name of the column containing the edge weights in the edge table. Default column name is 'weight'.
      • +
    +

    +
    +
    source_vertex
    +

    INTEGER or BIGINT. The source vertex id for the algorithm to start. This vertex id must exist in the 'vertex_id' column of 'vertex_table'.

    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the result of SSSP. It contains a row for every vertex of every group and have the following columns (in addition to the grouping columns):

      +
    • vertex_id : The id for the destination. Will use the input parameter 'vertex_id' for column naming.
      • +
    • weight : The total weight of the shortest path from the source vertex to this particular vertex. Will use the input parameter 'weight' for column naming.
      • +
    • parent : The parent of this vertex in the shortest path from source. Will use 'parent' for column naming.
      • +
    +

    A summary table named <out_table>_summary is also created. This is an internal table that keeps a record of the input parameters and is used by the path function described below.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default = NULL. List of columns used to group the input into discrete subgraphs. These columns must exist in the edge table. When this value is null, no grouping is used and a single SSSP result is generated.
    +
    +
    Path Retrieval
    +

    The path retrieval function returns the shortest path from the source vertex to a specified desination vertex.

    +
    +graph_sssp_get_path( sssp_table,
+                     dest_vertex,
+                     path_table
+                    )
+

    Arguments

    +
    sssp_table
    +

    TEXT. Name of the table that contains the SSSP output.

    +

    +
    +
    dest_vertex
    +

    INTEGER or BIGINT. The vertex that will be the destination of the desired path.

    +

    +
    +
    path_table
    +

    TEXT. Name of the output table that contains the path. It contains a row for every group and has the following columns:

      +
    • grouping_cols : The grouping columns given in the creation of the SSSP table. If there are no grouping columns, these columns will not exist and the table will have a single row.
      • +
    • path (ARRAY) : The shortest path from the source vertex (as specified in the SSSP execution) to the destination vertex.
      • +
    +

    +
    +
    +

    Examples
    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+        id INTEGER
+        );
+CREATE TABLE edge(
+        src INTEGER,
+        dest INTEGER,
+        weight FLOAT8
+        );
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6),
+(7);
+INSERT INTO edge VALUES
+(0, 1, 1.0),
+(0, 2, 1.0),
+(0, 4, 10.0),
+(1, 2, 2.0),
+(1, 3, 10.0),
+(2, 3, 1.0),
+(2, 5, 1.0),
+(2, 6, 3.0),
+(3, 0, 1.0),
+(4, 0, -2.0),
+(5, 6, 1.0),
+(6, 7, 1.0);
+
      2. +
    2. Calculate the shortest paths from vertex 0: 
      +DROP TABLE IF EXISTS out, out_summary;
+SELECT madlib.graph_sssp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertix id column (NULL means use default naming)
+                         'edge',        -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         0,             -- Source vertex for path calculation
+                         'out');        -- Output table of shortest paths
+SELECT * FROM out ORDER BY id;
+
      + id | weight | parent
+----+--------+--------
+  0 |      0 |      0
+  1 |      1 |      0
+  2 |      1 |      0
+  3 |      2 |      2
+  4 |     10 |      0
+  5 |      2 |      2
+  6 |      3 |      5
+  7 |      4 |      6
+(8 rows)
+
      3. +
    3. Get the shortest path to vertex 5: 
      +DROP TABLE IF EXISTS out_path;
+SELECT madlib.graph_sssp_get_path('out',5,'out_path');
+SELECT * FROM out_path;
+
      +  path
+---------
+ {0,2,5}
+
      4. +
    4. Now let's do a similar example except using different column names in the tables (i.e., not the defaults). Create the vertex and edge tables: 
      +DROP TABLE IF EXISTS vertex_alt, edge_alt;
+CREATE TABLE vertex_alt AS SELECT id AS v_id FROM vertex;
+CREATE TABLE edge_alt AS SELECT src AS e_src, dest, weight AS e_weight FROM edge;
+
      5. +
    5. Get the shortest path from vertex 1: 
      +DROP TABLE IF EXISTS out_alt, out_alt_summary;
+SELECT madlib.graph_sssp(
+                         'vertex_alt',                  -- Vertex table
+                         'v_id',                        -- Vertex id column (NULL means use default naming)
+                         'edge_alt',                    -- Edge table
+                         'src=e_src, weight=e_weight',  -- Edge arguments (NULL means use default naming)
+                         1,                             -- Source vertex for path calculation
+                         'out_alt');                    -- Output table of shortest paths
+SELECT * FROM out_alt ORDER BY v_id;
+
      + v_id | e_weight | parent
+------+----------+--------
+    0 |        4 |      3
+    1 |        0 |      1
+    2 |        2 |      1
+    3 |        3 |      2
+    4 |       14 |      0
+    5 |        3 |      2
+    6 |        4 |      5
+    7 |        5 |      6
+(8 rows)
+
      6. +
    6. Create a graph with 2 groups: 
      +DROP TABLE IF EXISTS edge_gr;
+CREATE TABLE edge_gr AS
+(
+  SELECT *, 0 AS grp FROM edge
+  UNION
+  SELECT *, 1 AS grp FROM edge WHERE src < 6 AND dest < 6
+);
+INSERT INTO edge_gr VALUES
+(4,5,-20,1);
+
      7. +
    7. Find SSSP for all groups 
      +DROP TABLE IF EXISTS out_gr, out_gr_summary;
+SELECT madlib.graph_sssp(
+                         'vertex',      -- Vertex table
+                         NULL,          -- Vertex id column (NULL means use default naming)
+                         'edge_gr',     -- Edge table
+                         NULL,          -- Edge arguments (NULL means use default naming)
+                         0,             -- Source vertex for path calculation
+                         'out_gr',      -- Output table of shortest paths
+                         'grp'          -- Grouping columns
+);
+SELECT * FROM out_gr ORDER BY grp,id;
+
      + grp | id | weight | parent
+-----+----+--------+--------
+   0 |  0 |      0 |      0
+   0 |  1 |      1 |      0
+   0 |  2 |      1 |      0
+   0 |  3 |      2 |      2
+   0 |  4 |     10 |      0
+   0 |  5 |      2 |      2
+   0 |  6 |      3 |      5
+   0 |  7 |      4 |      6
+   1 |  0 |      0 |      0
+   1 |  1 |      1 |      0
+   1 |  2 |      1 |      0
+   1 |  3 |      2 |      2
+   1 |  4 |     10 |      0
+   1 |  5 |    -10 |      4
+
      8. +
    8. Find the path to vertex 5 in every group 
      +DROP TABLE IF EXISTS out_gr_path;
+SELECT madlib.graph_sssp_get_path('out_gr',5,'out_gr_path');
+SELECT * FROM out_gr_path ORDER BY grp;
+
      + grp |  path
+-----+---------
+   0 | {0,2,5}
+   1 | {0,4,5}
+
      9. +
    +

    Notes
    +
      +
    1. On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance.
      2. +
    2. The Bellman-Ford algorithm [1] is used to implement SSSP. This algorithm allows negative edges but not negative cycles. In the case of graphs with negative cycles, an error will be given and no output table will be generated.
      3. +
    3. Also see the Grail project [2] for more background on graph analytics processing in relational databases.
      4. +
    +

    Literature
    +

    [1] Bellman–Ford algorithm. https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm

    +

    [2] The case against specialized graph analytics engines, J. Fan, G. Soosai Raj, and J. M. Patel. CIDR 2015. http://cidrdb.org/cidr2015/Papers/CIDR15_Paper20.pdf

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__stats.html b/docs/docs/v2.1.0/group__grp__stats.html new file mode 100644 index 00000000..cfb45d5a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__stats.html @@ -0,0 +1,136 @@ + + + + + + + + +MADlib: Statistics + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Statistics
    +
    +
    +

    Detailed Description

    +

    A collection of probability and statistics modules.

    + + + + + + + + + + + +

    +Modules

     Descriptive Statistics
     Methods to compute descriptive statistics of a dataset.
     
     Inferential Statistics
     Methods to compute inferential statistics of a dataset.
     
     Probability Functions
     Provides cumulative distribution, density/mass, and quantile functions for a wide range of probability distributions.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__stats.js b/docs/docs/v2.1.0/group__grp__stats.js new file mode 100644 index 00000000..0828141e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__stats.js @@ -0,0 +1,6 @@ +var group__grp__stats = +[ + [ "Descriptive Statistics", "group__grp__desc__stats.html", "group__grp__desc__stats" ], + [ "Inferential Statistics", "group__grp__inf__stats.html", "group__grp__inf__stats" ], + [ "Probability Functions", "group__grp__prob.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__stats__tests.html b/docs/docs/v2.1.0/group__grp__stats__tests.html new file mode 100644 index 00000000..46b3f38b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__stats__tests.html @@ -0,0 +1,532 @@ + + + + + + + + +MADlib: Hypothesis Tests + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Hypothesis Tests
    Statistics » Inferential Statistics
    +
    +
    +
    Contents +

    Hypothesis tests are used to confirm or reject a null hypothesis \( H_0 \) about the distribution of random variables, given realizations of these random variables. Since in general it is not possible to make statements with certainty, one is interested in the probability \( p \) of seeing random variates at least as extreme as the ones observed, assuming that \( H_0 \) is true. If this probability \( p \) is small, \( H_0 \) will be rejected by the test with significance level \( p \). Falsifying \( H_0 \) is the canonic goal when employing a hypothesis test. That is, hypothesis tests are typically used in order to substantiate that instead the alternative hypothesis \( H_1 \) is true.

    +

    Hypothesis tests may be divided into parametric and non-parametric tests. A parametric test assumes certain distributions and makes inferences about parameters of the distributions (e.g., the mean of a normal distribution). Formally, there is a given domain of possible parameters \( \Gamma \) and the null hypothesis \( H_0 \) is the event that the true parameter \( \gamma_0 \in \Gamma_0 \), where \( \Gamma_0 \subsetneq \Gamma \). Non-parametric tests, on the other hand, do not assume any particular distribution of the sample (e.g., a non-parametric test may simply test if two distributions are similar).

    +

    The first step of a hypothesis test is to compute a test statistic, which is a function of the random variates, i.e., a random variate itself. A hypothesis test relies on the distribution of the test statistic being (approximately) known. Now, the \( p \)-value is the probability of seeing a test statistic at least as extreme as the one observed, assuming that \( H_0 \) is true. In a case where the null hypothesis corresponds to a family of distributions (e.g., in a parametric test where \( \Gamma_0 \) is not a singleton set), the \( p \)-value is the supremum, over all possible distributions according to the null hypothesis, of these probabilities.

    +
    Note
    Please refer to hypothesis_tests.sql_in for additional technical information on the MADlib implementation of hypothesis tests, and for detailed function signatures for all tests.
    +

    Input
    +

    Input data is assumed to be normalized with all values stored row-wise. In general, the following inputs are expected.

    +

    One-sample tests expect the following form: 

    {TABLE|VIEW} source (
+    ...
+    value DOUBLE PRECISION
+    ...
+)

    Two-sample tests expect the following form: 

    {TABLE|VIEW} source (
+    ...
+    first BOOLEAN,
+    value DOUBLE PRECISION
+    ...
+)

    The first column indicates whether a value is from the first sample (if TRUE) or the second sample (if FALSE).

    +

    Many-sample tests expect the following form: 

    {TABLE|VIEW} source (
+    ...
+    group INTEGER,
+    value DOUBLE PRECISION
+    ...
+)

    Usage
    +

    All tests are implemented as aggregate functions. The non-parametric (rank-based) tests are implemented as ordered aggregate functions and thus necessitate an ORDER BY clause. In the following, the most simple forms of usage are given. Specific function signatures, as described in hypothesis_tests.sql_in, may require more arguments or a different ORDER BY clause.

    +
      +
    • Run a parametric one-sample test: 
      SELECT test(value) FROM source
      where 'test' can be one of
        +
      • t_test_one (one-sample or dependent paired Student's t-test)
        • +
      • chi2_gof_test (Pearson's chi-squared goodness of fit test, also used for chi-squared independence test as shown in example section below)
        • +
      +
      • +
    • Run a parametric two-sample/multi-sample test: 
      SELECT test(first/group, value) FROM source
      where 'test' can be one of
        +
      • f_test (Fisher F-test)
        • +
      • t_test_two_pooled (two-sample pooled Student’s t-test, i.e. equal variances)
        • +
      • t_test_two_unpooled (two-sample unpooled t-test, i.e., unequal variances, also known as Welch's t-test)
        • +
      • one_way_anova (one-way analysis of variance, multi-sample)
        • +
      +
      • +

    • Run a non-parametric two-sample/multi-sample test: 

      SELECT test(first/group, value ORDER BY value) FROM source

      where 'test' can be one of

        +
      • ks_test (Kolmogorov-Smirnov test)
        • +
      • mw_test (Mann-Whitney test)
        • +
      • wsr_test (Wilcoxon signed-rank test, multi-sample)
        • +
      +

      Note on non-parametric tests: Kolomogov-Smirnov two-sample test is based on the asymptotic theory. The p-value is given by comparing the test statistics with the Kolomogov distribution. The p-value is also adjusted for data with heavy tail distribution, which may give different results than those given by R function's ks.test. See [3] for a detailed explanation. The literature is not unanimous about the definitions of the Wilcoxon rank sum and Mann-Whitney tests. There are two possible definitions for the statistic; MADlib outputs the minimum of the two and uses it for significance testing. This might give different results for both mw_test and wsr_test compared to statistical functions in other popular packages (like R's wilcox.test function). See [4] for a detailed explanation.

      +
      • +
    +

    Examples
    +
      +
    • One-sample and two-sample t-test (data is subset of mpg data from NIST/SEMATECH)
      • +
    +
    +-- Load data
+DROP TABLE IF EXISTS auto83b;
+CREATE TABLE auto83b (
+    id SERIAL,
+    mpg_us DOUBLE PRECISION,
+    mpg_j DOUBLE PRECISION
+);
+COPY auto83b (mpg_us, mpg_j) FROM stdin DELIMITER '|';
+18|24
+15|27
+18|27
+16|25
+17|31
+15|35
+14|24
+14|19
+21|31
+10|32
+10|24
+11|26
+9| 9
+\N|32
+\N|37
+\N|38
+\N|34
+\N|34
+\N|32
+\N|33
+\N|32
+\N|25
+\N|24
+\N|37
+13|\N
+12|\N
+18|\N
+21|\N
+19|\N
+21|\N
+15|\N
+16|\N
+15|\N
+11|\N
+20|\N
+21|\N
+19|\N
+15|\N
+\.
+
    +-- Create table for one sample tests
+DROP TABLE IF EXISTS auto83b_one_sample;
+CREATE TABLE auto83b_one_sample AS
+    SELECT mpg_us AS mpg
+    FROM auto83b
+    WHERE mpg_us is not NULL;
+-- Print table
+SELECT * FROM auto83b_one_sample;
+
    +mpg
+  18
+  15
+  18
+  16
+  17
+  15
+  14
+  14
+  21
+  10
+  10
+  11
+   9
+  13
+  12
+  18
+  21
+  19
+  21
+  15
+  16
+  15
+  11
+  20
+  21
+  19
+  15
+(27 rows)
+
    +-- Create table for two sample tests
+DROP TABLE IF EXISTS auto83b_two_sample;
+CREATE TABLE auto83b_two_sample AS
+SELECT TRUE AS is_us, mpg_us AS mpg
+    FROM auto83b
+    WHERE mpg_us is not NULL
+    UNION ALL
+    SELECT FALSE, mpg_j
+    FROM auto83b
+    WHERE mpg_j is not NULL;
+-- Print table
+SELECT * FROM auto83b_two_sample;
+
    + is_us | mpg
+-------+-----
+ t     |  18
+ t     |  15
+ t     |  18
+ t     |  16
+ t     |  17
+ t     |  15
+ t     |  14
+ t     |  14
+ t     |  21
+ t     |  10
+ t     |  10
+ t     |  11
+ t     |   9
+ t     |  13
+ t     |  12
+ t     |  18
+ t     |  21
+ t     |  19
+ t     |  21
+ t     |  15
+ t     |  16
+ t     |  15
+ t     |  11
+ t     |  20
+ t     |  21
+ t     |  19
+ t     |  15
+ f     |  24
+ f     |  27
+ f     |  27
+ f     |  25
+ f     |  31
+ f     |  35
+ f     |  24
+ f     |  19
+ f     |  31
+ f     |  32
+ f     |  24
+ f     |  26
+ f     |   9
+ f     |  32
+ f     |  37
+ f     |  38
+ f     |  34
+ f     |  34
+ f     |  32
+ f     |  33
+ f     |  32
+ f     |  25
+ f     |  24
+ f     |  37
+(51 rows)
+
    +-- One sample tests
+SELECT (madlib.t_test_one(mpg - 20)).* FROM auto83b_one_sample;  -- test rejected for mean = 20
+
    +     statistic     | df | p_value_one_sided |  p_value_two_sided
+ ------------------+----+-------------------+----------------------
+  -6.0532478722666 | 26 | 0.999998926789141 | 2.14642171769697e-06
+ 
    +SELECT (madlib.t_test_one(mpg - 15.7)).* FROM auto83b_one_sample;  -- test not rejected
+
    +       statistic      | df | p_value_one_sided | p_value_two_sided
+ ---------------------+----+-------------------+-------------------
+  0.00521831713126531 | 26 | 0.497938118950661 | 0.995876237901321
+
    +-- Two sample tests
+SELECT (madlib.t_test_two_pooled(is_us, mpg)).* FROM auto83b_two_sample;
+
    +     statistic     | df | p_value_one_sided |  p_value_two_sided
+ -------------------+----+-------------------+----------------------
+  -8.89342267075968 | 49 | 0.999999999995748 | 8.50408632402377e-12
+ 
    +SELECT (madlib.t_test_two_unpooled(is_us, mpg)).* FROM auto83b_two_sample;
+
    +      statistic     |        df        | p_value_one_sided |  p_value_two_sided
+ -------------------+------------------+-------------------+----------------------
+  -8.61746388524314 | 35.1283818346179 | 0.999999999821218 | 3.57563867403599e-10
+
      +
    • F-Test (Uses same data as above t-test)
      • +
    +
    +SELECT (madlib.f_test(is_us, mpg)).* FROM auto83b_two_sample;
+-- Test result indicates that the two distributions have different variances
+
    +      statistic     | df1 | df2 | p_value_one_sided |  p_value_two_sided
+ -------------------+-----+-----+-------------------+---------------------
+  0.311786921089247 |  26 |  23 | 0.997559863672441 | 0.00488027265511803
+
    +
    +CREATE TABLE chi2_test_blood_group (
+    id SERIAL,
+    blood_group VARCHAR,
+    observed BIGINT,
+    expected DOUBLE PRECISION
+);
+INSERT INTO chi2_test_blood_group(blood_group, observed, expected) VALUES
+    ('O', 67, 82.28),
+    ('A', 83, 84.15),
+    ('B', 29, 14.96),
+    ('AB', 8, 5.61);
+SELECT (madlib.chi2_gof_test(observed, expected)).* FROM chi2_test_blood_group;
+
    +     statistic     |       p_value        | df |       phi        | contingency_coef
+ ------------------+----------------------+----+------------------+-------------------
+  17.0481013341976 | 0.000690824622923826 |  3 | 2.06446732440826 | 0.899977280680593
+
    +

    The Chi-squared independence test uses the Chi-squared goodness-of-fit function, as shown in the example below. The expected value needs to be computed and passed to the goodness-of-fit function. The expected value for MADlib is computed as sum of rows * sum of columns, for each element of the input matrix. For e.g., expected value for element (2,1) would be sum of row 2 * sum of column 1.

    +
    +CREATE TABLE chi2_test_friendly (
+    id_x SERIAL,
+    values INTEGER[]
+);
+INSERT INTO chi2_test_friendly(values) VALUES
+    (array[5, 29, 14, 16]),
+    (array[15, 54, 14, 10]),
+    (array[20, 84, 17, 94]),
+    (array[68, 119, 26, 7]);
    -- Input table is expected to be unpivoted, so need to pivot it
+CREATE TABLE chi2_test_friendly_unpivoted AS
+SELECT id_x, id_y, values[id_y] AS observed
+FROM
+    chi2_test_friendly,
+    generate_series(1,4) AS id_y;
    -- Compute Chi-squared independence statistic, by calculating expected value in the SQL and calling the goodness-of-fit function
+SELECT (madlib.chi2_gof_test(observed, expected, deg_freedom)).*
+FROM (
+    -- Compute expected values and degrees of freedom
+    SELECT
+        observed,
+        sum(observed) OVER (PARTITION BY id_x)::DOUBLE PRECISION *
+        sum(observed) OVER (PARTITION BY id_y) AS expected
+    FROM chi2_test_friendly_unpivoted
+) p, (
+    SELECT
+        (count(DISTINCT id_x) - 1) * (count(DISTINCT id_y) - 1) AS deg_freedom
+    FROM chi2_test_friendly_unpivoted
+) q;
+
    +     statistic     |       p_value        | df |       phi        | contingency_coef
+ ------------------+----------------------+----+------------------+-------------------
+  138.289841626008 | 2.32528678709871e-25 |  9 | 2.93991753313346 | 0.946730727519112
+
    +
    +CREATE TABLE nist_anova_test (
+    id SERIAL,
+    resistance FLOAT8[]
+);
+INSERT INTO nist_anova_test(resistance) VALUES
+    (array[6.9,8.3,8.0]),
+    (array[5.4,6.8,10.5]),
+    (array[5.8,7.8,8.1]),
+    (array[4.6,9.2,6.9]),
+    (array[4.0,6.5,9.3]);
    SELECT (madlib.one_way_anova(level, value)).* FROM (
+    SELECT level, resistance[level] AS value
+    FROM
+        nist_anova_test, (SELECT * FROM generate_series(1,3) level) q1
+) q2;
+
    +  sum_squares_between | sum_squares_within | df_between | df_within | mean_squares_between | mean_squares_within |    statistic     |      p_value
+ ---------------------+--------------------+------------+-----------+----------------------+---------------------+------------------+--------------------
+     27.8973333333333 |             17.452 |          2 |        12 |     13.9486666666667 |    1.45433333333333 | 9.59110703644281 | 0.0032482226008593
+
    +
    +CREATE TABLE ks_sample_1 AS
+SELECT
+    TRUE AS first,
+    unnest(ARRAY[0.22, -0.87, -2.39, -1.79, 0.37, -1.54, 1.28, -0.31, -0.74, 1.72, 0.38, -0.17, -0.62, -1.10, 0.30, 0.15, 2.30, 0.19, -0.50, -0.09]) AS value
+UNION ALL
+SELECT
+    FALSE,
+    unnest(ARRAY[-5.13, -2.19, -2.43, -3.83, 0.50, -3.25, 4.32, 1.63, 5.18, -0.43, 7.11, 4.87, -3.10, -5.81, 3.76, 6.31, 2.58, 0.07, 5.76, 3.50]);
    SELECT (madlib.ks_test(first, value,
+    (SELECT count(value) FROM ks_sample_1 WHERE first),
+    (SELECT count(value) FROM ks_sample_1 WHERE NOT first)
+    ORDER BY value)).*
+FROM ks_sample_1;
+
    +  statistic |   k_statistic   |      p_value
+ -----------+-----------------+--------------------
+       0.45 | 1.4926782214936 | 0.0232132758544496
+
      +
    • Mann-Whitney test (use same data as t-test)
      • +
    +
    +SELECT (madlib.mw_test(is_us, mpg ORDER BY mpg)).* from auto83b_two_sample;
+-- Note first parameter above is BOOLEAN
+
    +      statistic     | u_statistic | p_value_one_sided |  p_value_two_sided
+ -------------------+-------------+-------------------+----------------------
+  -5.50097925755249 |        32.5 | 0.999999981115618 | 3.77687645883758e-08
+
      +
    • Wilcoxon signed-rank test
      • +
    +
    +DROP TABLE IF EXISTS test_wsr;
+CREATE TABLE test_wsr (
+    x DOUBLE PRECISION,
+    y DOUBLE PRECISION
+);
+COPY test_wsr (x, y) FROM stdin DELIMITER '|';
+0.32|0.39
+0.4|0.47
+0.11|0.11
+0.47|0.43
+0.32|0.42
+0.35|0.3
+0.32|0.43
+0.63|0.98
+0.5|0.86
+0.6|0.79
+0.38|0.33
+0.46|0.45
+0.2|0.22
+0.31|0.3
+0.62|0.6
+0.52|0.53
+0.77|0.85
+0.23|0.21
+0.3|0.33
+0.7|0.57
+0.41|0.43
+0.53|0.49
+0.19|0.2
+0.31|0.35
+0.48|0.4
+\.
+
+SELECT (madlib.wsr_test(
+    x - y,
+    2 * 2^(-52) * greatest(x,y)
+    ORDER BY abs(x - y)
+)).*
+FROM test_wsr;
+
    +  statistic | rank_sum_pos | rank_sum_neg | num |    z_statistic    | p_value_one_sided | p_value_two_sided
+ -----------+--------------+--------------+-----+-------------------+-------------------+-------------------
+      105.5 |        105.5 |        194.5 |  24 | -1.27318365656729 | 0.898523560667509 | 0.202952878664983
+

    Literature
    +

    [1] M. Hollander, D. Wolfe: Nonparametric Statistical Methods, 2nd edition, Wiley, 1999

    +

    [2] E. Lehmann, J. Romano: Testing Statistical Hypotheses, 3rd edition, Springer, 2005

    +

    [3] M. Stephens: Use of the Kolmogorov-Smirnov, Cramer-Von Mises and related statistics without extensive tables, Journal of the Royal Statistical Society. Series B (Methodological) (1970): 115-122.

    +

    [4] Wikipedia: Mann–Whitney U test calculation, http://en.wikipedia.org/wiki/Mann-Whitney_test#Calculations

    +

    Related Topics
    +

    File hypothesis_tests.sql_in documenting the SQL functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__stemmer.html b/docs/docs/v2.1.0/group__grp__stemmer.html new file mode 100644 index 00000000..e137451d --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__stemmer.html @@ -0,0 +1,231 @@ + + + + + + + + +MADlib: Stemming + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Stemming
    Data Types and Transformations
    +
    +
    +
    Contents +

    This module provides a basic stemming operation for text input. It is a support module for several machine learning algorithms that require a stemmer. Currently, it only supports English words.

    +

    This function is a SQL interface to the implementation of the Porter Stemming Algorithm. The original stemming algorithm is written and maintained by Martin Porter

    +

    Implementation Notes
    +

    All functions described in this module work with text OR text array.

    +

    Several of the function require TEXT VALUES, and returns NULL for a NULL input. See details in description of individual functions.

    +

    Stemmer Operations
    + + + + +
    stem_token()

    Returns the stem of the token. Returns NULL if input is NULL.

    +

    +
    stem_token_arr()

    Returns the stems in an array of input token array. The stem would be NULL for corresponding NULL token.

    +

    +
    +
    +
    Examples
    +
      +
    1. Create a table with some words to be stemmed. 
      +CREATE TABLE token_tbl ( id integer,
+                         word text
+                       );
+INSERT INTO token_tbl VALUES
+ (1, 'kneel'),
+ (2, 'kneeled'),
+ (3, 'kneeling'),
+ (4, 'kneels'),
+ (5, 'knees'),
+ (6, 'knell'),
+ (7, 'knelt'),
+ (8, 'knew'),
+ (9, 'knick'),
+ (10, 'knif'),
+ (11, 'knife'),
+ (12, 'knight'),
+ (13, 'knightly'),
+ (14, 'knights'),
+ (15, 'knit'),
+ (16, 'knits'),
+ (17, 'knitted'),
+ (18, 'knitting'),
+ (19, 'knives'),
+ (20, 'knob'),
+ (21, 'knobs'),
+ (22, 'knock'),
+ (23, 'knocked'),
+ (24, 'knocker'),
+ (25, 'knockers'),
+ (26, 'knocking'),
+ (27, 'knocks'),
+ (28, 'knopp'),
+ (29, 'knot'),
+ (30, 'knots');
+
      2. +
    2. Return the stem words 
      +SELECT madlib.stem_token(word) FROM token_tbl;
+
      + stem_token
+ ------------
+ kneel
+ kneel
+ kneel
+ kneel
+ knee
+ knell
+ knelt
+ knew
+ knick
+ knif
+ knife
+ knight
+ knight
+ knight
+ knit
+ knit
+ knit
+ knit
+ knive
+ knob
+ knob
+ knock
+ knock
+ knocker
+ knocker
+ knock
+ knock
+ knopp
+ knot
+ knot
+(30 rows)
+
      3. +
    3. The input can be processed as an array 
      +SELECT madlib.stem_token_arr(array_agg(word order by word)) FROM token_tbl;
+
      +  stem_token_arr
+ -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+ {kneel,kneel,kneel,kneel,knee,knell,knelt,knew,knick,knif,knife,knight,knight,knight,knit,knit,knit,knit,knive,knob,knob,knock,knock,knocker,knocker,knock,knock,knopp,knot,knot}
+(1 row)
+
      4. +
    +

    Related Topics
    +

    File porter_stemmer.sql_in for list of functions and usage.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__strs.html b/docs/docs/v2.1.0/group__grp__strs.html new file mode 100644 index 00000000..6e5674da --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__strs.html @@ -0,0 +1,253 @@ + + + + + + + + +MADlib: Stratified Sampling + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Stratified Sampling
    Sampling
    +
    +
    +
    Contents +

    Stratified sampling is a method for independently sampling subpopulations (strata). It is commonly used to reduce sampling error by ensuring that subgroups are adequately represented in the sample.

    +

    Stratified Sampling
    +
    +stratified_sample(  source_table,
+                    output_table,
+                    proportion,
+                    grouping_cols,
+                    target_cols,
+                    with_replacement
+                  )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the input data.

    +

    +
    +
    output_table
    +

    TEXT. Name of output table that contains the sampled data. The output table contains all columns present in the source table unless otherwise specified in the 'target_cols' parameter below.

    +

    +
    +
    proportion
    +

    FLOAT8 in the range (0,1). Each stratum is sampled independently.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. A single column or a list of comma-separated columns that defines the strata. When this parameter is NULL, no grouping is used so the sampling is non-stratified, that is, the whole table is treated as a single group.

    +

    +
    +
    target_cols (optional)
    +

    TEXT, default NULL. A comma-separated list of columns to appear in the 'output_table'. If NULL or '*', all columns from the 'source_table' will appear in the 'output_table'.

    +

    Note
    Do not include 'grouping_cols' in the parameter 'target_cols', because they are always included in the 'output_table'.
    +
    +
    with_replacement (optional)
    +
    BOOLEAN, default FALSE. Determines whether to sample with replacement or without replacement (default). With replacement means that it is possible that the same row may appear in the sample set more than once. Without replacement means a given row can be selected only once.
    +
    +

    Examples
    +

    Please note that due to the random nature of sampling, your results may look different from those below.

    +
      +
    1. Create an input table: 
      +DROP TABLE IF EXISTS test;
+CREATE TABLE test(
+    id1 INTEGER,
+    id2 INTEGER,
+    gr1 INTEGER,
+    gr2 INTEGER
+);
+INSERT INTO test VALUES
+(1,0,1,1),
+(2,0,1,1),
+(3,0,1,1),
+(4,0,1,1),
+(5,0,1,1),
+(6,0,1,1),
+(7,0,1,1),
+(8,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(0,1,1,2),
+(0,2,1,2),
+(0,3,1,2),
+(0,4,1,2),
+(0,5,1,2),
+(0,6,1,2),
+(10,10,2,2),
+(20,20,2,2),
+(30,30,2,2),
+(40,40,2,2),
+(50,50,2,2),
+(60,60,2,2),
+(70,70,2,2);
+
      2. +
    2. Sample without replacement: 
      +DROP TABLE IF EXISTS out;
+SELECT madlib.stratified_sample(
+                                'test',    -- Source table
+                                'out',     -- Output table
+                                0.5,       -- Sample proportion
+                                'gr1,gr2', -- Strata definition
+                                'id1,id2', -- Columns to output
+                                FALSE);    -- Sample without replacement
+SELECT * FROM out ORDER BY gr1,gr2,id1,id2;
+
      + gr1 | gr2 | id1 | id2
+-----+-----+-----+-----
+   1 |   1 |   2 |   0
+   1 |   1 |   4 |   0
+   1 |   1 |   7 |   0
+   1 |   1 |   8 |   0
+   1 |   1 |   9 |   0
+   1 |   1 |   9 |   0
+   1 |   2 |   0 |   2
+   1 |   2 |   0 |   3
+   1 |   2 |   0 |   4
+   2 |   2 |  20 |  20
+   2 |   2 |  30 |  30
+   2 |   2 |  40 |  40
+   2 |   2 |  60 |  60
+(13 rows)
+
      3. +
    3. Sample with replacement: 
      +DROP TABLE IF EXISTS out;
+SELECT madlib.stratified_sample(
+                                'test',    -- Source table
+                                'out',     -- Output table
+                                0.5,       -- Sample proportion
+                                'gr1,gr2', -- Strata definition
+                                'id1,id2', -- Columns to output
+                                TRUE);     -- Sample with replacement
+SELECT * FROM out ORDER BY gr1,gr2,id1,id2;
+
      + gr1 | gr2 | id1 | id2
+----—+----—+----—+----—
+   1 |   1 |   3 |   0
+   1 |   1 |   6 |   0
+   1 |   1 |   6 |   0
+   1 |   1 |   7 |   0
+   1 |   1 |   7 |   0
+   1 |   1 |   9 |   0
+   1 |   2 |   0 |   1
+   1 |   2 |   0 |   2
+   1 |   2 |   0 |   6
+   2 |   2 |  20 |  20
+   2 |   2 |  30 |  30
+   2 |   2 |  50 |  50
+   2 |   2 |  50 |  50
+
      4. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__summary.html b/docs/docs/v2.1.0/group__grp__summary.html new file mode 100644 index 00000000..2de7ece0 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__summary.html @@ -0,0 +1,488 @@ + + + + + + + + +MADlib: Summary + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Summary
    Statistics » Descriptive Statistics
    +
    +
    +
    Contents +

    The MADlib summary() function produces summary statistics for any data table. The function invokes various methods from the MADlib library to provide the data overview.

    +

    Summary Function Syntax
    The summary() function has the following syntax:
    +
    +summary ( source_table,
+          output_table,
+          target_cols,
+          grouping_cols,
+          get_distinct,
+          get_quartiles,
+          ntile_array,
+          how_many_mfv,
+          get_estimates,
+          n_cols_per_run
+        )
+

    The summary() function returns a composite type containing three fields:

    + + + + + + +
    output_table TEXT. The name of the output table.
    num_col_summarized INTEGER. The number of columns from the source table that have been summarized.
    duration FLOAT8. The time taken (in seconds) to compute the summary.
    +

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the input data.

    +

    +
    +
    output_table
    +

    TEXT. Name of the table for the output summary statistics. This table contains the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    group_by Group-by column name. NULL if none provided.
    group_by_value Value of the group-by column. NULL if there is no grouping.
    target_column Targeted column values for which summary is requested.
    column_number Physical column number for the target column, as described in pg_attribute catalog.
    data_type Data type of the target column. Standard GPDB type descriptors are displayed.
    row_count Number of rows for the target column.
    distinct_values Number of distinct values in the target column. If the summary() function is called with the get_estimates argument set to TRUE (default), then this is an estimated statistic based on the Flajolet-Martin distinct count estimator. If the get_estimates argument set to FALSE, will use PostgreSQL COUNT DISTINCT.
    missing_values Number of missing values in the target column.
    blank_values Number of blank values. Blanks are defined by this regular expression:
    '^\w*$'
    fraction_missing Percentage of total rows that are missing, as a decimal value, e.g. 0.3.
    fraction_blank Percentage of total rows that are blank, as a decimal value, e.g. 0.3.
    positive_values Number of positive values in the target column if target is numeric, otherwise NULL.
    negative_values Number of negative values in the target column if target is numeric, otherwise NULL.
    zero_values Number of zero values in the target column if target is numeric, otherwise NULL. Note that we are reporting exact equality to 0.0 here, so even if you have a float value that is extremely small (say due to rounding), it will not be reported as a zero value.
    mean Mean value of target column if target is numeric, otherwise NULL.
    variance Variance of target column if target is numeric, otherwise NULL.
    confidence_interval Confidence interval (95% using z-score) of the mean value for the target column if target is numeric, otherwise NULL. Presented as an array of two elements in the form {lower bound, upper bound}.
    min Minimum value of target column. For strings this is the length of the shortest string.
    max Maximum value of target column. For strings this is the length of the longest string.
    first_quartile First quartile (25th percentile), only for numeric columns. (Unavailable for PostgreSQL 9.3 or lower.)
    median Median value of target column, if target is numeric, otherwise NULL. (Unavailable for PostgreSQL 9.3 or lower.)
    third_quartile Third quartile (25th percentile), only for numeric columns. (Unavailable for PostgreSQL 9.3 or lower.)
    quantile_array Percentile values corresponding to ntile_array. (Unavailable for PostgreSQL 9.3 or lower.)
    most_frequent_values An array containing the most frequently occurring values. The how_many_mfv argument determines the length of the array, which is 10 by default. If the summary() function is called with the get_estimates argument set to TRUE (default), the frequent values computation is performed using a parallel aggregation method that is faster, but in some cases may fail to detect the exact most frequent values.
    mfv_frequencies Array containing the frequency count for each of the most frequent values.
    +

    +
    +
    target_columns (optional)
    +

    TEXT, default NULL. A comma-separated list of columns to summarize. If NULL, summaries are produced for all columns.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default: null. A comma-separated list of columns on which to group results. If NULL, summaries are produced for the complete table.
    Note
    Please note that summary statistics are calculated for each grouping column independently. That is, grouping columns are not combined together as in the regular PostgreSQL style GROUP BY directive. (This was done to reduce long run time and huge output table size which would otherwise result in the case of large input tables with a lot of grouping_cols and target_cols specified.)
    +
    +
    get_distinct (optional)
    +

    BOOLEAN, default TRUE. If true, distinct values are counted. The method for computing distinct values depends on the setting of the 'get_estimates' parameter below.

    +

    +
    +
    get_quartiles (optional)
    +

    BOOLEAN, default TRUE. If TRUE, quartiles are computed.

    +

    +
    +
    ntile_array (optional)
    +
    FLOAT8[], default NULL. An array of quantile values to compute. If NULL, quantile values are not computed.
    Note
    Quartile and quantile functions are not available in PostgreSQL 9.3 or lower. If you are using PostgreSQL 9.3 or lower, the output table will not contain these values, even if you set 'get_quartiles' = TRUE or provide an array of quantile values for the parameter 'ntile_array'.
    +
    +
    how_many_mfv (optional)
    +

    INTEGER, default: 10. The number of most-frequent-values to compute. The method for computing MFV depends on the setting of the 'get_estimates' parameter below.

    +

    +
    +
    get_estimates (optional)
    +

    BOOLEAN, default TRUE. If TRUE, estimated values are produced for distinct values and most frequent values. If FALSE, exact values are calculated which will take longer to run, with the impact depending on data size.

    +

    +
    +
    n_cols_per_run (optional)
    +
    INTEGER, default: 15. The number of columns to collect summary statistics in one pass of the data. This parameter determines the number of passes through the data. For e.g., with a total of 40 columns to summarize and 'n_cols_per_run = 15', there will be 3 passes through the data, with each pass summarizing a maximum of 15 columns.
    Note
    This parameter should be used with caution. Increasing this parameter could decrease the total run time (if number of passes decreases), but will increase the memory consumption during each run. Since PostgreSQL limits the memory available for a single aggregate run, this increased memory consumption could result in an out-of-memory termination error.
    +
    +
    +

    Examples
    +
      +
    1. View online help for the summary() function. 
      +SELECT * FROM madlib.summary();
+
      2. +
    2. Create an input data table using part of the well known iris data set. 
      +DROP TABLE IF EXISTS iris;
+CREATE TABLE iris (id INT, sepal_length FLOAT, sepal_width FLOAT,
+                    petal_length FLOAT, petal_width FLOAT,
+                   class_name text);
+INSERT INTO iris VALUES
+(1,5.1,3.5,1.4,0.2,'Iris-setosa'),
+(2,4.9,3.0,1.4,0.2,'Iris-setosa'),
+(3,4.7,3.2,1.3,0.2,'Iris-setosa'),
+(4,4.6,3.1,1.5,0.2,'Iris-setosa'),
+(5,5.0,3.6,1.4,0.2,'Iris-setosa'),
+(6,5.4,3.9,1.7,0.4,'Iris-setosa'),
+(7,4.6,3.4,1.4,0.3,'Iris-setosa'),
+(8,5.0,3.4,1.5,0.2,'Iris-setosa'),
+(9,4.4,2.9,1.4,0.2,'Iris-setosa'),
+(10,4.9,3.1,1.5,0.1,'Iris-setosa'),
+(11,7.0,3.2,4.7,1.4,'Iris-versicolor'),
+(12,6.4,3.2,4.5,1.5,'Iris-versicolor'),
+(13,6.9,3.1,4.9,1.5,'Iris-versicolor'),
+(14,5.5,2.3,4.0,1.3,'Iris-versicolor'),
+(15,6.5,2.8,4.6,1.5,'Iris-versicolor'),
+(16,5.7,2.8,4.5,1.3,'Iris-versicolor'),
+(17,6.3,3.3,4.7,1.6,'Iris-versicolor'),
+(18,4.9,2.4,3.3,1.0,'Iris-versicolor'),
+(19,6.6,2.9,4.6,1.3,'Iris-versicolor'),
+(20,5.2,2.7,3.9,1.4,'Iris-versicolor'),
+(21,6.3,3.3,6.0,2.5,'Iris-virginica'),
+(22,5.8,2.7,5.1,1.9,'Iris-virginica'),
+(23,7.1,3.0,5.9,2.1,'Iris-virginica'),
+(24,6.3,2.9,5.6,1.8,'Iris-virginica'),
+(25,6.5,3.0,5.8,2.2,'Iris-virginica'),
+(26,7.6,3.0,6.6,2.1,'Iris-virginica'),
+(27,4.9,2.5,4.5,1.7,'Iris-virginica'),
+(28,7.3,2.9,6.3,1.8,'Iris-virginica'),
+(29,6.7,2.5,5.8,1.8,'Iris-virginica'),
+(30,7.2,3.6,6.1,2.5,'Iris-virginica');
+
      3. +
    3. Run the summary() function using all defaults. 
      +DROP TABLE IF EXISTS iris_summary;
+SELECT * FROM madlib.summary( 'iris',            -- Source table
+                              'iris_summary'     -- Output table
+                            );
+
      Result: 
      + output_table | num_col_summarized |     duration
+--------------+--------------------+-------------------
+ iris_summary |                  6 | 0.574938058853149
+(1 row)
+
      View the summary data. 
      +-- Turn on expanded display for readability.
+\x on
+SELECT * FROM iris_summary;
+
      Result (partial): 
      +...
+ -[ RECORD 2 ]--------+---------------------------------------------
+group_by             |
+group_by_value       |
+target_column        | sepal_length
+column_number        | 2
+data_type            | float8
+row_count            | 30
+distinct_values      | 22
+missing_values       | 0
+blank_values         |
+fraction_missing     | 0
+fraction_blank       |
+positive_values      | 30
+negative_values      | 0
+zero_values          | 0
+mean                 | 5.84333333333333
+variance             | 0.929436781609188
+confidence_interval  | {5.49834423494374,6.18832243172292}
+min                  | 4.4
+max                  | 7.6
+first_quartile       | 4.925
+median               | 5.75
+third_quartile       | 6.575
+most_frequent_values | {4.9,6.3,5,6.5,4.6,7.2,5.5,5.7,7.3,6.7}
+mfv_frequencies      | {4,3,2,2,2,1,1,1,1,1}
+...
+ -[ RECORD 6 ]--------+---------------------------------------------
+group_by             |
+group_by_value       |
+target_column        | class_name
+column_number        | 6
+data_type            | text
+row_count            | 30
+distinct_values      | 3
+missing_values       | 0
+blank_values         | 0
+fraction_missing     | 0
+fraction_blank       | 0
+positive_values      |
+negative_values      |
+zero_values          |
+mean                 |
+variance             |
+confidence_interval  |
+min                  | 11
+max                  | 15
+first_quartile       |
+median               |
+third_quartile       |
+most_frequent_values | {Iris-setosa,Iris-versicolor,Iris-virginica}
+mfv_frequencies      | {10,10,10}
+
      Note that for the text column in record 6, some statistics are n/a, and the min and max values represent the length of the shortest and longest strings respectively.
      4. +
    4. Now group by the class of iris: 
      +DROP TABLE IF EXISTS iris_summary;
+SELECT * FROM madlib.summary( 'iris',                       -- Source table
+                              'iris_summary',               -- Output table
+                              'sepal_length, sepal_width',  -- Columns to summarize
+                              'class_name'                  -- Grouping column
+                            );
+SELECT * FROM iris_summary;
+
      Result (partial): 
      + -[ RECORD 1 ]--------+----------------------------------------
+group_by             | class_name
+group_by_value       | Iris-setosa
+target_column        | sepal_length
+column_number        | 2
+data_type            | float8
+row_count            | 10
+distinct_values      | 7
+missing_values       | 0
+blank_values         |
+fraction_missing     | 0
+fraction_blank       |
+positive_values      | 10
+negative_values      | 0
+zero_values          | 0
+mean                 | 4.86
+variance             | 0.0848888888888875
+confidence_interval  | {4.67941507384182,5.04058492615818}
+min                  | 4.4
+max                  | 5.4
+first_quartile       | 4.625
+median               | 4.9
+third_quartile       | 5
+most_frequent_values | {4.9,5,4.6,5.1,4.7,5.4,4.4}
+mfv_frequencies      | {2,2,2,1,1,1,1}
+...
+ -[ RECORD 3 ]--------+----------------------------------------
+group_by             | class_name
+group_by_value       | Iris-versicolor
+target_column        | sepal_length
+column_number        | 2
+data_type            | float8
+row_count            | 10
+distinct_values      | 10
+missing_values       | 0
+blank_values         |
+fraction_missing     | 0
+fraction_blank       |
+positive_values      | 10
+negative_values      | 0
+zero_values          | 0
+mean                 | 6.1
+variance             | 0.528888888888893
+confidence_interval  | {5.64924734548141,6.55075265451859}
+min                  | 4.9
+max                  | 7
+first_quartile       | 5.55
+median               | 6.35
+third_quartile       | 6.575
+most_frequent_values | {6.9,5.5,6.5,5.7,6.3,4.9,6.6,5.2,7,6.4}
+mfv_frequencies      | {1,1,1,1,1,1,1,1,1,1}
+...
+
      5. +
    5. Trying some other parameters: 
      +DROP TABLE IF EXISTS iris_summary;
+SELECT * FROM madlib.summary( 'iris',                       -- Source table
+                              'iris_summary',               -- Output table
+                              'sepal_length, sepal_width',  -- Columns to summarize
+                               NULL,                        -- No grouping
+                               TRUE,                        -- Get distinct values
+                               FALSE,                       -- Dont get quartiles
+                               ARRAY[0.33, 0.66],           -- Get ntiles
+                               3,                           -- Number of MFV to compute
+                               FALSE                        -- Get exact values
+                            );
+SELECT * FROM iris_summary;
+
      Result: 
      + -[ RECORD 1 ]--------+------------------------------------
+group_by             |
+group_by_value       |
+target_column        | sepal_length
+column_number        | 2
+data_type            | float8
+row_count            | 30
+distinct_values      | 22
+missing_values       | 0
+blank_values         |
+fraction_missing     | 0
+fraction_blank       |
+positive_values      | 30
+negative_values      | 0
+zero_values          | 0
+mean                 | 5.84333333333333
+variance             | 0.929436781609175
+confidence_interval  | {5.49834423494375,6.18832243172292}
+min                  | 4.4
+max                  | 7.6
+quantile_array       | {5.057,6.414}
+most_frequent_values | {4.9,6.3,6.5}
+mfv_frequencies      | {4,3,2}
+ -[ RECORD 2 ]--------+------------------------------------
+group_by             |
+group_by_value       |
+target_column        | sepal_width
+column_number        | 3
+data_type            | float8
+row_count            | 30
+distinct_values      | 14
+missing_values       | 0
+blank_values         |
+fraction_missing     | 0
+fraction_blank       |
+positive_values      | 30
+negative_values      | 0
+zero_values          | 0
+mean                 | 3.04
+variance             | 0.13903448275862
+confidence_interval  | {2.90656901047539,3.17343098952461}
+min                  | 2.3
+max                  | 3.9
+quantile_array       | {2.9,3.2}
+most_frequent_values | {2.9,3,3.2}
+mfv_frequencies      | {4,4,3}
+
      6. +
    +

    Notes
      +
    • Table names can be optionally schema qualified (current_schemas() would be searched if a schema name is not provided) and table and column names should follow case-sensitivity and quoting rules per the database. (For instance, 'mytable' and 'MyTable' both resolve to the same entity, i.e. 'mytable'. If mixed-case or multi-byte characters are desired for entity names then the string should be double-quoted; in this case the input would be '"MyTable"').
      • +
    • The get_estimates parameter controls computation for both distinct count and most frequent values:
        +
      • If get_estimates is TRUE then the distinct value computation is estimated using Flajolet-Martin. MFV is computed using a fast method that does parallel aggregation in Greenplum Database at the expense of missing or duplicating some of the most frequent values.
        • +
      • If get_estimates is FALSE then the distinct values are computed in a slower but exact method using PostgreSQL COUNT DISTINCT. MFV is computed using a faithful implementation that preserves the approximation guarantees of the Cormode/Muthukrishnan method (more information at MFV (Most Frequent Values)).
        • +
      +
      • +
    +
    +

    Related Topics
    File summary.sql_in documenting the summary() function
    +

    FM (Flajolet-Martin)
    + MFV (Most Frequent Values)
    + CountMin (Cormode-Muthukrishnan)

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__super.html b/docs/docs/v2.1.0/group__grp__super.html new file mode 100644 index 00000000..eb33a654 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__super.html @@ -0,0 +1,145 @@ + + + + + + + + +MADlib: Supervised Learning + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Supervised Learning
    +
    +
    +

    Detailed Description

    +

    Methods to perform a variety of supervised learning tasks.

    + + + + + + + + + + + + + + + + + + + + +

    +Modules

     Conditional Random Field
     Constructs a Conditional Random Fields (CRF) model for labeling sequential data.
     
     k-Nearest Neighbors
     Finds \(k\) nearest data points to the given data point and outputs majority vote value of output classes for classification, or average value of target values for regression.
     
     Neural Network
     Solves classification and regression problems with several fully connected layers and non-linear activation functions.
     
     Regression Models
     A collection of methods for modeling conditional expectation of a response variable.
     
     Support Vector Machines
     Solves classification and regression problems by separating data with a hyperplane or other nonlinear decision boundary.
     
     Tree Methods
     A collection of recursive partitioning (tree) methods.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__super.js b/docs/docs/v2.1.0/group__grp__super.js new file mode 100644 index 00000000..67b1b347 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__super.js @@ -0,0 +1,9 @@ +var group__grp__super = +[ + [ "Conditional Random Field", "group__grp__crf.html", null ], + [ "k-Nearest Neighbors", "group__grp__knn.html", null ], + [ "Neural Network", "group__grp__nn.html", null ], + [ "Regression Models", "group__grp__regml.html", "group__grp__regml" ], + [ "Support Vector Machines", "group__grp__svm.html", null ], + [ "Tree Methods", "group__grp__tree.html", "group__grp__tree" ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__svd.html b/docs/docs/v2.1.0/group__grp__svd.html new file mode 100644 index 00000000..773e3710 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__svd.html @@ -0,0 +1,408 @@ + + + + + + + + +MADlib: Singular Value Decomposition + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Singular Value Decomposition
    Data Types and Transformations » Arrays and Matrices » Matrix Factorization
    +
    +
    +
    Contents +

    In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics.

    +

    Let \(A\) be a \(mxn\) matrix, where \(m \ge n\). Then \(A\) can be decomposed as follows:

    +\[ A = U \Sigma V^T, \] +

    +

    where \(U\) is a \(m \times n\) orthonormal matrix, \(\Sigma\) is a \(n \times n\) diagonal matrix, and \(V\) is an \(n \times n\) orthonormal matrix. The diagonal elements of \(\Sigma\) are called the singular values.

    +

    SVD Functions
    +

    SVD factorizations are provided for dense and sparse matrices. In addition, a native implementation is provided for very sparse matrices for improved performance.

    +

    SVD Function for Dense Matrices

    +
    +svd( source_table,
+     output_table_prefix,
+     row_id,
+     k,
+     n_iterations,
+     result_summary_table
+);
+

    Arguments

    +
    source_table
    +

    TEXT. Source table name (dense matrix).

    +

    The table contains a row_id column that identifies each row, with numbering starting from 1. The other columns contain the data for the matrix. There are two possible dense formats as illustrated by the 2x2 matrix example below. You can use either of these dense formats:

      +
    1. +            row_id     col1     col2
+row1         1           1         0
+row2         2           0         1
+
      2. +
    2. +        row_id     row_vec
+row1        1       {1, 0}
+row2        2       {0, 1}
+
      3. +
    +
    +
    output_table_prefix
    +
    TEXT. Prefix for output tables. See Output Tables below for a description of the convention used.
    +
    row_id
    +
    TEXT. ID for each row.
    +
    k
    +
    INTEGER. Number of singular values to compute.
    +
    n_iterations (optional).
    +
    INTEGER. Number of iterations to run.
    Note
    The number of iterations must be in the range [k, column dimension], where k is number of singular values.
    +
    +
    result_summary_table (optional)
    +
    TEXT. The name of the table to store the result summary.
    +
    +
    +

    SVD Function for Sparse Matrices

    +

    Use this function for matrices that are represented in the sparse-matrix format (example below). Note that the input matrix is converted to a dense matrix before the SVD operation, for efficient computation reasons.

    +
    +svd_sparse( source_table,
+            output_table_prefix,
+            row_id,
+            col_id,
+            value,
+            row_dim,
+            col_dim,
+            k,
+            n_iterations,
+            result_summary_table
+          );
+

    Arguments

    +
    source_table
    +

    TEXT. Source table name (sparse matrix).

    +

    A sparse matrix is represented using the row and column indices for each non-zero entry of the matrix. This representation is useful for matrices containing multiple zero elements. Below is an example of a sparse 4x7 matrix with just 6 out of 28 entries being non-zero. The dimensionality of the matrix is inferred using the max value in row and col columns. Note the last entry is included (even though it is 0) to provide the dimensionality of the matrix, indicating that the 4th row and 7th column contain all zeros. 

    + row_id | col_id | value
+--------+--------+-------
+      1 |      1 |     9
+      1 |      5 |     6
+      1 |      6 |     6
+      2 |      1 |     8
+      3 |      1 |     3
+      3 |      2 |     9
+      4 |      7 |     0
+(6 rows)
+

    +
    +
    output_table_prefix
    +
    TEXT. Prefix for output tables. See Output Tables below for a description of the convention used.
    +
    row_id
    +
    TEXT. Name of the column containing the row index for each entry in sparse matrix.
    +
    col_id
    +
    TEXT. Name of the column containing the column index for each entry in sparse matrix.
    +
    value
    +
    TEXT. Name of column containing the non-zero values of the sparse matrix.
    +
    row_dim
    +
    INTEGER. Number of rows in matrix.
    +
    col_dim
    +
    INTEGER. Number of columns in matrix.
    +
    k
    +
    INTEGER. Number of singular values to compute.
    +
    n_iterations (optional)
    +
    INTEGER. Number of iterations to run.
    Note
    The number of iterations must be in the range [k, column dimension], where k is number of singular values.
    +
    +
    result_summary_table (optional)
    +
    TEXT. The name of the table to store the result summary.
    +
    +
    +

    Native Implementation for Sparse Matrices

    +

    Use this function for matrices that are represented in the sparse-matrix format (see sparse matrix example above). This function uses the native sparse representation while computing the SVD.

    Note
    Note that this function should be favored if the matrix is highly sparse, since it computes very sparse matrices efficiently.
    +
    +svd_sparse_native( source_table,
+                   output_table_prefix,
+                   row_id,
+                   col_id,
+                   value,
+                   row_dim,
+                   col_dim,
+                   k,
+                   n_iterations,
+                   result_summary_table
+                 );
+

    Arguments

    +
    source_table
    +
    TEXT. Source table name (sparse matrix - see example above).
    +
    output_table_prefix
    +
    TEXT. Prefix for output tables. See Output Tables below for a description of the convention used.
    +
    row_id
    +
    TEXT. ID for each row.
    +
    col_id
    +
    TEXT. ID for each column.
    +
    value
    +
    TEXT. Non-zero values of the sparse matrix.
    +
    row_dim
    +
    INTEGER. Row dimension of sparse matrix.
    +
    col_dim
    +
    INTEGER. Col dimension of sparse matrix.
    +
    k
    +
    INTEGER. Number of singular values to compute.
    +
    n_iterations (optional)
    +
    INTEGER. Number of iterations to run.
    Note
    The number of iterations must be in the range [k, column dimension], where k is number of singular values.
    +
    +
    result_summary_table (optional)
    +
    TEXT. Table name to store result summary.
    +
    +
    +

    Output Tables
    +

    Output for eigenvectors/values is in the following three tables:

      +
    • Left singular matrix: Table is named <output_table_prefix>_u (e.g. ‘netflix_u’)
      • +
    • Right singular matrix: Table is named <output_table_prefix>_v (e.g. ‘netflix_v’)
      • +
    • Singular values: Table is named <output_table_prefix>_s (e.g. ‘netflix_s’)
      • +
    +

    The left and right singular vector tables are of the format:

    + + + + +
    row_id INTEGER. The ID corresponding to each eigenvalue (in decreasing order).
    row_vec FLOAT8[]. Singular vector elements for this row_id. Each array is of size k.
    +

    The singular values table is in sparse table format, since only the diagonal elements of the matrix are non-zero:

    + + + + + + +
    row_id INTEGER. i for ith eigenvalue.
    col_id INTEGER. i for ith eigenvalue (same as row_id).
    value FLOAT8. Eigenvalue.
    +

    All row_id and col_id in the above tables start from 1.

    +

    The result summary table has the following columns:

    + + + + + + + + + + +
    rows_used INTEGER. Number of rows used for SVD calculation.
    exec_time FLOAT8. Total time for executing SVD.
    iter INTEGER. Total number of iterations run.
    recon_error FLOAT8. Total quality score (i.e. approximation quality) for this set of orthonormal basis.
    relative_recon_error FLOAT8. Relative quality score.
    +

    In the result summary table, the reconstruction error is computed as \( \sqrt{mean((X - USV^T)_{ij}^2)} \), where the average is over all elements of the matrices. The relative reconstruction error is then computed as ratio of the reconstruction error and \( \sqrt{mean(X_{ij}^2)} \).

    +

    Examples
    +
      +
    1. View online help for the SVD function. 
      +SELECT madlib.svd();
+
      2. +
    2. Create an input dataset (dense matrix). 
      +DROP TABLE IF EXISTS mat, mat_sparse, svd_summary_table, svd_u, svd_v, svd_s;
+CREATE TABLE mat (
+    row_id integer,
+    row_vec double precision[]
+);
+INSERT INTO mat VALUES
+(1,'{396,840,353,446,318,886,15,584,159,383}'),
+(2,'{691,58,899,163,159,533,604,582,269,390}'),
+(3,'{293,742,298,75,404,857,941,662,846,2}'),
+(4,'{462,532,787,265,982,306,600,608,212,885}'),
+(5,'{304,151,337,387,643,753,603,531,459,652}'),
+(6,'{327,946,368,943,7,516,272,24,591,204}'),
+(7,'{877,59,260,302,891,498,710,286,864,675}'),
+(8,'{458,959,774,376,228,354,300,669,718,565}'),
+(9,'{824,390,818,844,180,943,424,520,65,913}'),
+(10,'{882,761,398,688,761,405,125,484,222,873}'),
+(11,'{528,1,860,18,814,242,314,965,935,809}'),
+(12,'{492,220,576,289,321,261,173,1,44,241}'),
+(13,'{415,701,221,503,67,393,479,218,219,916}'),
+(14,'{350,192,211,633,53,783,30,444,176,932}'),
+(15,'{909,472,871,695,930,455,398,893,693,838}'),
+(16,'{739,651,678,577,273,935,661,47,373,618}');
+
      3. +
    3. Run SVD function for a dense matrix. 
      +SELECT madlib.svd( 'mat',       -- Input table
+                   'svd',       -- Output table prefix
+                   'row_id',    -- Column name with row index
+                   10,          -- Number of singular values to compute
+                   NULL,        -- Use default number of iterations
+                   'svd_summary_table'  -- Result summary table
+                 );
+
      4. +
    4. Print out the singular values and the summary table. For the singular values: 
      +SELECT * FROM svd_s ORDER BY row_id;
+
      Result: 
      + row_id | col_id |      value
+ --------+--------+------------------
+      1 |      1 | 6475.67225281804
+      2 |      2 | 1875.18065580415
+      3 |      3 | 1483.25228429636
+      4 |      4 | 1159.72262897427
+      5 |      5 | 1033.86092570574
+      6 |      6 | 948.437358703966
+      7 |      7 | 795.379572772455
+      8 |      8 | 709.086240684469
+      9 |      9 | 462.473775959371
+     10 |     10 | 365.875217945698
+     10 |     10 |
+(11 rows)
+
      For the summary table: 
      +SELECT * FROM svd_summary_table;
+
      Result: 
      + rows_used | exec_time (ms) | iter |    recon_error    | relative_recon_error
+ -----------+----------------+------+-------------------+----------------------
+        16 |        1332.47 |   10 | 4.36920148766e-13 |    7.63134130332e-16
+(1 row)
+
      5. +
    5. Create a sparse matrix by running the matrix_sparsify() utility function on the dense matrix. 
      +SELECT madlib.matrix_sparsify('mat',
+                              'row=row_id, val=row_vec',
+                              'mat_sparse',
+                              'row=row_id, col=col_id, val=value');
+
      6. +
    6. Run the SVD function for a sparse matrix. 
      +SELECT madlib.svd_sparse( 'mat_sparse',   -- Input table
+                          'svd',          -- Output table prefix
+                          'row_id',       -- Column name with row index
+                          'col_id',       -- Column name with column index
+                          'value',        -- Matrix cell value
+                          16,             -- Number of rows in matrix
+                          10,             -- Number of columns in matrix
+                          10              -- Number of singular values to compute
+                          );
+
      7. +
    7. Run the SVD function for a very sparse matrix. 
      +SELECT madlib.svd_sparse_native ( 'mat_sparse',   -- Input table
+                          'svd',          -- Output table prefix
+                          'row_id',       -- Column name with row index
+                          'col_id',       -- Column name with column index
+                          'value',        -- Matrix cell value
+                          16,             -- Number of rows in matrix
+                          10,             -- Number of columns in matrix
+                          10              -- Number of singular values to compute
+                          );
+
      Technical Background
      In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics. Let \(A\) be a \(m \times n\) matrix, where \(m \ge n\). Then \(A\) can be decomposed as follows:

      +\[ A = U \Sigma V^T, \] +

      + where \(U\) is a \(m \times n\) orthonormal matrix, \(\Sigma\) is a \(n \times n\) diagonal matrix, and \(V\) is an \(n \times n\) orthonormal matrix. The diagonal elements of \(\Sigma\) are called the singular values. It is possible to formulate the problem of computing the singular triplets ( \(\sigma_i, u_i, v_i\)) of \(A\) as an eigenvalue problem involving a Hermitian matrix related to \(A\). There are two possible ways of achieving this:
      +
      8. +
    +
      +
    • With the cross product matrix, \(A^TA\) and \(AA^T\)
      • +
    • With the cyclic matrix

      +\[ H(A) = \begin{bmatrix} 0 & A\\ A^* & 0 \end{bmatrix} \] +

      + The singular values are the nonnegative square roots of the eigenvalues of the cross product matrix. This approach may imply a severe loss of accuracy in the smallest singular values. The cyclic matrix approach is an alternative that avoids this problem, but at the expense of significantly increasing the cost of the computation. Computing the cross product matrix explicitly is not recommended, especially in the case of sparse A. Bidiagonalization was proposed by Golub and Kahan [citation?] as a way of tridiagonalizing the cross product matrix without forming it explicitly. Consider the following decomposition

      +\[ A = P B Q^T, \] +

      + where \(P\) and \(Q\) are unitary matrices and \(B\) is an \(m \times n\) upper bidiagonal matrix. Then the tridiagonal matrix \(B*B\) is unitarily similar to \(A*A\). Additionally, specific methods exist that compute the singular values of \(B\) without forming \(B*B\). Therefore, after computing the SVD of B,

      +\[ B = X\Sigma Y^T, \] +

      + it only remains to compute the SVD of the original matrix with \(U = PX\) and \(V = QY\).
      • +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__svec.html b/docs/docs/v2.1.0/group__grp__svec.html new file mode 100644 index 00000000..54d3587e --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__svec.html @@ -0,0 +1,439 @@ + + + + + + + + +MADlib: Sparse Vectors + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Sparse Vectors
    Data Types and Transformations » Arrays and Matrices
    +
    +
    +
    Contents +

    This module implements a sparse vector data type, named "svec", which provides compressed storage of vectors that have many duplicate elements.

    +

    Arrays of floating point numbers for various calculations sometimes have long runs of zeros (or some other default value). This is common in applications like scientific computing, retail optimization, and text processing. Each floating point number takes 8 bytes of storage in memory and/or disk, so saving those zeros is often worthwhile. There are also many computations that can benefit from skipping over the zeros.

    +

    Consider, for example, the following array of doubles stored as a Postgres/Greenplum "float8[]" data type:

    +
    +'{0, 33,...40,000 zeros..., 12, 22 }'::float8[]
+

    This array would occupy slightly more than 320KB of memory or disk, most of it zeros. Even if we were to exploit the null bitmap and store the zeros as nulls, we would still end up with a 5KB null bitmap, which is still not nearly as memory efficient as we'd like. Also, as we perform various operations on the array, we do work on 40,000 fields that turn out to be unimportant.

    +

    To solve the problems associated with the processing of vectors discussed above, the svec type employs a simple Run Length Encoding (RLE) scheme to represent sparse vectors as pairs of count-value arrays. For example, the array above would be represented as

    +
    +'{1,1,40000,1,1}:{0,33,0,12,22}'::madlib.svec
+

    which says there is 1 occurrence of 0, followed by 1 occurrence of 33, followed by 40,000 occurrences of 0, etc. This uses just 5 integers and 5 floating point numbers to store the array. Further, it is easy to implement vector operations that can take advantage of the RLE representation to make computations faster. The SVEC module provides a library of such functions.

    +

    The current version only supports sparse vectors of float8 values. Future versions will support other base types.

    +

    Using Sparse Vectors
    +

    An SVEC can be constructed directly with a constant expression, as follows: 

    +SELECT '{n1,n2,...,nk}:{v1,v2,...vk}'::madlib.svec;
+

    where n1,n2,...,nk specifies the counts for the values v1,v2,...,vk.

    +

    A float array can be cast to an SVEC: 

    +SELECT ('{v1,v2,...vk}'::float[])::madlib.svec;
+

    An SVEC can be created with an aggregation: 

    +SELECT madlib.svec_agg(v1) FROM generate_series(1,k);
+

    An SVEC can be created using the madlib.svec_cast_positions_float8arr() function by supplying an array of positions and an array of values at those positions: 

    +SELECT madlib.svec_cast_positions_float8arr(
+    array[n1,n2,...nk],    -- positions of values in vector
+    array[v1,v2,...vk],    -- values at each position
+    length,                -- length of vector
+    base)                  -- value at unspecified positions
+

    For example, the following expression: 

    +SELECT madlib.svec_cast_positions_float8arr(
+    array[1,3,5],
+    array[2,4,6],
+    10,
+    0.0)
+

    produces this SVEC: 

    + svec_cast_positions_float8arr
+  ------------------------------
+ {1,1,1,1,1,5}:{2,0,4,0,6,0}
+

    Add madlib to the search_path to use the svec operators defined in the module.

    +

    Document Vectorization into Sparse Vectors
    This module implements an efficient way for document vectorization, converting text documents into sparse vector representation (MADlib.svec), required by various machine learning algorithms in MADlib.
    +

    The function accepts two tables as input, dictionary table and documents table, and produces the specified output table containing sparse vectors for the represented documents (in documents table).

    +
    +madlib.gen_doc_svecs(output_tbl,
+                     dictionary_tbl,
+                     dict_id_col,
+                     dict_term_col,
+                     documents_tbl,
+                     doc_id_col,
+                     doc_term_col,
+                     doc_term_info_col
+                    )
+

    Arguments

    +
    output_tbl
    +

    TEXT. Name of the output table to be created containing the sparse vector representation of the documents. It has the following columns:

    + + + + +
    doc_id __TYPE_DOC__. Document id.
    + __TYPE_DOC__: Column type depends on the type of doc_id_col in documents_tbl.
    sparse_vector MADlib.svec. Corresponding sparse vector representation.
    +

    +
    +
    dictionary_tbl
    +

    TEXT. Name of the dictionary table containing features.

    + + + + +
    dict_id_col TEXT. Name of the id column in the dictionary_tbl.
    + Expected Type: INTEGER or BIGINT.
    + NOTE: Values must be continuous ranging from 0 to total number of elements in the dictionary - 1.
    dict_term_col TEXT. Name of the column containing term (features) in dictionary_tbl.
    +

    +
    +
    documents_tbl
    +
    TEXT. Name of the documents table representing documents. + + + + + + +
    doc_id_col TEXT. Name of the id column in the documents_tbl.
    doc_term_col TEXT. Name of the term column in the documents_tbl.
    doc_term_info_col TEXT. Name of the term info column in documents_tbl. The expected type of this column should be:
    + - INTEGER, BIGINT or DOUBLE PRECISION: Values directly used to populate vector.
    + - ARRAY: Length of the array used to populate the vector.
    + ** For an example use case on using these types of column types, please refer to the example below.
    +
    +
    +

    Example:
    + Consider a corpus consisting of set of documents consisting of features (terms) along with doc ids: 

    +1, {this,is,one,document,in,the,corpus}
+2, {i,am,the,second,document,in,the,corpus}
+3, {being,third,never,really,bothered,me,until,now}
+4, {the,document,before,me,is,the,third,document}
+
      +
    1. Prepare documents table in appropriate format.
      + The corpus specified above can be represented by any of the following documents_table: 
      +SELECT * FROM documents_table ORDER BY id;
+
      Result: 
      +  id |   term   | count                 id |   term   | positions
+ ----+----------+-------               ----+----------+-----------
+   1 | is       |     1                  1 | is       | {1}
+   1 | in       |     1                  1 | in       | {4}
+   1 | one      |     1                  1 | one      | {2}
+   1 | this     |     1                  1 | this     | {0}
+   1 | the      |     1                  1 | the      | {5}
+   1 | document |     1                  1 | document | {3}
+   1 | corpus   |     1                  1 | corpus   | {6}
+   2 | second   |     1                  2 | second   | {3}
+   2 | document |     1                  2 | document | {4}
+   2 | corpus   |     1                  2 | corpus   | {7}
+   . | ...      |    ..                  . | ...      | ...
+   4 | document |     2                  4 | document | {1,7}
+...
+
      2. +
    2. Prepare dictionary table in appropriate format. 
      +SELECT * FROM dictionary_table ORDER BY id;
+
      Result: 
      +  id |   term
+ ----+----------
+   0 | am
+   1 | before
+   2 | being
+   3 | bothered
+   4 | corpus
+   5 | document
+   6 | i
+   7 | in
+   8 | is
+   9 | me
+...
+
      3. +
    3. Generate sparse vector for the documents using dictionary_table and documents_table.
      + doc_term_info_col (count) of type INTEGER: 
      +SELECT * FROM madlib.gen_doc_svecs('svec_output', 'dictionary_table', 'id', 'term',
+                            'documents_table', 'id', 'term', 'count');
+
      doc_term_info_col (positions) of type ARRAY: 
      +SELECT * FROM madlib.gen_doc_svecs('svec_output', 'dictionary_table', 'id', 'term',
+                            'documents_table', 'id', 'term', 'positions');
+
      Result: 
      +                                 gen_doc_svecs
+ --------------------------------------------------------------------------------------
+ Created table svec_output (doc_id, sparse_vector) containing sparse vectors
+(1 row)
+
      4. +
    4. Analyze the sparse vectors created. 
      +SELECT * FROM svec_output ORDER by doc_id;
+
      Result: 
      + doc_id |                  sparse_vector
+ --------+-------------------------------------------------
+      1 | {4,2,1,2,3,1,2,1,1,1,1}:{0,1,0,1,0,1,0,1,0,1,0}
+      2 | {1,3,4,6,1,1,3}:{1,0,1,0,1,2,0}
+      3 | {2,2,5,3,1,1,2,1,1,1}:{0,1,0,1,0,1,0,1,0,1}
+      4 | {1,1,3,1,2,2,5,1,1,2}:{0,1,0,2,0,1,0,2,1,0}
+(4 rows)
+
      5. +
    +

    See the file svec.sql_in for complete syntax.

    +

    Examples
    +

    We can use operations with svec type like <, >, *, **, /, =, +, SUM, etc, and they have meanings associated with typical vector operations. For example, the plus (+) operator adds each of the terms of two vectors having the same dimension together. 

    +SELECT ('{0,1,5}'::float8[]::madlib.svec + '{4,3,2}'::float8[]::madlib.svec)::float8[];
+

    Result: 

    + float8
+ --------
+ {4,4,7}
+

    Without the casting into float8[] at the end, we get: 

    +SELECT '{0,1,5}'::float8[]::madlib.svec + '{4,3,2}'::float8[]::madlib.svec;
+

    Result: 

    + ?column?
+ ---------
+{2,1}:{4,7}
+

    A dot product (%*%) between the two vectors will result in a scalar result of type float8. The dot product should be (0*4 + 1*3 + 5*2) = 13, like this: 

    +SELECT '{0,1,5}'::float8[]::madlib.svec %*% '{4,3,2}'::float8[]::madlib.svec;
+
    + ?column?
+ ---------
+    13
+

    Special vector aggregate functions are also available. SUM is self explanatory. SVEC_COUNT_NONZERO evaluates the count of non-zero terms in each column found in a set of n-dimensional svecs and returns an svec with the counts. For instance, if we have the vectors {0,1,5}, {10,0,3},{0,0,3},{0,1,0}, then executing the SVEC_COUNT_NONZERO() aggregate function would result in {1,2,3}:

    +
    +CREATE TABLE list (a madlib.svec);
+INSERT INTO list VALUES ('{0,1,5}'::float8[]), ('{10,0,3}'::float8[]), ('{0,0,3}'::float8[]),('{0,1,0}'::float8[]);
+SELECT madlib.svec_count_nonzero(a)::float8[] FROM list;
+

    Result: 

    +svec_count_nonzero
+ ----------------
+    {1,2,3}
+

    We do not use null bitmaps in the svec data type. A null value in an svec is represented explicitly as an NVP (No Value Present) value. For example, we have: 

    +SELECT '{1,2,3}:{4,null,5}'::madlib.svec;
+

    Result: 

    +      svec
+ ------------------
+ {1,2,3}:{4,NVP,5}
+

    Adding svecs with null values results in NVPs in the sum: 

    +SELECT '{1,2,3}:{4,null,5}'::madlib.svec + '{2,2,2}:{8,9,10}'::madlib.svec;
+

    Result: 

    +         ?column?
+  -------------------------
+  {1,2,1,2}:{12,NVP,14,15}
+

    An element of an svec can be accessed using the svec_proj() function, which takes an svec and the index of the element desired. 

    +SELECT madlib.svec_proj('{1,2,3}:{4,5,6}'::madlib.svec, 1) + madlib.svec_proj('{4,5,6}:{1,2,3}'::madlib.svec, 15);
+

    Result: 

     ?column?
+ ---------
+    7
+

    A subvector of an svec can be accessed using the svec_subvec() function, which takes an svec and the start and end index of the subvector desired. 

    +SELECT madlib.svec_subvec('{2,4,6}:{1,3,5}'::madlib.svec, 2, 11);
+

    Result: 

       svec_subvec
+ ----------------
+ {1,4,5}:{1,3,5}
+

    The elements/subvector of an svec can be changed using the function svec_change(). It takes three arguments: an m-dimensional svec sv1, a start index j, and an n-dimensional svec sv2 such that j + n - 1 <= m, and returns an svec like sv1 but with the subvector sv1[j:j+n-1] replaced by sv2. An example follows: 

    +SELECT madlib.svec_change('{1,2,3}:{4,5,6}'::madlib.svec,3,'{2}:{3}'::madlib.svec);
+

    Result: 

         svec_change
+ --------------------
+ {1,1,2,2}:{4,5,3,6}
+

    There are also higher-order functions for processing svecs. For example, the following is the corresponding function for lapply() in R. 

    +SELECT madlib.svec_lapply('sqrt', '{1,2,3}:{4,5,6}'::madlib.svec);
+

    Result: 

    +                  svec_lapply
+ ----------------------------------------------
+ {1,2,3}:{2,2.23606797749979,2.44948974278318}
+

    The full list of functions available for operating on svecs are available in svec.sql-in.

    +

    A More Extensive Example

    +

    For a text classification example, let's assume we have a dictionary composed of words in a sorted text array: 

    +CREATE TABLE features (a text[]);
+INSERT INTO features VALUES
+            ('{am,before,being,bothered,corpus,document,i,in,is,me,
+               never,now,one,really,second,the,third,this,until}');
+

    We have a set of documents, each represented as an array of words: 

    +CREATE TABLE documents(a int,b text[]);
+INSERT INTO documents VALUES
+            (1,'{this,is,one,document,in,the,corpus}'),
+            (2,'{i,am,the,second,document,in,the,corpus}'),
+            (3,'{being,third,never,really,bothered,me,until,now}'),
+            (4,'{the,document,before,me,is,the,third,document}');
+

    Now we have a dictionary and some documents, we would like to do some document categorization using vector arithmetic on word counts and proportions of dictionary words in each document.

    +

    To start this process, we'll need to find the dictionary words in each document. We'll prepare what is called a Sparse Feature Vector or SFV for each document. An SFV is a vector of dimension N, where N is the number of dictionary words, and in each cell of an SFV is a count of each dictionary word in the document.

    +

    Inside the sparse vector library, we have a function that will create an SFV from a document, so we can just do this (For a more efficient way for converting documents into sparse vectors, especially for larger datasets, please refer to Document Vectorization into Sparse Vectors):

    +
    +SELECT madlib.svec_sfv((SELECT a FROM features LIMIT 1),b)::float8[]
+         FROM documents;
+

    Result: 

    +                svec_sfv
+ ----------------------------------------
+ {0,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0}
+ {0,0,1,1,0,0,0,0,0,1,1,1,0,1,0,0,1,0,1}
+ {1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,2,0,0,0}
+ {0,1,0,0,0,2,0,0,1,1,0,0,0,0,0,2,1,0,0}
+

    Note that the output of madlib.svec_sfv() is an svec for each document containing the count of each of the dictionary words in the ordinal positions of the dictionary. This can more easily be understood by lining up the feature vector and text like this:

    +
    +SELECT madlib.svec_sfv((SELECT a FROM features LIMIT 1),b)::float8[]
+                , b
+         FROM documents;
+

    Result: 

    +                svec_sfv                 |                        b
+ ----------------------------------------+--------------------------------------------------
+ {1,0,0,0,1,1,1,1,0,0,0,0,0,0,1,2,0,0,0} | {i,am,the,second,document,in,the,corpus}
+ {0,1,0,0,0,2,0,0,1,1,0,0,0,0,0,2,1,0,0} | {the,document,before,me,is,the,third,document}
+ {0,0,0,0,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0} | {this,is,one,document,in,the,corpus}
+ {0,0,1,1,0,0,0,0,0,1,1,1,0,1,0,0,1,0,1} | {being,third,never,really,bothered,me,until,now}
+
    +SELECT * FROM features;
+
    +                                                a
+ -------------------------------------------------------------------------------------------------------
+{am,before,being,bothered,corpus,document,i,in,is,me,never,now,one,really,second,the,third,this,until}
+

    Now when we look at the document "i am the second document in the corpus", its SFV is {1,3*0,1,1,1,1,6*0,1,2}. The word "am" is the first ordinate in the dictionary and there is 1 instance of it in the SFV. The word "before" has no instances in the document, so its value is "0" and so on.

    +

    The function madlib.svec_sfv() can process large numbers of documents into their SFVs in parallel at high speed.

    +

    The rest of the categorization process is all vector math. The actual count is hardly ever used. Instead, it's turned into a weight. The most common weight is called tf/idf for Term Frequency / Inverse Document Frequency. The calculation for a given term in a given document is

    +
    +{#Times in document} * log {#Documents / #Documents the term appears in}.
+

    For instance, the term "document" in document A would have weight 1 * log (4/3). In document D, it would have weight 2 * log (4/3). Terms that appear in every document would have tf/idf weight 0, since log (4/4) = log(1) = 0. (Our example has no term like that.) That usually sends a lot of values to 0.

    +

    For this part of the processing, we'll need to have a sparse vector of the dictionary dimension (19) with the values 

    +log(#documents/#Documents each term appears in).
+

    There will be one such vector for the whole list of documents (aka the "corpus"). The #documents is just a count of all of the documents, in this case 4, but there is one divisor for each dictionary word and its value is the count of all the times that word appears in the document. This single vector for the whole corpus can then be scalar product multiplied by each document SFV to produce the Term Frequency/Inverse Document Frequency weights.

    +

    This can be done as follows: 

    +CREATE TABLE corpus AS
+            (SELECT a, madlib.svec_sfv((SELECT a FROM features LIMIT 1),b) sfv
+         FROM documents);
+CREATE TABLE weights AS
+          (SELECT a docnum, madlib.svec_mult(sfv, logidf) tf_idf
+           FROM (SELECT madlib.svec_log(madlib.svec_div(count(sfv)::madlib.svec,madlib.svec_count_nonzero(sfv))) logidf
+                FROM corpus) foo, corpus ORDER BYdocnum);
+SELECT * FROM weights;
+

    Result 

    +docnum |                tf_idf
+ ------+----------------------------------------------------------------------
+     1 | {4,1,1,1,2,3,1,2,1,1,1,1}:{0,0.69,0.28,0,0.69,0,1.38,0,0.28,0,1.38,0}
+     2 | {1,3,1,1,1,1,6,1,1,3}:{1.38,0,0.69,0.28,1.38,0.69,0,1.38,0.57,0}
+     3 | {2,2,5,1,2,1,1,2,1,1,1}:{0,1.38,0,0.69,1.38,0,1.38,0,0.69,0,1.38}
+     4 | {1,1,3,1,2,2,5,1,1,2}:{0,1.38,0,0.57,0,0.69,0,0.57,0.69,0}
+

    We can now get the "angular distance" between one document and the rest of the documents using the ACOS of the dot product of the document vectors: The following calculates the angular distance between the first document and each of the other documents: 

    +SELECT docnum,
+                180. * ( ACOS( madlib.svec_dmin( 1., madlib.svec_dot(tf_idf, testdoc)
+                    / (madlib.svec_l2norm(tf_idf)*madlib.svec_l2norm(testdoc))))/3.141592654) angular_distance
+         FROM weights,(SELECT tf_idf testdoc FROM weights WHERE docnum = 1 LIMIT 1) foo
+         ORDER BY 1;
+

    Result: 

    +docnum | angular_distance
+ -------+------------------
+     1 |                0
+     2 | 78.8235846096986
+     3 | 89.9999999882484
+     4 | 80.0232034288617
+

    We can see that the angular distance between document 1 and itself is 0 degrees and between document 1 and 3 is 90 degrees because they share no features at all. The angular distance can now be plugged into machine learning algorithms that rely on a distance measure between data points.

    +

    SVEC also provides functionality for declaring array given an array of positions and array of values, intermediate values betweens those are declared to be base value that user provides in the same function call. In the example below the fist array of integers represents the positions for the array two (array of floats). Positions do not need to come in the sorted order. Third value represents desired maximum size of the array. This assures that array is of that size even if last position is not. If max size < 1 that value is ignored and array will end at the last position in the position vector. Final value is a float representing the base value to be used between the declared ones (0 would be a common candidate):

    +
    +SELECT madlib.svec_cast_positions_float8arr(ARRAY[1,2,7,5,87],ARRAY[.1,.2,.7,.5,.87],90,0.0);
+

    Result: 

    +        svec_cast_positions_float8arr
+ ----------------------------------------------------
+{1,1,2,1,1,1,79,1,3}:{0.1,0.2,0,0.5,0,0.7,0,0.87,0}
+(1 row)
+

    Related Topics
    +

    Other examples of svecs usage can be found in the k-means module, k-Means Clustering.

    +

    File svec.sql_in documenting the SQL functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__svm.html b/docs/docs/v2.1.0/group__grp__svm.html new file mode 100644 index 00000000..a2f17a07 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__svm.html @@ -0,0 +1,861 @@ + + + + + + + + +MADlib: Support Vector Machines + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Support Vector Machines
    Supervised Learning
    +
    +
    +
    Contents +

    Support vector machines are models for regression and classification tasks. SVM models have two particularly desirable features: robustness in the presence of noisy data and applicability to a variety of data configurations. At its core, a linear SVM model is a hyperplane separating two distinct classes of data (in the case of classification problems), in such a way that the distance between the hyperplane and the nearest training data point (called the margin) is maximized. Vectors that lie on this margin are called support vectors. With the support vectors fixed, perturbations of vectors beyond the margin will not affect the model; this contributes to the model’s robustness. By substituting a kernel function for the usual inner product, one can approximate a large variety of decision boundaries in addition to linear hyperplanes.

    Classification Training Function
    The SVM binary classification training function has the following format: 
    +svm_classification(
+    source_table,
+    model_table,
+    dependent_varname,
+    independent_varname,
+    kernel_func,
+    kernel_params,
+    grouping_col,
+    params,
+    verbose
+    )
+
    Arguments
    +
    source_table
    +

    TEXT. Name of the table containing the training data.

    +

    +
    +
    model_table
    +

    TEXT. Name of the output table containing the model. Details of the output tables are provided below.

    +

    +
    +
    dependent_varname
    +

    TEXT. Name of the dependent variable column. For classification, this column can contain values of any type, but must assume exactly two distinct values since only binary classification is currently supported.

    +

    +
    +
    independent_varname
    +

    TEXT. Expression list to evaluate for the independent variables. An intercept variable should not be included as part of this expression. See 'fit_intercept' in the kernel params for info on intercepts. Please note that expression should be able to be cast to DOUBLE PRECISION[].

    +

    +
    +
    kernel_func (optional)
    +

    TEXT, default: 'linear'. Type of kernel. Currently three kernel types are supported: 'linear', 'gaussian', and 'polynomial'. The text can be any subset of the three strings; for e.g., kernel_func='ga' will create a Gaussian kernel.

    +

    +
    +
    kernel_params (optional)
    +

    TEXT, defaults: NULL. Parameters for non-linear kernel in a comma-separated string of key-value pairs. The actual parameters differ depending on the value of kernel_func. See the description below for details.

    +

    +
    +
    grouping_col (optional)
    +

    TEXT, default: NULL. An expression list used to group the input dataset into discrete groups, which results in running one model per group. Similar to the SQL "GROUP BY" clause. When this value is NULL, no grouping is used and a single model is generated. Please note that cross validation is not supported if grouping is used.

    +

    +
    +
    params (optional)
    +

    TEXT, default: NULL. Parameters for optimization and regularization in a comma-separated string of key-value pairs. If a list of values is provided, then cross-validation will be performed to select the best value from the list. See the description below for details.

    +

    +
    +
    verbose (optional)
    +
    BOOLEAN default: FALSE. Verbose output of the results of training.
    +
    +
    +

    Output tables
    + The model table produced by SVM contains the following columns:

    + + + + + + + + + + + + + + + + +
    coef FLOAT8. Vector of coefficients.
    grouping_key TEXT Identifies the group to which the datum belongs.
    num_rows_processed BIGINT. Numbers of rows processed.
    num_rows_skipped BIGINT. Numbers of rows skipped due to missing values or failures.
    num_iterations INTEGER. Number of iterations completed by stochastic gradient descent algorithm. The algorithm either converged in this number of iterations or hit the maximum number specified in the optimization parameters.
    loss FLOAT8. Value of the objective function of SVM, expressed as an average loss per row over the source_table. See Technical Background section below for more details.
    norm_of_gradient FLOAT8. Value of the L2-norm of the (sub)-gradient of the objective function.
    __dep_var_mapping TEXT[]. Vector of dependent variable labels. The first entry corresponds to -1 and the second to +1. For internal use only.
    +

    An auxiliary table named <model_table>_random is created if the kernel is not linear. It contains data needed to embed test data into a random feature space (see references [2,3]). This data is used internally by svm_predict and not meaningful on its own to the user, so you can ignore it.

    +

    A summary table named <model_table>_summary is also created, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    method 'svm'
    version_number Version of MADlib which was used to generate the model.
    source_table The data source table name.
    model_table The model table name.
    dependent_varname The dependent variable.
    independent_varname The independent variables.
    kernel_func The kernel function.
    kernel_parameters The kernel parameters, as well as random feature map data.
    grouping_col Columns on which to group.
    optim_params A string containing the optimization parameters.
    reg_params A string containing the regularization parameters.
    num_all_groups Number of groups in SVM training.
    num_failed_groups Number of failed groups in SVM training.
    total_rows_processed Total numbers of rows processed in all groups.
    total_rows_skipped Total numbers of rows skipped in all groups due to missing values or failures.
    +

    If cross validation is used, a table is created with a user specified name having the following columns:

    + + + + + + +
    ... Names of cross validation parameters
    mean_score Mean value of accuracy when predicted on the validation fold, averaged over all folds and all rows.
    std_dev_score Standard deviation of accuracy when predicted on the validation fold, averaged over all folds and all rows.
    +

    Regression Training Function
    The SVM regression training function has the following format: 
    +svm_regression(source_table,
+    model_table,
+    dependent_varname,
+    independent_varname,
+    kernel_func,
+    kernel_params,
+    grouping_col,
+    params,
+    verbose
+    )
+
    +

    Arguments

    +

    Specifications for regression are largely the same as for classification. In the model table, there is no dependent variable mapping. The following arguments have specifications which differ from svm_classification:

    +
    dependent_varname
    +
    TEXT. Name of the dependent variable column. For regression, this column can contain only values or expressions that can be cast to DOUBLE PRECISION. Otherwise, an error will be thrown.
    +
    params (optional)
    +
    TEXT, default: NULL. The parameters epsilon and eps_table are only meaningful for regression. See description below for more details.
    +
    +

    Novelty Detection Training Function
    The novelty detection function is a one-class SVM classifier, and has the following format: 
    +svm_one_class(
+    source_table,
+    model_table,
+    independent_varname,
+    kernel_func,
+    kernel_params,
+    grouping_col,
+    params,
+    verbose
+    )
+
    Arguments
    +

    Specifications for novelty detection are largely the same as for classification, except the dependent variable name is not specified. The model table is the same as that for classification.

    +

    Kernel Parameters
    Kernel parameters are supplied in a string containing a comma-delimited list of name-value pairs. All of these named parameters are optional, and their order does not matter. You must use the format "<param_name> = <value>" to specify the value of a parameter, otherwise the parameter is ignored.
    +
    +
    Parameters common to all kernels
    +
    +
    fit_intercept
    +
    Default: True. The parameter fit_intercept is an indicator to add an intercept to the independent_varname array expression. The intercept is added to the end of the feature list - thus the last element of the coefficient list is the intercept.
    +
    n_components
    +
    Default: max(100, 2*num_features). The dimensionality of the transformed feature space. A larger value lowers the variance of the estimate of the kernel but requires more memory and takes longer to train.
    Note
    Setting the n_components kernel parameter properly is important to generate an accurate decision boundary and can make the difference between a good model and a useless model. Try increasing the value of n_components if you are not getting an accurate decision boundary. This parameter arises from using the primal formulation, in which we map data into a relatively low-dimensional randomized feature space [2, 3]. The parameter n_components is the dimension of that feature space. We use the primal in MADlib to support scaling to large data sets, compared to R or other single node implementations that use the dual formulation and hence do not have this type of mapping, since the the dimensionality of the transformed feature space in the dual is effectively infinite.
    +
    +
    random_state
    +
    Default: 1. Seed used by a random number generator.
    +
    +
    +
    Parameters for 'gaussian' kernel
    +
    +
    gamma
    +
    Default: 1/num_features. The parameter \(\gamma\) in the Radius Basis Function kernel, i.e., \(\exp(-\gamma||x-y||^2)\). Choosing a proper value for gamma is critical to the performance of kernel machine; e.g., while a large gamma tends to cause overfitting, a small gamma will make the model too constrained to capture the complexity of the data.
    +
    +
    +
    Parameters for 'polynomial' kernel
    +
    +
    coef0
    +
    Default: 1.0. The independent term \(q\) in \( (\langle x,y\rangle + q)^r \). Must be larger than or equal to 0. When it is 0, the polynomial kernel is in homogeneous form.
    +
    degree
    +
    Default: 3. The parameter \(r\) in \( (\langle x,y\rangle + q)^r \).
    +
    +

    Other Parameters
    Parameters in this section are supplied in the params argument as a string containing a comma-delimited list of name-value pairs. All of these named parameters are optional, and their order does not matter. You must use the format "<param_name> = <value>" to specify the value of a parameter, otherwise the parameter is ignored.
    +

    Hyperparameter optimization can be carried out using the built-in cross validation mechanism, which is activated by assigning a value greater than 1 to the parameter n_folds in params. Please note that cross validation is not supported if grouping is used.

    +

    The values of a parameter to cross validate should be provided in a list. For example, if one wanted to regularize with the L1 norm and use a lambda value from the set {0.3, 0.4, 0.5}, one might input 'lambda={0.3, 0.4, 0.5}, norm=L1, n_folds=10' in params. Note that the use of '{}' and '[]' are both valid here.

    Note
    Note that not all of the parameters below can be cross-validated. For parameters where cross validation is allowed, their default values are presented in list format; e.g., [0.01].
    +
    +  'init_stepsize = <value>,
+   decay_factor = <value>,
+   max_iter = <value>,
+   tolerance = <value>,
+   lambda = <value>,
+   norm = <value>,
+   epsilon = <value>,
+   eps_table = <value>,
+   validation_result = <value>,
+   n_folds = <value>,
+   class_weight = <value>'
+

    Parameters

    +
    init_stepsize
    +

    Default: [0.01]. Also known as the initial learning rate. A small value is usually desirable to ensure convergence, while a large value provides more room for progress during training. Since the best value depends on the condition number of the data, in practice one often searches in an exponential grid using built-in cross validation; e.g., "init_stepsize = [1, 0.1, 0.001]". To reduce training time, it is common to run cross validation on a subsampled dataset, since this usually provides a good estimate of the condition number of the whole dataset. Then the resulting init_stepsize can be run on the whole dataset.

    +

    +

    +
    +
    decay_factor
    +

    Default: [0.9]. Control the learning rate schedule: 0 means constant rate; <-1 means inverse scaling, i.e., stepsize = init_stepsize / iteration; > 0 means <exponential decay, i.e., stepsize = init_stepsize * decay_factor^iteration.

    +

    +
    +
    max_iter
    +

    Default: [100]. The maximum number of iterations allowed.

    +

    +
    +
    tolerance
    +

    Default: 1e-10. The criterion to end iterations. The training stops whenever the difference between the training models of two consecutive iterations is smaller than tolerance or the iteration number is larger than max_iter.

    +

    +
    +
    lambda
    +

    Default: [0.01]. Regularization parameter. Must be non-negative.

    +

    +
    +
    norm
    +

    Default: 'L2'. Name of the regularization, either 'L2' or 'L1'.

    +

    +
    +
    epsilon
    +

    Default: [0.01]. Determines the \(\epsilon\) for \(\epsilon\)-regression. Ignored during classification. When training the model, differences of less than \(\epsilon\) between estimated labels and actual labels are ignored. A larger \(\epsilon\) will yield a model with fewer support vectors, but will not generalize as well to future data. Generally, it has been suggested that epsilon should increase with noisier data, and decrease with the number of samples. See [5].

    +

    +
    +
    eps_table
    +

    Default: NULL. Name of the input table that contains values of epsilon for different groups. Ignored when grouping_col is NULL. Define this input table if you want different epsilon values for different groups. The table consists of a column named epsilon which specifies the epsilon values, and one or more columns for grouping_col. Extra groups are ignored, and groups not present in this table will use the epsilon value specified in parameter epsilon.

    +

    +
    +
    validation_result
    +

    Default: NULL. Name of the table to store the cross validation scores. This table is only created if the name is not NULL. The cross validation scores are the mean and standard deviation of the accuracy when predicted on the validation fold, averaged over all folds and all rows. For classification, the accuracy metric used is the ratio of correct classifications. For regression, the accuracy metric used is the negative of mean squared error (negative to make it a concave problem, thus selecting max means the highest accuracy).

    +

    +
    +
    n_folds
    +

    Default: 0. Number of folds (k). Must be at least 2 to activate cross validation. If a value of k > 2 is specified, each fold is then used as a validation set once, while the other k - 1 folds form the training set.

    +

    +
    +
    class_weight
    +

    Default: NULL for classification, 'balanced' for one-class novelty detection, this param is not applicable for regression.

    +

    Set the weight for the classes. If not given (empty/NULL), all classes are set to have equal weight. If 'class_weight = balanced', values of y are automatically adjusted as inversely proportional to class frequencies in the input data i.e. the weights are set as n_samples / (2 * bincount(y)).

    +

    Alternatively, 'class_weight' can be a mapping, giving the weight for each class. E.g., for dependent variable values 'a' and 'b', the 'class_weight' might be {a: 1, b: 3}. This gives three times the weight to observations with class value 'b' compared to 'a'. (In the SVM algorithm, this translates into observations with class value 'b' contributing 3x to learning in the stochastic gradient step compared to 'a'.)

    +

    For regression, the class weights are always one.

    +
    +
    +

    Prediction Function
    The prediction function is used to estimate the conditional mean given a new predictor. The same syntax is used for classification, regression and novelty detection: 
    +svm_predict(model_table,
+            new_data_table,
+            id_col_name,
+            output_table)
+
    +

    Arguments

    +
    model_table
    +

    TEXT. Model table produced by the training function.

    +

    +
    +
    new_data_table
    +

    TEXT. Name of the table containing the prediction data. This table is expected to contain the same features that were used during training. The table should also contain id_col_name used for identifying each row.

    +

    +
    +
    id_col_name
    +

    TEXT. The name of the id column in the input table.

    +

    +
    +
    output_table
    +
    TEXT. Name of the table where output predictions are written. If this table name is already in use, then an error is returned. Table contains: + + + + + + +
    id Gives the 'id' for each prediction, corresponding to each row from the new_data_table.
    prediction Provides the prediction for each row in new_data_table. For regression this would be the same as decision_function. For classification, this will be one of the dependent variable values.
    decision_function Provides the distance between each point and the separating hyperplane.
    +
    +
    +

    Examples
    +

    Classification

    +
      +
    1. Create an input data set. 
      +DROP TABLE IF EXISTS houses;
+CREATE TABLE houses (id INT, tax INT, bedroom INT, bath FLOAT, price INT,
+            size INT, lot INT);
+INSERT INTO houses VALUES
+  (1 ,  590 ,       2 ,    1 ,  50000 ,  770 , 22100),
+  (2 , 1050 ,       3 ,    2 ,  85000 , 1410 , 12000),
+  (3 ,   20 ,       3 ,    1 ,  22500 , 1060 ,  3500),
+  (4 ,  870 ,       2 ,    2 ,  90000 , 1300 , 17500),
+  (5 , 1320 ,       3 ,    2 , 133000 , 1500 , 30000),
+  (6 , 1350 ,       2 ,    1 ,  90500 ,  820 , 25700),
+  (7 , 2790 ,       3 ,  2.5 , 260000 , 2130 , 25000),
+  (8 ,  680 ,       2 ,    1 , 142500 , 1170 , 22000),
+  (9 , 1840 ,       3 ,    2 , 160000 , 1500 , 19000),
+ (10 , 3680 ,       4 ,    2 , 240000 , 2790 , 20000),
+ (11 , 1660 ,       3 ,    1 ,  87000 , 1030 , 17500),
+ (12 , 1620 ,       3 ,    2 , 118600 , 1250 , 20000),
+ (13 , 3100 ,       3 ,    2 , 140000 , 1760 , 38000),
+ (14 , 2070 ,       2 ,    3 , 148000 , 1550 , 14000),
+ (15 ,  650 ,       3 ,  1.5 ,  65000 , 1450 , 12000);
+
      2. +
    2. Train linear classification model and view the model. Categorical variable is price < $100,0000. 
      +DROP TABLE IF EXISTS houses_svm, houses_svm_summary;
+SELECT madlib.svm_classification('houses',
+                                 'houses_svm',
+                                 'price < 100000',
+                                 'ARRAY[1, tax, bath, size]'
+                           );
+-- Set extended display on for easier reading of output
+\x on
+SELECT * FROM houses_svm;
+
      +-[ RECORD 1 ]------+--------------------------------------------------------------------------------
+coef               | {0.103994021495116,-0.00288252192097756,0.0540748706580464,0.00131729978010033}
+loss               | 0.928463796644648
+norm_of_gradient   | 7849.34910604307
+num_iterations     | 100
+num_rows_processed | 15
+num_rows_skipped   | 0
+dep_var_mapping    | {f,t}
+
      3. +
    3. Predict using linear model. We want to predict if house price is less than $100,000. We use the training data set for prediction as well, which is not usual but serves to show the syntax. The predicted results are in the prediction column and the actual data is in the actual column. 
      +DROP TABLE IF EXISTS houses_pred;
+SELECT madlib.svm_predict('houses_svm',
+                          'houses',
+                          'id',
+                          'houses_pred');
+\x off
+SELECT *, price < 100000 AS actual FROM houses JOIN houses_pred USING (id) ORDER BY id;
+
      +  id | tax  | bedroom | bath | price  | size |  lot  | prediction | decision_function  | actual
+----+------+---------+------+--------+------+-------+------------+--------------------+--------
+  1 |  590 |       2 |    1 |  50000 |  770 | 22100 | t          |  0.211310440574799 | t
+  2 | 1050 |       3 |    2 |  85000 | 1410 | 12000 | t          |   0.37546191651855 | t
+  3 |   20 |       3 |    1 |  22500 | 1060 |  3500 | t          |    2.4021783278516 | t
+  4 |  870 |       2 |    2 |  90000 | 1300 | 17500 | t          |   0.63967342411632 | t
+  5 | 1320 |       3 |    2 | 133000 | 1500 | 30000 | f          | -0.179964783767855 | f
+  6 | 1350 |       2 |    1 |  90500 |  820 | 25700 | f          |  -1.78347623159173 | t
+  7 | 2790 |       3 |  2.5 | 260000 | 2130 | 25000 | f          |  -2.86795504439645 | f
+  8 |  680 |       2 |    1 | 142500 | 1170 | 22000 | t          |  0.811108105668757 | f
+  9 | 1840 |       3 |    2 | 160000 | 1500 | 19000 | f          |  -1.61739505790168 | f
+ 10 | 3680 |       4 |    2 | 240000 | 2790 | 20000 | f          |  -3.96700444824078 | f
+ 11 | 1660 |       3 |    1 |  87000 | 1030 | 17500 | f          |  -2.19489938920329 | t
+ 12 | 1620 |       3 |    2 | 118600 | 1250 | 20000 | f          |  -1.53961627668269 | f
+ 13 | 3100 |       3 |    2 | 140000 | 1760 | 38000 | f          |  -4.54881979553637 | f
+ 14 | 2070 |       2 |    3 | 148000 | 1550 | 14000 | f          |  -2.06911803381861 | f
+ 15 |  650 |       3 |  1.5 |  65000 | 1450 | 12000 | t          |   1.52704061329968 | t
+(15 rows)
+
      Count the miss-classifications: 
      +SELECT COUNT(*) FROM houses_pred JOIN houses USING (id)
+WHERE houses_pred.prediction != (houses.price < 100000);
+
      + count
+-------+
+     3
+
      4. +
    4. Train using Gaussian kernel. This time we specify the initial step size and maximum number of iterations to run. As part of the kernel parameter, we choose 10 as the dimension of the space where we train SVM. As a result, the model will be a 10 dimensional vector, instead of 4 as in the case of linear model. 
      +DROP TABLE IF EXISTS houses_svm_gaussian, houses_svm_gaussian_summary, houses_svm_gaussian_random;
+SELECT madlib.svm_classification( 'houses',
+                                  'houses_svm_gaussian',
+                                  'price < 100000',
+                                  'ARRAY[1, tax, bath, size]',
+                                  'gaussian',
+                                  'n_components=10',
+                                  '',
+                                  'init_stepsize=1, max_iter=200'
+                           );
+\x on
+SELECT * FROM houses_svm_gaussian;
+
      +-[ RECORD 1 ]------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+coef               | {-1.67275666209207,1.5191640881642,-0.503066422926727,1.33250956564454,2.23009854231314,-0.0602475029497936,1.97466397155921,2.3668779833279,0.577739846910355,2.81255996089824}
+loss               | 0.0571869097340991
+norm_of_gradient   | 1.18281830047046
+num_iterations     | 177
+num_rows_processed | 15
+num_rows_skipped   | 0
+dep_var_mapping    | {f,t}
+
      5. +
    5. Prediction using the Gaussian model. The predicted results are in the prediction column and the actual data is in the actual column. 
      +DROP TABLE IF EXISTS houses_pred_gaussian;
+SELECT madlib.svm_predict('houses_svm_gaussian',
+                          'houses',
+                          'id',
+                          'houses_pred_gaussian');
+\x off
+SELECT *, price < 100000 AS actual FROM houses JOIN houses_pred_gaussian USING (id) ORDER BY id;
+
      + id | tax  | bedroom | bath | price  | size |  lot  | prediction | decision_function  | actual
+----+------+---------+------+--------+------+-------+------------+--------------------+--------
+  1 |  590 |       2 |    1 |  50000 |  770 | 22100 | t          |   1.89855833083557 | t
+  2 | 1050 |       3 |    2 |  85000 | 1410 | 12000 | t          |   1.47736856649617 | t
+  3 |   20 |       3 |    1 |  22500 | 1060 |  3500 | t          |  0.999999992995691 | t
+  4 |  870 |       2 |    2 |  90000 | 1300 | 17500 | t          |  0.999999989634351 | t
+  5 | 1320 |       3 |    2 | 133000 | 1500 | 30000 | f          |  -1.03645694166465 | f
+  6 | 1350 |       2 |    1 |  90500 |  820 | 25700 | t          |   1.16430515664766 | t
+  7 | 2790 |       3 |  2.5 | 260000 | 2130 | 25000 | f          | -0.545622670134529 | f
+  8 |  680 |       2 |    1 | 142500 | 1170 | 22000 | f          |  -1.00000000207512 | f
+  9 | 1840 |       3 |    2 | 160000 | 1500 | 19000 | f          |   -1.4748622470053 | f
+ 10 | 3680 |       4 |    2 | 240000 | 2790 | 20000 | f          |  -1.00085274698056 | f
+ 11 | 1660 |       3 |    1 |  87000 | 1030 | 17500 | t          |    1.8614251155696 | t
+ 12 | 1620 |       3 |    2 | 118600 | 1250 | 20000 | f          |  -1.77616417509695 | f
+ 13 | 3100 |       3 |    2 | 140000 | 1760 | 38000 | f          |  -1.07759348149549 | f
+ 14 | 2070 |       2 |    3 | 148000 | 1550 | 14000 | f          |  -3.42475835116536 | f
+ 15 |  650 |       3 |  1.5 |  65000 | 1450 | 12000 | t          |   1.00000008401961 | t
+(15 rows)
+
      Count the miss-classifications. Note this produces a more accurate result than the linear case for this data set: 
      +SELECT COUNT(*) FROM houses_pred_gaussian JOIN houses USING (id)
+WHERE houses_pred_gaussian.prediction != (houses.price < 100000);
+
      + count
+-------+
+     0
+(1 row)
+
      6. +
    6. In the case of an unbalanced class-size dataset, use the 'balanced' parameter to classify when building the model: 
      +DROP TABLE IF EXISTS houses_svm_gaussian, houses_svm_gaussian_summary, houses_svm_gaussian_random;
+SELECT madlib.svm_classification( 'houses',
+                                  'houses_svm_gaussian',
+                                  'price < 150000',
+                                  'ARRAY[1, tax, bath, size]',
+                                  'gaussian',
+                                  'n_components=10',
+                                  '',
+                                  'init_stepsize=1, max_iter=200, class_weight=balanced'
+                           );
+\x on
+SELECT * FROM houses_svm_gaussian;
+
      +-[ RECORD 1 ]------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+coef               | {0.891926151039837,0.169282494673541,-2.26539133689874,0.526518499596676,-0.900664505989526,0.508112011288015,-0.355474591147659,1.23127975981665,1.53694964239487,1.46496058633682}
+loss               | 0.56900274445785
+norm_of_gradient   | 0.989597662458527
+num_iterations     | 183
+num_rows_processed | 15
+num_rows_skipped   | 0
+dep_var_mapping    | {f,t}
+
      7. +
    +

    Regression

    +
      +
    1. Create input data set. For regression we use part of the well known abalone data set https://archive.ics.uci.edu/ml/datasets/abalone : 
      +DROP TABLE IF EXISTS abalone;
+CREATE TABLE abalone (id INT, sex TEXT, length FLOAT, diameter FLOAT, height FLOAT, rings INT);
+INSERT INTO abalone VALUES
+(1,'M',0.455,0.365,0.095,15),
+(2,'M',0.35,0.265,0.09,7),
+(3,'F',0.53,0.42,0.135,9),
+(4,'M',0.44,0.365,0.125,10),
+(5,'I',0.33,0.255,0.08,7),
+(6,'I',0.425,0.3,0.095,8),
+(7,'F',0.53,0.415,0.15,20),
+(8,'F',0.545,0.425,0.125,16),
+(9,'M',0.475,0.37,0.125,9),
+(10,'F',0.55,0.44,0.15,19),
+(11,'F',0.525,0.38,0.14,14),
+(12,'M',0.43,0.35,0.11,10),
+(13,'M',0.49,0.38,0.135,11),
+(14,'F',0.535,0.405,0.145,10),
+(15,'F',0.47,0.355,0.1,10),
+(16,'M',0.5,0.4,0.13,12),
+(17,'I',0.355,0.28,0.085,7),
+(18,'F',0.44,0.34,0.1,10),
+(19,'M',0.365,0.295,0.08,7),
+(20,'M',0.45,0.32,0.1,9);
+
      2. +
    2. Train a linear regression model: 
      +DROP TABLE IF EXISTS abalone_svm_regression, abalone_svm_regression_summary;
+SELECT madlib.svm_regression('abalone',
+                             'abalone_svm_regression',
+                             'rings',
+                             'ARRAY[1, length, diameter, height]'
+                           );
+\x on
+SELECT * FROM abalone_svm_regression;
+
      +-[ RECORD 1 ]------+-----------------------------------------------------------------------
+coef               | {1.998949892503,0.918517478913099,0.712125856084095,0.229379472956877}
+loss               | 8.29033295818392
+norm_of_gradient   | 23.225177785827
+num_iterations     | 100
+num_rows_processed | 20
+num_rows_skipped   | 0
+dep_var_mapping    | {NULL}
+
      3. +
    3. Predict using the linear regression model: 
      +DROP TABLE IF EXISTS abalone_regr;
+SELECT madlib.svm_predict('abalone_svm_regression',
+                          'abalone',
+                          'id',
+                          'abalone_regr');
+\x off
+SELECT * FROM abalone JOIN abalone_regr USING (id) ORDER BY id;
+
      + id | sex | length | diameter | height | rings |    prediction    | decision_function
+----+-----+--------+----------+--------+-------+------------------+-------------------
+  1 | M   |  0.455 |    0.365 |  0.095 |    15 | 2.69859240928376 |  2.69859240928376
+  2 | M   |   0.35 |    0.265 |   0.09 |     7 | 2.52978857282818 |  2.52978857282818
+  3 | F   |   0.53 |     0.42 |  0.135 |     9 | 2.81582333426116 |  2.81582333426116
+  4 | M   |   0.44 |    0.365 |  0.125 |    10 | 2.69169603073001 |  2.69169603073001
+  5 | I   |   0.33 |    0.255 |   0.08 |     7 | 2.50200316683054 |  2.50200316683054
+  6 | I   |  0.425 |      0.3 |  0.095 |     8 | 2.62474869654157 |  2.62474869654157
+  7 | F   |   0.53 |    0.415 |   0.15 |    20 | 2.81570339722408 |  2.81570339722408
+  8 | F   |  0.545 |    0.425 |  0.125 |    16 | 2.83086793257882 |  2.83086793257882
+  9 | M   |  0.475 |     0.37 |  0.125 |     9 | 2.72740477577673 |  2.72740477577673
+ 10 | F   |   0.55 |     0.44 |   0.15 |    19 |  2.8518768970598 |   2.8518768970598
+ 11 | F   |  0.525 |     0.38 |   0.14 |    14 | 2.78389260680315 |  2.78389260680315
+ 12 | M   |   0.43 |     0.35 |   0.11 |    10 | 2.66838827339779 |  2.66838827339779
+ 13 | M   |   0.49 |     0.38 |  0.135 |    11 | 2.75059759385832 |  2.75059759385832
+ 14 | F   |  0.535 |    0.405 |  0.145 |    10 | 2.81202782833915 |  2.81202782833915
+ 15 | F   |   0.47 |    0.355 |    0.1 |    10 | 2.70639581129576 |  2.70639581129576
+ 16 | M   |    0.5 |      0.4 |   0.13 |    12 | 2.77287839069521 |  2.77287839069521
+ 17 | I   |  0.355 |     0.28 |  0.085 |     7 | 2.54391615211472 |  2.54391615211472
+ 18 | F   |   0.44 |     0.34 |    0.1 |    10 | 2.66815839489651 |  2.66815839489651
+ 19 | M   |  0.365 |    0.295 |   0.08 |     7 | 2.56263631931732 |  2.56263631931732
+ 20 | M   |   0.45 |     0.32 |    0.1 |     9 | 2.66310105219146 |  2.66310105219146
+(20 rows)
+
      RMS error: 
      +SELECT SQRT(AVG((rings-prediction)*(rings-prediction))) as rms_error FROM abalone
+JOIN abalone_regr USING (id);
+
      +    rms_error
+-----------------+
+ 9.0884271818321
+(1 row)
+
      4. +
    4. Train a non-linear regression model using a Gaussian kernel: 
      DROP TABLE IF EXISTS abalone_svm_gaussian_regression, abalone_svm_gaussian_regression_summary, abalone_svm_gaussian_regression_random;
+SELECT madlib.svm_regression( 'abalone',
+                              'abalone_svm_gaussian_regression',
+                              'rings',
+                              'ARRAY[1, length, diameter, height]',
+                              'gaussian',
+                              'n_components=10',
+                              '',
+                              'init_stepsize=1, max_iter=200'
+                           );
+\x on
+SELECT * FROM abalone_svm_gaussian_regression;
+
      +-[ RECORD 1 ]------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+coef               | {4.49016341280977,2.19062972461334,-2.04673653356154,1.11216153651262,2.83478599238881,-4.23122821845785,4.17684533744501,-5.36892552740644,0.775782561685621,-3.62606941016707}
+loss               | 2.66850539541894
+norm_of_gradient   | 0.97440079536379
+num_iterations     | 163
+num_rows_processed | 20
+num_rows_skipped   | 0
+dep_var_mapping    | {NULL}
+
      5. +
    5. Predict using Gaussian regression model: 
      +DROP TABLE IF EXISTS abalone_gaussian_regr;
+SELECT madlib.svm_predict('abalone_svm_gaussian_regression',
+                          'abalone',
+                          'id',
+                          'abalone_gaussian_regr');
+\x off
+SELECT * FROM abalone JOIN abalone_gaussian_regr USING (id) ORDER BY id;
+
      + id | sex | length | diameter | height | rings |    prediction    | decision_function
+----+-----+--------+----------+--------+-------+------------------+-------------------
+  1 | M   |  0.455 |    0.365 |  0.095 |    15 | 9.92189555675422 |  9.92189555675422
+  2 | M   |   0.35 |    0.265 |   0.09 |     7 | 9.81553107620013 |  9.81553107620013
+  3 | F   |   0.53 |     0.42 |  0.135 |     9 | 10.0847384862759 |  10.0847384862759
+  4 | M   |   0.44 |    0.365 |  0.125 |    10 | 10.0100000075406 |  10.0100000075406
+  5 | I   |   0.33 |    0.255 |   0.08 |     7 | 9.74093262454458 |  9.74093262454458
+  6 | I   |  0.425 |      0.3 |  0.095 |     8 | 9.94807651709641 |  9.94807651709641
+  7 | F   |   0.53 |    0.415 |   0.15 |    20 | 10.1448936105369 |  10.1448936105369
+  8 | F   |  0.545 |    0.425 |  0.125 |    16 | 10.0579420659954 |  10.0579420659954
+  9 | M   |  0.475 |     0.37 |  0.125 |     9 |  10.055724626407 |   10.055724626407
+ 10 | F   |   0.55 |     0.44 |   0.15 |    19 | 10.1225030222559 |  10.1225030222559
+ 11 | F   |  0.525 |     0.38 |   0.14 |    14 |  10.160706707435 |   10.160706707435
+ 12 | M   |   0.43 |     0.35 |   0.11 |    10 | 9.95760174386841 |  9.95760174386841
+ 13 | M   |   0.49 |     0.38 |  0.135 |    11 | 10.0981242315617 |  10.0981242315617
+ 14 | F   |  0.535 |    0.405 |  0.145 |    10 | 10.1501121415596 |  10.1501121415596
+ 15 | F   |   0.47 |    0.355 |    0.1 |    10 | 9.97689437628973 |  9.97689437628973
+ 16 | M   |    0.5 |      0.4 |   0.13 |    12 | 10.0633271219326 |  10.0633271219326
+ 17 | I   |  0.355 |     0.28 |  0.085 |     7 | 9.79492924255328 |  9.79492924255328
+ 18 | F   |   0.44 |     0.34 |    0.1 |    10 | 9.94856833428783 |  9.94856833428783
+ 19 | M   |  0.365 |    0.295 |   0.08 |     7 | 9.78278863173308 |  9.78278863173308
+ 20 | M   |   0.45 |     0.32 |    0.1 |     9 | 9.98822477687532 |  9.98822477687532
+(20 rows)
+
      Compute the RMS error. Note this produces a more accurate result than the linear case for this data set: 
      +SELECT SQRT(AVG((rings-prediction)*(rings-prediction))) as rms_error FROM abalone
+JOIN abalone_gaussian_regr USING (id);
+
      +    rms_error
+------------------+
+ 3.83678516581768
+(1 row)
+
      6. +
    6. Cross validation. Let's run cross validation for different initial step sizes and lambda values: 
      +DROP TABLE IF EXISTS abalone_svm_gaussian_regression, abalone_svm_gaussian_regression_summary,
+abalone_svm_gaussian_regression_random, abalone_svm_gaussian_regression_cv;
+SELECT madlib.svm_regression( 'abalone',
+                              'abalone_svm_gaussian_regression',
+                              'rings',
+                              'ARRAY[1, length, diameter, height]',
+                              'gaussian',
+                              'n_components=10',
+                              '',
+                              'init_stepsize=[0.01,1], n_folds=3, max_iter=100, lambda=[0.01, 0.1, 0.5],
+                              validation_result=abalone_svm_gaussian_regression_cv'
+                           );
+\x on
+SELECT * FROM abalone_svm_gaussian_regression;
+
      +-[ RECORD 1 ]------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+coef               | {4.78843909576373,1.82443514279869,-2.36814051329038,1.48570658714655,1.77828407859486,-6.38446590203159,3.99631488328669,-6.52441625480202,3.82342434407222,-3.67579802967837}
+loss               | 2.5002301320973
+norm_of_gradient   | 0.692031063542266
+num_iterations     | 100
+num_rows_processed | 20
+num_rows_skipped   | 0
+dep_var_mapping    | {NULL}
+
      View the summary table showing the final model parameters are those that produced the lowest error in the cross validation runs: 
      +SELECT * FROM abalone_svm_gaussian_regression_summary;
+
      +-[ RECORD 1 ]--------+------------------------------------------------------------------------------------
+method               | SVR
+version_number       | 2.1.0
+source_table         | abalone
+model_table          | abalone_svm_gaussian_regression
+dependent_varname    | rings
+independent_varname  | ARRAY[1, length, diameter, height]
+kernel_func          | gaussian
+kernel_params        | gamma=0.25, n_components=10,random_state=1, fit_intercept=False, fit_in_memory=True
+grouping_col         | NULL
+optim_params         | init_stepsize=1.0,
+                     | decay_factor=0.9,
+                     | max_iter=100,
+                     | tolerance=1e-10,
+                     | epsilon=0.01,
+                     | eps_table=,
+                     | class_weight=
+reg_params           | lambda=0.01, norm=l2, n_folds=3
+num_all_groups       | 1
+num_failed_groups    | 0
+total_rows_processed | 20
+total_rows_skipped   | 0
      7. +
    +
    (6 rows)
+

    View the statistics for the various cross validation values: 

    +\x off
+SELECT * FROM abalone_svm_gaussian_regression_cv;
+
    + init_stepsize | lambda |   mean_score   | std_dev_score
+---------------+--------+----------------+---------------
+          0.01 |    0.5 | -10.3718064203 | 1.70034854924
+           1.0 |    0.5 | -4.03598164681 | 2.03645607616
+          0.01 |   0.01 | -10.3424727426 | 1.70103511744
+          0.01 |    0.1 | -10.3479312204 | 1.70090715482
+           1.0 |   0.01 | -3.59999345219 | 1.80351978881
+           1.0 |    0.1 | -3.74710586166 | 1.91455355654
+(6 rows)
+
      +
    1. Predict using the cross-validated Gaussian regression model: 
      +DROP TABLE IF EXISTS abalone_gaussian_regr;
+SELECT madlib.svm_predict('abalone_svm_gaussian_regression',
+                          'abalone',
+                          'id',
+                          'abalone_gaussian_regr');
+
      Compute the RMS error. Note this produces a more accurate result than the previous run with the Gaussian kernel: 
      +SELECT SQRT(AVG((rings-prediction)*(rings-prediction))) as rms_error FROM abalone
+JOIN abalone_gaussian_regr USING (id);
+
      +    rms_error
+------------------+
+ 3.64653492872019
+(1 row)
+
      2. +
    +

    Novelty Detection

    +
      +
    1. Now train a non-linear one-class SVM for novelty detection, using a Gaussian kernel. Note that the dependent variable is not a parameter for one-class: 
      +DROP TABLE IF EXISTS houses_one_class_gaussian, houses_one_class_gaussian_summary, houses_one_class_gaussian_random;
+SELECT madlib.svm_one_class('houses',
+                            'houses_one_class_gaussian',
+                            'ARRAY[1,tax,bedroom,bath,size,lot,price]',
+                            'gaussian',
+                            'gamma=0.5,n_components=55, random_state=3',
+                            NULL,
+                            'max_iter=100, init_stepsize=10,lambda=10, tolerance=0'
+                            );
+\x on
+SELECT * FROM houses_one_class_gaussian;
+
      Result: 
      +-[ RECORD 1 ]------+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+coef               | {redacted for brevity}
+loss               | 0.944016313708205
+norm_of_gradient   | 14.5271059047443
+num_iterations     | 100
+num_rows_processed | 16
+num_rows_skipped   | -1
+dep_var_mapping    | {-1,1}
+
      2. +
    2. For the novelty detection using one-class, let's create a test data set using the last 3 values from the training set plus an outlier at the end (10x price): 
      +DROP TABLE IF EXISTS houses_one_class_test;
+CREATE TABLE houses_one_class_test (id INT, tax INT, bedroom INT, bath FLOAT, price INT,
+            size INT, lot INT);
+INSERT INTO houses_one_class_test VALUES
+ (1 , 3100 ,       3 ,    2 , 140000 , 1760 , 38000),
+ (2 , 2070 ,       2 ,    3 , 148000 , 1550 , 14000),
+ (3 ,  650 ,       3 ,  1.5 ,  65000 , 1450 , 12000),
+ (4 ,  650 ,       3 ,  1.5 ,  650000 , 1450 , 12000);
+
      Now run prediction on the Gaussian one-class novelty detection model. Result shows the last row predicted to be novel: 
      +DROP TABLE IF EXISTS houses_pred;
+SELECT madlib.svm_predict('houses_one_class_gaussian',
+                          'houses_one_class_test',
+                          'id',
+                          'houses_pred');
+\x off
+SELECT * FROM houses_one_class_test JOIN houses_pred USING (id) ORDER BY id;
+
      Result showing the last row predicted to be novel: 
      + id | tax  | bedroom | bath | price  | size |  lot  | prediction |  decision_function
+----+------+---------+------+--------+------+-------+------------+---------------------
+  1 | 3100 |       3 |    2 | 140000 | 1760 | 38000 |          1 |   0.111497008121437
+  2 | 2070 |       2 |    3 | 148000 | 1550 | 14000 |          1 |  0.0996021345169148
+  3 |  650 |       3 |  1.5 |  65000 | 1450 | 12000 |          1 |  0.0435064008756942
+  4 |  650 |       3 |  1.5 | 650000 | 1450 | 12000 |         -1 | -0.0168967845338403
+
      3. +
    +

    Technical Background
    +

    To solve linear SVM, the following objective function is minimized:

    +\[ \underset{w,b}{\text{Minimize }} \lambda||w||^2 + \frac{1}{n}\sum_{i=1}^n \ell(y_i,f_{w,b}(x_i)) \] +

    +

    where \((x_1,y_1),\ldots,(x_n,y_n)\) are labeled training data and \(\ell(y,f(x))\) is a loss function. When performing classification, \(\ell(y,f(x)) = \max(0,1-yf(x))\) is the hinge loss. For regression, the loss function \(\ell(y,f(x)) = \max(0,|y-f(x)|-\epsilon)\) is used.

    +

    If \( f_{w,b}(x) = \langle w, x\rangle + b\) is linear, then the objective function is convex and incremental gradient descent (IGD, or SGD) can be applied to find a global minimum. See Feng, et al. [1] for more details.

    +

    To learn with Gaussian or polynomial kernels, the training data is first mapped via a random feature map in such a way that the usual inner product in the feature space approximates the kernel function in the input space. The linear SVM training function is then run on the resulting data. See the papers [2,3] for more information on random feature maps.

    +

    Also, see the book [4] by Scholkopf and Smola for more details on SVMs in general.

    +

    Literature
    +

    [1] Xixuan Feng, Arun Kumar, Ben Recht, and Christopher Re: Towards a Unified Architecture for in-RDBMS analytics, in SIGMOD Conference, 2012 http://www.eecs.berkeley.edu/~brecht/papers/12.FengEtAl.SIGMOD.pdf

    +

    [2] Purushottam Kar and Harish Karnick: Random Feature Maps for Dot Product Kernels, Proceedings of the 15th International Conference on Artificial Intelligence and Statistics, 2012, http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2012_KarK12.pdf

    +

    [3] Ali Rahmini and Ben Recht: Random Features for Large-Scale Kernel Machines, Neural Information Processing Systems 2007, http://www.eecs.berkeley.edu/~brecht/papers/07.rah.rec.nips.pdf

    +

    [4] Bernhard Scholkopf and Alexander Smola: Learning with Kernels, The MIT Press, Cambridge, MA, 2002.

    +

    [5] Vladimir Cherkassky and Yunqian Ma: Practical Selection of SVM Parameters and Noise Estimation for SVM Regression, Neural Networks, 2004 http://www.ece.umn.edu/users/cherkass/N2002-SI-SVM-13-whole.pdf

    +

    Related Topics
    +

    File svm.sql_in documenting the training function

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__text__utilities.html b/docs/docs/v2.1.0/group__grp__text__utilities.html new file mode 100644 index 00000000..824e235c --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__text__utilities.html @@ -0,0 +1,349 @@ + + + + + + + + +MADlib: Term Frequency + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Term Frequency
    Utilities
    +
    +
    +
    Contents +

    Term frequency computes the number of times that a word or term occurs in a document. Term frequency is often used as part of a larger text processing pipeline, which may include operations such as stemming, stop word removal and topic modelling.

    +

    Function Syntax
    +
    +    term_frequency(input_table,
+                   doc_id_col,
+                   word_col,
+                   output_table,
+                   compute_vocab)
+

    Arguments:

    +
    input_table
    +

    TEXT. The name of the table containing the documents, with one document per row. Each row is in the form <doc_id, word_vector> where doc_id is an id unique to each document, and word_vector is a text array containing the words in the document. The word_vector should contain multiple entries of a word if the document contains multiple occurrence of that word.

    +

    +
    +
    doc_id_col
    +

    TEXT. The name of the column containing the document id.

    +

    +
    +
    word_col
    +

    TEXT. The name of the column containing the vector of words/terms in the document. This column should be of type that can be cast to TEXT[].

    +

    +
    +
    output_table
    +

    TEXT. The name of the table to store the term frequency output. The output table contains the following columns:

      +
    • doc_id_col: This the document id column (name will be same as the one provided as input).
      • +
    • word: Word/term present in a document. Depending on the value of compute_vocab below, this is either the original word as it appears in word_col, or an id representing the word. Note that word id's start from 0 not 1.
      • +
    • count: The number of times this word is found in the document.
      • +
    +

    +
    +
    compute_vocab
    +
    BOOLEAN. (Optional, Default=FALSE) Flag to indicate if a vocabulary table is to be created. If TRUE, an additional output table is created containing the vocabulary of all words, with an id assigned to each word in alphabetical order. The table is called output_table_vocabulary (i.e., suffix added to the output_table name) and contains the following columns:
      +
    • wordid: An id for each word in alphabetical order.
      • +
    • word: The word/term corresponding to the id.
      • +
    +
    +
    +

    Examples
    +
      +
    1. First we create a document table with one document per row: 
      +DROP TABLE IF EXISTS documents;
+CREATE TABLE documents(docid INT4, contents TEXT);
+INSERT INTO documents VALUES
+(0, 'I like to eat broccoli and bananas. I ate a banana and spinach smoothie for breakfast.'),
+(1, 'Chinchillas and kittens are cute.'),
+(2, 'My sister adopted two kittens yesterday.'),
+(3, 'Look at this cute hamster munching on a piece of broccoli.');
+
      You can apply stemming, stop word removal and tokenization at this point in order to prepare the documents for text processing. Depending upon your database version, various tools are available. Databases based on more recent versions of PostgreSQL may do something like: 
      +SELECT tsvector_to_array(to_tsvector('english',contents)) from documents;
+
      +                    tsvector_to_array
++----------------------------------------------------------
+ {ate,banana,breakfast,broccoli,eat,like,smoothi,spinach}
+ {chinchilla,cute,kitten}
+ {adopt,kitten,sister,two,yesterday}
+ {broccoli,cute,hamster,look,munch,piec}
+(4 rows)
+
      In this example, we assume a database based on an older version of PostgreSQL and just perform basic punctuation removal and tokenization. The array of words is added as a new column to the documents table: 
      +ALTER TABLE documents ADD COLUMN words TEXT[];
+UPDATE documents SET words =
+    regexp_split_to_array(lower(
+    regexp_replace(contents, E'[,.;\']','', 'g')
+    ), E'[\\s+]');
+\x on
+SELECT * FROM documents ORDER BY docid;
+
      +-[ RECORD 1 ]------------------------------------------------------------------------------------
+docid    | 0
+contents | I like to eat broccoli and bananas. I ate a banana and spinach smoothie for breakfast.
+words    | {i,like,to,eat,broccoli,and,bananas,i,ate,a,banana,and,spinach,smoothie,for,breakfast}
+-[ RECORD 2 ]------------------------------------------------------------------------------------
+docid    | 1
+contents | Chinchillas and kittens are cute.
+words    | {chinchillas,and,kittens,are,cute}
+-[ RECORD 3 ]------------------------------------------------------------------------------------
+docid    | 2
+contents | My sister adopted two kittens yesterday.
+words    | {my,sister,adopted,two,kittens,yesterday}
+-[ RECORD 4 ]------------------------------------------------------------------------------------
+docid    | 3
+contents | Look at this cute hamster munching on a piece of broccoli.
+words    | {look,at,this,cute,hamster,munching,on,a,piece,of,broccoli}
+
      2. +
    2. Compute the frequency of each word in each document: 
      +DROP TABLE IF EXISTS documents_tf, documents_tf_vocabulary;
+SELECT madlib.term_frequency('documents',    -- input table
+                             'docid',        -- document id column
+                             'words',        -- vector of words in document
+                             'documents_tf'  -- output table
+                            );
+\x off
+SELECT * FROM documents_tf ORDER BY docid;
+
      + docid |    word     | count
+-------+-------------+-------
+     0 | a           |     1
+     0 | breakfast   |     1
+     0 | banana      |     1
+     0 | and         |     2
+     0 | eat         |     1
+     0 | smoothie    |     1
+     0 | to          |     1
+     0 | like        |     1
+     0 | broccoli    |     1
+     0 | bananas     |     1
+     0 | spinach     |     1
+     0 | i           |     2
+     0 | ate         |     1
+     0 | for         |     1
+     1 | are         |     1
+     1 | cute        |     1
+     1 | kittens     |     1
+     1 | chinchillas |     1
+     1 | and         |     1
+     2 | two         |     1
+     2 | yesterday   |     1
+     2 | kittens     |     1
+     2 | sister      |     1
+     2 | my          |     1
+     2 | adopted     |     1
+     3 | this        |     1
+     3 | at          |     1
+     3 | a           |     1
+     3 | broccoli    |     1
+     3 | of          |     1
+     3 | look        |     1
+     3 | hamster     |     1
+     3 | on          |     1
+     3 | piece       |     1
+     3 | cute        |     1
+     3 | munching    |     1
+(36 rows)
+
      3. +
    3. Next we create a vocabulary of the words and store a wordid in the output table instead of the actual word: 
      +DROP TABLE IF EXISTS documents_tf, documents_tf_vocabulary;
+SELECT madlib.term_frequency('documents',    -- input table
+                             'docid',        -- document id column
+                             'words',        -- vector of words in document
+                             'documents_tf',-- output table
+                             TRUE
+                            );
+SELECT * FROM documents_tf ORDER BY docid;
+
      + docid | wordid | count
+-------+--------+-------
+     0 |     17 |     1
+     0 |      9 |     1
+     0 |     25 |     1
+     0 |     12 |     1
+     0 |     13 |     1
+     0 |     15 |     2
+     0 |      0 |     1
+     0 |      2 |     2
+     0 |     28 |     1
+     0 |      5 |     1
+     0 |      6 |     1
+     0 |      7 |     1
+     0 |      8 |     1
+     0 |     26 |     1
+     1 |     16 |     1
+     1 |     11 |     1
+     1 |     10 |     1
+     1 |      2 |     1
+     1 |      3 |     1
+     2 |     30 |     1
+     2 |      1 |     1
+     2 |     16 |     1
+     2 |     20 |     1
+     2 |     24 |     1
+     2 |     29 |     1
+     3 |      4 |     1
+     3 |     21 |     1
+     3 |     22 |     1
+     3 |     23 |     1
+     3 |      0 |     1
+     3 |     11 |     1
+     3 |      9 |     1
+     3 |     27 |     1
+     3 |     14 |     1
+     3 |     18 |     1
+     3 |     19 |     1
+(36 rows)
+
      Note above that wordid's start at 0 not 1. The vocabulary table maps wordid to the actual word: 
      +SELECT * FROM documents_tf_vocabulary ORDER BY wordid;
+
      + wordid |    word
+--------+-------------
+      0 | a
+      1 | adopted
+      2 | and
+      3 | are
+      4 | at
+      5 | ate
+      6 | banana
+      7 | bananas
+      8 | breakfast
+      9 | broccoli
+     10 | chinchillas
+     11 | cute
+     12 | eat
+     13 | for
+     14 | hamster
+     15 | i
+     16 | kittens
+     17 | like
+     18 | look
+     19 | munching
+     20 | my
+     21 | of
+     22 | on
+     23 | piece
+     24 | sister
+     25 | smoothie
+     26 | spinach
+     27 | this
+     28 | to
+     29 | two
+     30 | yesterday
+(31 rows)
+
      4. +
    +

    Related Topics
    +

    See text_utilities.sql_in for the term frequency SQL function definition and porter_stemmer.sql_in for the stemmer function.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__topic__modelling.html b/docs/docs/v2.1.0/group__grp__topic__modelling.html new file mode 100644 index 00000000..e1e7f35b --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__topic__modelling.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: Topic Modelling + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Topic Modelling
    Unsupervised Learning
    +
    +
    +

    Detailed Description

    +

    A collection of methods to uncover abstract topics in a document corpus.

    + + + + + +

    +Modules

     Latent Dirichlet Allocation
     Generates a Latent Dirichlet Allocation predictive model for a collection of documents.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__topic__modelling.js b/docs/docs/v2.1.0/group__grp__topic__modelling.js new file mode 100644 index 00000000..249097bb --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__topic__modelling.js @@ -0,0 +1,4 @@ +var group__grp__topic__modelling = +[ + [ "Latent Dirichlet Allocation", "group__grp__lda.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__train__test__split.html b/docs/docs/v2.1.0/group__grp__train__test__split.html new file mode 100644 index 00000000..0fc5b393 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__train__test__split.html @@ -0,0 +1,298 @@ + + + + + + + + +MADlib: Train-Test Split + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Train-Test Split
    Model Selection
    +
    +
    +
    Contents +

    Train-test split is a utility to create training and testing sets from a single data set.

    +

    Train-Test Split
    +
    +train_test_split(   source_table,
+                    output_table,
+                    train_proportion,
+                    test_proportion,
+                    grouping_cols,
+                    target_cols,
+                    with_replacement,
+                    separate_output_tables
+                )
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the input data.

    +

    +
    +
    output_table
    +

    Name of output table. A new INTEGER column on the right called 'split' will identify 1 for train set and 0 for test set, unless the 'separate_output_tables' parameter below is TRUE, in which case two output tables will be created using the 'output_table' name with the suffixes '_train' and '_test'. The output table contains all the columns present in the source table unless otherwise specified in the 'target_cols' parameter below.

    +

    +
    +
    train_proportion
    +

    FLOAT8 in the range (0,1). Proportion of the dataset to include in the train split. If the 'grouping_col' parameter is specified below, each group will be sampled independently using the train proportion, i.e., in a stratified fashion.

    +

    +
    +
    test_proportion (optional)
    +

    FLOAT8 in the range (0,1). Proportion of the dataset to include in the test split. Default is the complement to the train proportion (1-'train_proportion'). If the 'grouping_col' parameter is specified below, each group will be sampled independently using the train proportion, i.e., in a stratified fashion.

    +

    +
    +
    grouping_cols (optional)
    +

    TEXT, default: NULL. A single column or a list of comma-separated columns that defines how to stratify. When this parameter is NULL, the train-test split is not stratified.

    +

    +
    +
    target_cols (optional)
    +

    TEXT, default NULL. A comma-separated list of columns to appear in the 'output_table'. If NULL or '*', all columns from the 'source_table' will appear in the 'output_table'.

    +

    Note
    Do not include 'grouping_cols' in the parameter 'target_cols', because they are always included in the 'output_table'.
    +
    +
    with_replacement (optional)
    +

    BOOLEAN, default FALSE. Determines whether to sample with replacement or without replacement (default). With replacement means that it is possible that the same row may appear in the sample set more than once. Without replacement means a given row can be selected only once.

    +

    +
    +
    separate_output_tables (optional)
    +
    BOOLEAN, default FALSE. If TRUE, two output tables will be created using the 'output_table' name with the suffixes '_train' and '_test'.
    +
    +

    Examples
    +

    Please note that due to the random nature of sampling, your results may look different from those below.

    +
      +
    1. Create an input table: 
      +DROP TABLE IF EXISTS test;
+CREATE TABLE test(
+    id1 INTEGER,
+    id2 INTEGER,
+    gr1 INTEGER,
+    gr2 INTEGER
+);
+INSERT INTO test VALUES
+(1,0,1,1),
+(2,0,1,1),
+(3,0,1,1),
+(4,0,1,1),
+(5,0,1,1),
+(6,0,1,1),
+(7,0,1,1),
+(8,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(9,0,1,1),
+(0,1,1,2),
+(0,2,1,2),
+(0,3,1,2),
+(0,4,1,2),
+(0,5,1,2),
+(0,6,1,2),
+(10,10,2,2),
+(20,20,2,2),
+(30,30,2,2),
+(40,40,2,2),
+(50,50,2,2),
+(60,60,2,2),
+(70,70,2,2);
+
      2. +
    2. Sample without replacement: 
      +DROP TABLE IF EXISTS out;
+SELECT madlib.train_test_split(
+                                'test',    -- Source table
+                                'out',     -- Output table
+                                0.5,       -- Sample proportion
+                                0.5,       -- Sample proportion
+                                'gr1,gr2', -- Strata definition
+                                'id1,id2', -- Columns to output
+                                FALSE,     -- Sample without replacement
+                                FALSE);    -- Do not separate output tables
+SELECT * FROM out ORDER BY split,gr1,gr2,id1,id2;
+
      + gr1 | gr2 | id1 | id2 | split
+-----+-----+-----+-----+-------
+   1 |   1 |   1 |   0 |     0
+   1 |   1 |   4 |   0 |     0
+   1 |   1 |   6 |   0 |     0
+   1 |   1 |   9 |   0 |     0
+   1 |   1 |   9 |   0 |     0
+   1 |   1 |   9 |   0 |     0
+   1 |   2 |   0 |   3 |     0
+   1 |   2 |   0 |   4 |     0
+   1 |   2 |   0 |   5 |     0
+   2 |   2 |  10 |  10 |     0
+   2 |   2 |  30 |  30 |     0
+   2 |   2 |  40 |  40 |     0
+   2 |   2 |  60 |  60 |     0
+   1 |   1 |   2 |   0 |     1
+   1 |   1 |   3 |   0 |     1
+   1 |   1 |   5 |   0 |     1
+   1 |   1 |   7 |   0 |     1
+   1 |   1 |   8 |   0 |     1
+   1 |   1 |   9 |   0 |     1
+   1 |   2 |   0 |   1 |     1
+   1 |   2 |   0 |   2 |     1
+   1 |   2 |   0 |   6 |     1
+   2 |   2 |  20 |  20 |     1
+   2 |   2 |  50 |  50 |     1
+   2 |   2 |  70 |  70 |     1
+(25 rows)
+
      3. +
    3. Sample with replacement and create separate train and test tables: 
      +DROP TABLE IF EXISTS out, out_train, out_test;
+SELECT madlib.train_test_split(
+                                'test',    -- Source table
+                                'out',     -- Output table
+                                0.5,       -- train_proportion
+                                NULL,      -- Default = 1 - train_proportion = 0.5
+                                'gr1,gr2', -- Strata definition
+                                'id1,id2', -- Columns to output
+                                TRUE,      -- Sample with replacement
+                                TRUE);     -- Separate output tables
+SELECT * FROM out_train ORDER BY gr1,gr2,id1,id2;
+
      + gr1 | gr2 | id1 | id2
+-----+-----+-----+-----
+   1 |   1 |   1 |   0
+   1 |   1 |   2 |   0
+   1 |   1 |   4 |   0
+   1 |   1 |   7 |   0
+   1 |   1 |   8 |   0
+   1 |   1 |   9 |   0
+   1 |   2 |   0 |   4
+   1 |   2 |   0 |   5
+   1 |   2 |   0 |   6
+   2 |   2 |  40 |  40
+   2 |   2 |  50 |  50
+   2 |   2 |  50 |  50
+(12 rows)
+
      +SELECT * FROM out_test ORDER BY gr1,gr2,id1,id2;
+
      + gr1 | gr2 | id1 | id2
+----—+----—+----—+---—
+   1 |   1 |   1 |   0
+   1 |   1 |   1 |   0
+   1 |   1 |   3 |   0
+   1 |   1 |   4 |   0
+   1 |   1 |   5 |   0
+   1 |   1 |   9 |   0
+   1 |   2 |   0 |   1
+   1 |   2 |   0 |   5
+   1 |   2 |   0 |   6
+   2 |   2 |  20 |  20
+   2 |   2 |  20 |  20
+   2 |   2 |  20 |  20
+   2 |   2 |  70 |  70
+(13 rows)
+
      4. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__tree.html b/docs/docs/v2.1.0/group__grp__tree.html new file mode 100644 index 00000000..b7edec72 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__tree.html @@ -0,0 +1,133 @@ + + + + + + + + +MADlib: Tree Methods + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Tree Methods
    Supervised Learning
    +
    +
    +

    Detailed Description

    +

    A collection of recursive partitioning (tree) methods.

    + + + + + + + + +

    +Modules

     Decision Tree
     Decision trees are tree-based supervised learning methods that can be used for classification and regression.
     
     Random Forest
     Random forest is an ensemble learning method for classification and regression that construct a multitude of decision trees at training time, then produces the class that is the mean (regression) or mode (classification) of the prediction produced by the individual trees.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__tree.js b/docs/docs/v2.1.0/group__grp__tree.js new file mode 100644 index 00000000..7e73e8c4 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__tree.js @@ -0,0 +1,5 @@ +var group__grp__tree = +[ + [ "Decision Tree", "group__grp__decision__tree.html", null ], + [ "Random Forest", "group__grp__random__forest.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__tsa.html b/docs/docs/v2.1.0/group__grp__tsa.html new file mode 100644 index 00000000..9fea4f70 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__tsa.html @@ -0,0 +1,130 @@ + + + + + + + + +MADlib: Time Series Analysis + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Time Series Analysis
    +
    +
    +

    Detailed Description

    +

    A collection of methods to analyze time series data.

    + + + + + +

    +Modules

     ARIMA
     Generates a model with autoregressive, moving average, and integrated components for a time series dataset.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__tsa.js b/docs/docs/v2.1.0/group__grp__tsa.js new file mode 100644 index 00000000..4895672a --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__tsa.js @@ -0,0 +1,4 @@ +var group__grp__tsa = +[ + [ "ARIMA", "group__grp__arima.html", null ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__unsupervised.html b/docs/docs/v2.1.0/group__grp__unsupervised.html new file mode 100644 index 00000000..e26eeeb9 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__unsupervised.html @@ -0,0 +1,139 @@ + + + + + + + + +MADlib: Unsupervised Learning + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Modules
    +
    +
    Unsupervised Learning
    +
    +
    +

    Detailed Description

    +

    A collection of methods for unsupervised learning tasks.

    + + + + + + + + + + + + + + +

    +Modules

     Association Rules
     Methods used to discover patterns in transactional datasets.
     
     Clustering
     Methods for clustering data.
     
     Dimensionality Reduction
     Methods for reducing the number of variables in a dataset to obtain a set of principle variables.
     
     Topic Modelling
     A collection of methods to uncover abstract topics in a document corpus.
     
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__unsupervised.js b/docs/docs/v2.1.0/group__grp__unsupervised.js new file mode 100644 index 00000000..26d22295 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__unsupervised.js @@ -0,0 +1,7 @@ +var group__grp__unsupervised = +[ + [ "Association Rules", "group__grp__association__rules.html", "group__grp__association__rules" ], + [ "Clustering", "group__grp__clustering.html", "group__grp__clustering" ], + [ "Dimensionality Reduction", "group__grp__pca.html", "group__grp__pca" ], + [ "Topic Modelling", "group__grp__topic__modelling.html", "group__grp__topic__modelling" ] +]; \ No newline at end of file diff --git a/docs/docs/v2.1.0/group__grp__utilities.html b/docs/docs/v2.1.0/group__grp__utilities.html new file mode 100644 index 00000000..16ce1659 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__utilities.html @@ -0,0 +1,168 @@ + + + + + + + + +MADlib: Database Functions + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
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    + +
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    +
    +
    Database Functions
    Utilities
    +
    +
    +
    Contents +

    Database functions are a collection of lower level utilities to assist data scientists and others in using MADlib.

    +

    Utility Functions
    + + + + + + + + + + + + + + + + + + + +
    version()

    Return MADlib build information.

    +

    +
    assert()

    Raise an exception if the given condition is not satisfied.

    +

    +
    check_if_raises_error()

    Check if a SQL statement raises an error.

    +

    +
    check_if_col_exists()

    Check if a column exists in a table.

    +

    +
    isnan()

    Check if a floating-point number is NaN (not a number)

    +

    +
    create_schema_pg_temp()

    Create the temporary schema if it does not exist yet.

    +

    +
    noop()

    Create volatile noop function.

    +

    +
    cleanup_madlib_temp_tables()

    Drop all tables matching pattern 'madlib_temp' in a given schema.

    +

    +
    dropcols()

    Create a new table with a subset of the columns dropped from a source table.

    +

    +
    +

    Note: If the function cleanup_madlib_temp_tables() gives an Out-of-memory error, then the number of tables to be dropped is too high to execute in one transaction. In such a case, please follow the instructions provided with the error to execute the command in multiple transactions.

    +

    Related Topics
    +

    File utilities.sql_in documenting the SQL functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__validation.html b/docs/docs/v2.1.0/group__grp__validation.html new file mode 100644 index 00000000..a1298a93 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__validation.html @@ -0,0 +1,405 @@ + + + + + + + + +MADlib: Cross Validation + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Cross Validation
    Model Selection
    +
    +
    +
    Contents +

    Estimates the fit of a predictive model given a data set and specifications for the training, prediction, and error estimation functions.

    +

    Cross validation, sometimes called rotation estimation, is a technique for assessing how the results of a statistical analysis will generalize to an independent data set. It is mainly used in settings where the goal is prediction, and you want to estimate how accurately a predictive model will perform in practice.

    +

    The cross-validation function provided by this module is very flexible and can work with algorithms you want to cross validate, including algorithms you write yourself. Among the inputs to the cross-validation function are specifications of the modelling, prediction, and error metric functions. These three-part specifications include the name of the function, an array of arguments to pass to the function, and an array of the data types of the arguments. This makes it possible to use functions from other MADlib modules or user-defined functions that you supply.

    +
      +
    • The modelling (training) function takes in a given data set with independent and dependent variables and produces a model, which is stored in an output table.
      • +
    • The prediction function takes in the model generated by the modelling function and a different data set with independent variables, and produces a prediction of the dependent variables based on the model, which is stored in an output table. The prediction function should take a unique ID column name in the data table as one of the inputs, so that the prediction result can be compared with the validation values. Note: Prediction function in some MADlib modules do not save results into an output table. These prediction functions are not suitable for this cross-validation module.
      • +
    • The error metric function compares the prediction results with the known values of the dependent variables in the data set that was fed into the prediction function. It computes the error metric using the specified error metric function, and stores the results in a table.
      • +
    +

    Other inputs include the output table name, k value for the k-fold cross validation, and how many folds to try. For example, you can choose to run a simple validation instead of a full cross validation.

    +

    Cross-Validation Function
    +
    +cross_validation_general( modelling_func,
+                          modelling_params,
+                          modelling_params_type,
+                          param_explored,
+                          explore_values,
+                          predict_func,
+                          predict_params,
+                          predict_params_type,
+                          metric_func,
+                          metric_params,
+                          metric_params_type,
+                          data_tbl,
+                          data_id,
+                          id_is_random,
+                          validation_result,
+                          data_cols,
+                          fold_num
+                        )

    Arguments

    +
    modelling_func
    +

    VARCHAR. The name of the function that trains the model.

    +

    +
    +
    modelling_params
    +

    VARCHAR[]. An array of parameters to supply to the modelling function.

    +

    +
    +
    modelling_params_type
    +

    VARCHAR[]. An array of data type names for each of the parameters supplied to the modelling function.

    +

    +
    +
    param_explored
    +

    VARCHAR. The name of the parameter that will be checked to find the optimum value. The name must appear in the modelling_params array.

    +

    +
    +
    explore_values
    +

    VARCHAR. The name of the parameter whose values are to be studied.

    +

    +
    +
    predict_func
    +

    VARCHAR. The name of the prediction function.

    +

    +
    +
    predict_params
    +

    VARCHAR[]. An array of parameters to supply to the prediction function.

    +

    +
    +
    predict_params_type
    +

    VARCHAR[]. An array of data type names for each of the parameters supplied to the prediction function.

    +

    +
    +
    metric_func
    +

    VARCHAR. The name of the function for measuring errors.

    +

    +
    +
    metric_params
    +

    VARCHAR[]. An array of parameters to supply to the error metric function.

    +

    +
    +
    metric_params_type
    +

    VARCHAR[]. An array of data type names for each of the parameters supplied to the metric function.

    +

    +
    +
    data_tbl
    +

    VARCHAR. The name of the data table that will be split into training and validation parts.

    +

    +
    +
    data_id
    +

    VARCHAR. The name of the column containing a unique ID associated with each row, or NULL if the table has no such column.

    +

    Ideally, the data set has a unique ID for each row so that it is easier to partition the data set into the training part and the validation part. Set the id_is_random argument to inform the cross-validation function whether the ID value is randomly assigned to each row. If it is not randomly assigned, the cross-validation function generates a random ID for each row.

    +

    +
    +
    id_is_random
    +

    BOOLEAN. TRUE if the provided ID is randomly assigned to each row.

    +

    +
    +
    validation_result
    +

    VARCHAR. The name of the table to store the output of the cross-validation function. The output table has the following columns:

    + + + + + + +
    param_explored The name of the parameter checked to find the optimum value. This is the same name specified in the param_explored argument of the cross_validation_general() function.
    average error The average of the errors computed by the error metric function.
    standard deviation of error The standard deviation of the errors.
    +

    +
    +
    data_cols
    +

    A comma-separated list of names of data columns to use in the calculation. When its value is NULL, the function will automatically figure out all the column names of the data table. This is only used if the data_id argument is NULL, otherwise it is ignored.

    +

    If the data set has no unique ID for each row, the cross-validation function copies the data set to a temporary table with a randomly assigned ID column. Setting this argument to the list of independent and dependent variables that are to be used in the calculation minimizes the copying workload by only copying the required data.

    +

    The new temporary table is dropped after the computation has finished.

    +
    +
    fold_num
    +
    INTEGER, default: 10. Value of k. How many folds validation? Each validation uses 1/fold_num fraction of the data for validation.
    +
    +

    The parameter arrays for the modelling, prediction and metric functions can include the following special keywords:

    +
      +
    • %data% – The argument position for training/validation data
      • +
    • %model% – The argument position for the output/input of modelling/prediction function
      • +
    • %id% – The argument position of the unique ID column (user-provided or generated by the cross-validation function, as described above)
      • +
    • %prediction% – The argument position for the output/input of prediction/metric function
      • +
    • %error% – The argument position for the output of the metric function
      • +
    +

    Note: If the argument explore_values is NULL or has zero length, then the cross-validation function will only run a data folding.

    +

    Examples
    +
      +
    1. Load some sample data: 
      +DROP TABLE IF EXISTS houses;
+CREATE TABLE houses ( id INT,
+                      tax INT,
+                      bedroom INT,
+                      bath FLOAT,
+                      size INT,
+                      lot INT,
+                      zipcode INT,
+                      price INT,
+                      high_priced BOOLEAN
+                      );
+INSERT INTO houses (id, tax, bedroom, bath, price, size, lot, zipcode, high_priced) VALUES
+(1  ,  590 ,       2 ,    1 ,  50000 ,  770 , 22100  , 94301, 'f'::boolean),
+(2  , 1050 ,       3 ,    2 ,  85000 , 1410 , 12000  , 94301, 'f'::boolean),
+(3  ,   20 ,       3 ,    1 ,  22500 , 1060 ,  3500  , 94301, 'f'::boolean),
+(4  ,  870 ,       2 ,    2 ,  90000 , 1300 , 17500  , 94301, 'f'::boolean),
+(5  , 1320 ,       3 ,    2 , 133000 , 1500 , 30000  , 94301, 't'::boolean),
+(6  , 1350 ,       2 ,    1 ,  90500 ,  820 , 25700  , 94301, 'f'::boolean),
+(7  , 2790 ,       3 ,  2.5 , 260000 , 2130 , 25000  , 94301, 't'::boolean),
+(8  ,  680 ,       2 ,    1 , 142500 , 1170 , 22000  , 94301, 't'::boolean),
+(9  , 1840 ,       3 ,    2 , 160000 , 1500 , 19000  , 94301, 't'::boolean),
+(10 , 3680 ,       4 ,    2 , 240000 , 2790 , 20000  , 94301, 't'::boolean),
+(11 , 1660 ,       3 ,    1 ,  87000 , 1030 , 17500  , 94301, 'f'::boolean),
+(12 , 1620 ,       3 ,    2 , 118600 , 1250 , 20000  , 94301, 't'::boolean),
+(13 , 3100 ,       3 ,    2 , 140000 , 1760 , 38000  , 94301, 't'::boolean),
+(14 , 2070 ,       2 ,    3 , 148000 , 1550 , 14000  , 94301, 't'::boolean),
+(15 ,  650 ,       3 ,  1.5 ,  65000 , 1450 , 12000  , 94301, 'f'::boolean),
+(16 ,  770 ,       2 ,    2 ,  91000 , 1300 , 17500  , 76010, 'f'::boolean),
+(17 , 1220 ,       3 ,    2 , 132300 , 1500 , 30000  , 76010, 't'::boolean),
+(18 , 1150 ,       2 ,    1 ,  91100 ,  820 , 25700  , 76010, 'f'::boolean),
+(19 , 2690 ,       3 ,  2.5 , 260011 , 2130 , 25000  , 76010, 't'::boolean),
+(20 ,  780 ,       2 ,    1 , 141800 , 1170 , 22000  , 76010, 't'::boolean),
+(21 , 1910 ,       3 ,    2 , 160900 , 1500 , 19000  , 76010, 't'::boolean),
+(22 , 3600 ,       4 ,    2 , 239000 , 2790 , 20000  , 76010, 't'::boolean),
+(23 , 1600 ,       3 ,    1 ,  81010 , 1030 , 17500  , 76010, 'f'::boolean),
+(24 , 1590 ,       3 ,    2 , 117910 , 1250 , 20000  , 76010, 'f'::boolean),
+(25 , 3200 ,       3 ,    2 , 141100 , 1760 , 38000  , 76010, 't'::boolean),
+(26 , 2270 ,       2 ,    3 , 148011 , 1550 , 14000  , 76010, 't'::boolean),
+(27 ,  750 ,       3 ,  1.5 ,  66000 , 1450 , 12000  , 76010, 'f'::boolean),
+(28 , 2690 ,       3 ,  2.5 , 260011 , 2130 , 25000  , 76010, 't'::boolean),
+(29 ,  780 ,       2 ,    1 , 141800 , 1170 , 22000  , 76010, 't'::boolean),
+(30 , 1910 ,       3 ,    2 , 160900 , 1500 , 19000  , 76010, 't'::boolean),
+(31 , 3600 ,       4 ,    2 , 239000 , 2790 , 20000  , 76010, 't'::boolean),
+(32 , 1600 ,       3 ,    1 ,  81010 , 1030 , 17500  , 76010, 'f'::boolean),
+(33 , 1590 ,       3 ,    2 , 117910 , 1250 , 20000  , 76010, 'f'::boolean),
+(34 , 3200 ,       3 ,    2 , 141100 , 1760 , 38000  , 76010, 't'::boolean),
+(35 , 2270 ,       2 ,    3 , 148011 , 1550 , 14000  , 76010, 't'::boolean),
+(36 ,  750 ,       3 ,  1.5 ,  66000 , 1450 , 12000  , 76010, 'f'::boolean);
+
      2. +
    2. Use the general function to explore lambda values for elastic net. (Note that elastic net also has a built in cross validation function for selecting elastic net control parameter alpha and regularization value lambda.) 
      +DROP TABLE IF EXISTS houses_cv_results;
+SELECT madlib.cross_validation_general(
+    -- modelling_func
+      'madlib.elastic_net_train',
+    -- modelling_params
+        '{%data%, %model%, price, "array[tax, bath, size]", gaussian, 0.5, lambda, TRUE, NULL, fista,
+          "{eta = 2, max_stepsize = 2, use_active_set = t}",
+          NULL, 200, 1e-6}'::varchar[],
+    -- modelling_params_type
+        '{varchar, varchar, varchar, varchar, varchar, double precision,
+          double precision, boolean, varchar, varchar, varchar, varchar,
+          integer, double precision}'::varchar[],
+    -- param_explored
+      'lambda',
+    -- explore_values
+      '{0.1, 0.2}'::varchar[],
+    -- predict_func
+      'madlib.elastic_net_predict',
+    -- predict_params
+        '{%model%, %data%, %id%, %prediction%}'::varchar[],
+    -- predict_params_type
+        '{text, text, text, text}'::varchar[],
+    -- metric_func
+      'madlib.mse_error',
+    -- metric_params
+        '{%prediction%, %data%, %id%, price, %error%}'::varchar[],
+    -- metric_params_type
+        '{varchar, varchar, varchar, varchar, varchar}'::varchar[],
+    -- data_tbl
+      'houses',
+    -- data_id
+      'id',
+    -- id_is_random
+      FALSE,
+    -- validation_result
+      'houses_cv_results',
+    -- data_cols
+      NULL,
+    -- fold_num
+      3
+);
+SELECT * FROM houses_cv_results;
+
      Results from the lambda values explored: 
      + lambda | mean_squared_error_avg | mean_squared_error_stddev
+--------+------------------------+---------------------------
+    0.1 |       1094965503.24269 |          411974996.039577
+    0.2 |       1093350170.40664 |          411072137.632718
+(2 rows)
+
      3. +
    3. Here we use the general function to explore maximum number of iterations for logistic regression: 
      +DROP TABLE IF EXISTS houses_logregr_cv;
+SELECT madlib.cross_validation_general(
+    -- modelling_func
+        'madlib.logregr_train',
+    -- modelling_params
+        '{%data%, %model%, high_priced, "ARRAY[1, bedroom, bath, size]", NULL, max_iter}'::varchar[],
+    -- modelling_params_type
+        '{varchar, varchar, varchar, varchar, varchar, integer}'::varchar[],
+    -- param_explored
+        'max_iter',
+    -- explore_values
+        '{2, 10, 40, 100}'::varchar[],
+    -- predict_func
+        'madlib.cv_logregr_predict',
+    -- predict_params
+        '{%model%, %data%, "ARRAY[1, bedroom, bath, size]", id, %prediction%}'::varchar[],
+    -- predict_params_type
+        '{varchar, varchar,varchar,varchar,varchar}'::varchar[],
+    -- metric_func
+        'madlib.misclassification_avg',
+    -- metric_params
+        '{%prediction%, %data%,  id, high_priced, %error%}'::varchar[],
+    -- metric_params_type
+        '{varchar, varchar, varchar, varchar, varchar}'::varchar[],
+    -- data_tbl
+        'houses',
+    -- data_id
+        'id',
+    -- id_is_random
+        FALSE,
+    -- validation_result
+        'houses_logregr_cv',
+    -- data_cols
+        NULL,
+    -- fold_num
+       5
+);
+SELECT * FROM houses_logregr_cv;
+
      Results from the explored number of iterations: 
      + max_iter |     error_rate_avg     |             error_rate_stddev
+----------+------------------------+--------------------------------------------
+        2 | 0.19285714285714285714 | 0.1589185390091927774733662830554976076700
+       10 | 0.22142857142857142857 | 0.1247446371183784331896638996881001527213
+       40 | 0.22142857142857142857 | 0.1247446371183784331896638996881001527213
+      100 | 0.22142857142857142857 | 0.1247446371183784331896638996881001527213
+(4 rows)
+
      4. +
    +

    Notes
    +

    The lock management parameter max_locks_per_transaction, which usually is set to the default value of 64, limits the number of tables that can be dropped inside a single transaction (the cross-validation function). Thus, the number of different values of param_explored (or the length of the explored_values array) cannot be too large. For 10-fold cross validation, the limit of length(explored_values) is around 40. If the limit is exceeded, you may get an "out of shared memory" error because max_locks_per_transaction is exceeded.

    +

    One way to overcome this limitation is to run the cross-validation function multiple times, with each run covering a different region of values of the parameter.

    +

    Note that MADlib implements cross-validation functions within certain individual modules, where it is possible to optimize the calculation to avoid dropping tables and prevent exceeding the max_locks_per_transaction limitation. Since module-specific cross-validation functions depend upon the implementation details of the modules to perform the optimization, they will not be as flexible as the generalized cross-validation function provided here.

    +

    Technical Background
    +

    One round of cross validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or test set). To reduce variability, multiple rounds of cross validation are performed using different partitions, and the validation results are averaged over the rounds.

    +

    In k-fold cross validation, the original sample is randomly partitioned into k equal sized subsamples. Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k−1 subsamples are used as training data. The cross-validation process is repeated k times (the folds), with each of the k subsamples used exactly once as the validation data. The k results from the folds can be averaged (or otherwise combined) to produce a single estimation. The advantage of this method over repeated random sub-sampling is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross validation is commonly used, but in general k remains an unfixed parameter.

    +

    Related Topics
    +

    File cross_validation.sql_in documenting the SQL functions.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__vec2cols.html b/docs/docs/v2.1.0/group__grp__vec2cols.html new file mode 100644 index 00000000..523865fb --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__vec2cols.html @@ -0,0 +1,323 @@ + + + + + + + + +MADlib: Vector to Columns + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Vector to Columns
    Utilities
    +
    +
    +
    Contents +
    About
    Converts a feature array in a single column into multiple columns. This process can be used to reverse the function cols2vec.
    +

    Given a table with a column of type array, this function will create an output table that splits this array into multiple columns, one per array element. It includes the option to name the new feature columns, and to include columns from the original table in the output.

    +

    Usage
    +
    +vec2cols(
+    source_table,
+    output_table,
+    vector_col,
+    feature_names,
+    cols_to_output
+)
+

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the source data..

    +

    +
    +
    output_table
    +

    TEXT. Name of the generated table containing the output. If a table with the same name already exists, an error will be returned.

    +

    +
    +
    vector_col
    +

    TEXT. Name of the column containing the feature array. Must be a one-dimensional array.

    +

    +
    +
    feature_names (optional)
    +
    TEXT[]. Array of names associated with the feature array. Note that this array exists in the summary table created by the function 'cols2vec'. If the 'feature_names' array is not specified, column names will be automatically generated of the form 'f1, f2, ...fn'.
    Note
    If you specify the 'feature_names' parameter, you will get exactly that number of feature columns in the 'output_table'. It means feature arrays from the 'vector_col' may be padded or truncated, if a particular feature array size does not match the target number of feature columns.
    +
    +If you do not specify the 'feature names' parameter, the number of feature columns generated in the 'output_table' will be the maximum array size from 'vector_col'. Feature arrays that are less than this maximum will be padded.
    +
    +
    cols_to_output (optional)
    +
    TEXT, default NULL. Comma-separated string of column names from the source table to keep in the output table, in addition to the feature columns. To keep all columns from the source table, use '*'. The total number of columns in a table cannot exceed the PostgreSQL limits.
    +
    +

    Output table
    + The output table produced by the vec2cols function contains the following columns:

    + + + + +
    <...> Columns from source table, depending on which ones are kept (if any).
    feature columns Columns for each of the features in 'vector_col'. Column type will depend on the feature array type in the source table. Column naming will depend on whether the parameter 'feature_names' is used.
    +

    Examples
      +
    1. Load sample data: 
      +DROP TABLE IF EXISTS golf CASCADE;
+CREATE TABLE golf (
+    id integer NOT NULL,
+    "OUTLOOK" text,
+    temperature double precision,
+    humidity double precision,
+    "Temp_Humidity" double precision[],
+    clouds_airquality text[],
+    windy boolean,
+    class text,
+    observation_weight double precision
+);
+INSERT INTO golf VALUES
+(1,'sunny', 85, 85, ARRAY[85, 85],ARRAY['none', 'unhealthy'], 'false','Don''t Play', 5.0),
+(2, 'sunny', 80, 90, ARRAY[80, 90], ARRAY['none', 'moderate'], 'true', 'Don''t Play', 5.0),
+(3, 'overcast', 83, 78, ARRAY[83, 78], ARRAY['low', 'moderate'], 'false', 'Play', 1.5),
+(4, 'rain', 70, 96, ARRAY[70, 96], ARRAY['low', 'moderate'], 'false', 'Play', 1.0),
+(5, 'rain', 68, 80, ARRAY[68, 80], ARRAY['medium', 'good'], 'false', 'Play', 1.0),
+(6, 'rain', 65, 70, ARRAY[65, 70], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play', 1.0),
+(7, 'overcast', 64, 65, ARRAY[64, 65], ARRAY['medium', 'moderate'], 'true', 'Play', 1.5),
+(8, 'sunny', 72, 95, ARRAY[72, 95], ARRAY['high', 'unhealthy'], 'false', 'Don''t Play', 5.0),
+(9, 'sunny', 69, 70, ARRAY[69, 70], ARRAY['high', 'good'], 'false', 'Play', 5.0),
+(10, 'rain', 75, 80, ARRAY[75, 80], ARRAY['medium', 'good'], 'false', 'Play', 1.0),
+(11, 'sunny', 75, 70, ARRAY[75, 70], ARRAY['none', 'good'], 'true', 'Play', 5.0),
+(12, 'overcast', 72, 90, ARRAY[72, 90], ARRAY['medium', 'moderate'], 'true', 'Play', 1.5),
+(13, 'overcast', 81, 75, ARRAY[81, 75], ARRAY['medium', 'moderate'], 'false', 'Play', 1.5),
+(14, 'rain', 71, 80, ARRAY[71, 80], ARRAY['low', 'unhealthy'], 'true', 'Don''t Play', 1.0);
+
      2. +
    2. Split the column "clouds_airquality" into new columns called "clouds" and "air_quality". Also keep columns id and "OUTLOOK" from the source table 
      +DROP TABLE IF EXISTS vec2cols_result;
+SELECT madlib.vec2cols(
+    'golf',                           -- source table
+    'vec2cols_result',                -- output table
+    'clouds_airquality',              -- column with array entries to split
+    ARRAY['clouds', 'air_quality'],   -- feature names
+    'id, "OUTLOOK"'                   -- columns to keep from source table
+);
+SELECT * FROM vec2cols_result ORDER BY id;
+
      + id | OUTLOOK  | clouds | air_quality
+----+----------+--------+-------------
+  1 | sunny    | none   | unhealthy
+  2 | sunny    | none   | moderate
+  3 | overcast | low    | moderate
+  4 | rain     | low    | moderate
+  5 | rain     | medium | good
+  6 | rain     | low    | unhealthy
+  7 | overcast | medium | moderate
+  8 | sunny    | high   | unhealthy
+  9 | sunny    | high   | good
+ 10 | rain     | medium | good
+ 11 | sunny    | none   | good
+ 12 | overcast | medium | moderate
+ 13 | overcast | medium | moderate
+ 14 | rain     | low    | unhealthy
+(14 rows)
+
      3. +
    3. Similar to the previous example, except now we keep all columns from source table and do not specify the feature names, so that default names are created. 
      +DROP TABLE IF EXISTS vec2cols_result;
+SELECT madlib.vec2cols(
+    'golf',                       -- source table
+    'vec2cols_result',            -- output table
+    'clouds_airquality',          -- column with array entries to split
+    NULL,                         -- feature names
+    '*'                           -- columns to keep from source table
+);
+SELECT * FROM vec2cols_result ORDER BY id;
+
      + id | OUTLOOK  | temperature | humidity | Temp_Humidity | clouds_airquality | windy |   class    | observation_weight |   f1   |    f2
+----+----------+-------------+----------+---------------+-------------------+-------+------------+--------------------+--------+-----------
+  1 | sunny    |          85 |       85 | {85,85}       | {none,unhealthy}  | f     | Don't Play |                  5 | none   | unhealthy
+  2 | sunny    |          80 |       90 | {80,90}       | {none,moderate}   | t     | Don't Play |                  5 | none   | moderate
+  3 | overcast |          83 |       78 | {83,78}       | {low,moderate}    | f     | Play       |                1.5 | low    | moderate
+  4 | rain     |          70 |       96 | {70,96}       | {low,moderate}    | f     | Play       |                  1 | low    | moderate
+  5 | rain     |          68 |       80 | {68,80}       | {medium,good}     | f     | Play       |                  1 | medium | good
+  6 | rain     |          65 |       70 | {65,70}       | {low,unhealthy}   | t     | Don't Play |                  1 | low    | unhealthy
+  7 | overcast |          64 |       65 | {64,65}       | {medium,moderate} | t     | Play       |                1.5 | medium | moderate
+  8 | sunny    |          72 |       95 | {72,95}       | {high,unhealthy}  | f     | Don't Play |                  5 | high   | unhealthy
+  9 | sunny    |          69 |       70 | {69,70}       | {high,good}       | f     | Play       |                  5 | high   | good
+ 10 | rain     |          75 |       80 | {75,80}       | {medium,good}     | f     | Play       |                  1 | medium | good
+ 11 | sunny    |          75 |       70 | {75,70}       | {none,good}       | t     | Play       |                  5 | none   | good
+ 12 | overcast |          72 |       90 | {72,90}       | {medium,moderate} | t     | Play       |                1.5 | medium | moderate
+ 13 | overcast |          81 |       75 | {81,75}       | {medium,moderate} | f     | Play       |                1.5 | medium | moderate
+ 14 | rain     |          71 |       80 | {71,80}       | {low,unhealthy}   | t     | Don't Play |                  1 | low    | unhealthy
+(14 rows)
+
      4. +
    4. Now let's run cols2vec then reverse it using vec2cols. In this case we will get feature names from the cols2vec summary table. First run cols2vec: 
      +DROP TABLE IF EXISTS cols2vec_result, cols2vec_result_summary;
+SELECT madlib.cols2vec(
+    'golf',
+    'cols2vec_result',
+    'temperature, humidity',
+    NULL,
+    'id, temperature, humidity'
+);
+SELECT * FROM cols2vec_result ORDER BY id;
+
      + id | temperature | humidity | feature_vector
+----+-------------+----------+----------------
+  1 |          85 |       85 | {85,85}
+  2 |          80 |       90 | {80,90}
+  3 |          83 |       78 | {83,78}
+  4 |          70 |       96 | {70,96}
+  5 |          68 |       80 | {68,80}
+  6 |          65 |       70 | {65,70}
+  7 |          64 |       65 | {64,65}
+  8 |          72 |       95 | {72,95}
+  9 |          69 |       70 | {69,70}
+ 10 |          75 |       80 | {75,80}
+ 11 |          75 |       70 | {75,70}
+ 12 |          72 |       90 | {72,90}
+ 13 |          81 |       75 | {81,75}
+ 14 |          71 |       80 | {71,80}
+(14 rows)
+
      View the summary table with the feature_names dictionary: 
      +\x on
+SELECT * FROM cols2vec_result_summary;
+\x off
+
      +-[ RECORD 1 ]---------------+-----------------------
+source_table                | golf
+list_of_features            | temperature, humidity
+list_of_features_to_exclude | None
+feature_names               | {temperature,humidity}
+
      Now use feature_names from the summary table above to name the columns of the split array: 
      +DROP TABLE IF EXISTS vec2cols_result;
+SELECT madlib.vec2cols(
+    'cols2vec_result',          -- source table containing the feature vector
+    'vec2cols_result',          -- output table
+    'feature_vector',           -- column with array entries to split
+    (SELECT feature_names from cols2vec_result_summary),    -- feature_names from summary table of cols2vec
+    'id'                        -- columns to keep from source table
+);
+SELECT * FROM vec2cols_result ORDER BY id;
+
      + id | temperature | humidity
+----+-------------+----------
+  1 |          85 |       85
+  2 |          80 |       90
+  3 |          83 |       78
+  4 |          70 |       96
+  5 |          68 |       80
+  6 |          65 |       70
+  7 |          64 |       65
+  8 |          72 |       95
+  9 |          69 |       70
+ 10 |          75 |       80
+ 11 |          75 |       70
+ 12 |          72 |       90
+ 13 |          81 |       75
+ 14 |          71 |       80
+(14 rows)
+
      This is the same as the format of the original 'golf' dataset that we started with.
      5. +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__wcc.html b/docs/docs/v2.1.0/group__grp__wcc.html new file mode 100644 index 00000000..bb15a9f4 --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__wcc.html @@ -0,0 +1,554 @@ + + + + + + + + +MADlib: Weakly Connected Components + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    Weakly Connected Components
    Graph
    +
    +
    +
    Contents +

    Given a directed graph, a weakly connected component (WCC) is a subgraph of the original graph where all vertices are connected to each other by some path, ignoring the direction of edges. In case of an undirected graph, a weakly connected component is also a strongly connected component. This module also includes a number of helper functions that operate on the WCC output.

    +

    Weakly Connected Components
    +weakly_connected_components( vertex_table,
+            vertex_id,
+            edge_table,
+            edge_args,
+            out_table,
+            grouping_cols,
+            iteration_limit,
+            warm_start
+          )
+
    +

    Arguments

    +
    vertex_table
    +

    TEXT. Name of the table containing the vertex data for the graph. Must contain the column specified in the 'vertex_id' parameter below.

    +

    +
    +
    vertex_id
    +

    TEXT, default = 'id'. Name of the column(s) in 'vertex_table' containing vertex ids. The vertex ids can be of type INTEGER or BIGINT with no duplicates. They do not need to be contiguous. If multiple columns are used as vertex ids, they are passed in the following format: [<vertex_id1>,<vertex_id2>,...]

    +

    +
    +
    edge_table
    +

    TEXT. Name of the table containing the edge data. The edge table must contain columns for source vertex and destination vertex.

    +

    +
    +
    edge_args
    +

    TEXT. A comma-delimited string containing multiple named arguments of the form "name=value". The following parameters are supported for this string argument:

      +
    • src (INTEGER or BIGINT): Name of the column(s) containing the source vertex ids in the edge table. Default column name is 'src'.
      • +
    • dest (INTEGER or BIGINT): Name of the column(s) containing the destination vertex ids in the edge table. Default column name is 'dest'.
      • +
    +

    +
    +
    out_table
    +

    TEXT. Name of the table to store the component ID associated with each vertex. It will contain a row for every vertex from 'vertex_table' with the following columns:

      +
    • vertex_id : The id of a vertex. Will use the input parameter 'vertex_id' for column naming. If multiple columns are used for identifying vertices, this column will be an array named "id".
      • +
    • component_id : Component that the vertex belongs to. We use the convention where 'component_id' is the id of the first vertex in a particular group. It means that component ids are generally not contiguous.
      • +
    • grouping_cols : Grouping column (if any) values associated with the vertex_id.
      • +
    +

    A summary table named <out_table>_summary is also created. This is an internal table that keeps a record of some of the input parameters and is used by the weakly connected component helper functions.

    +

    +
    +
    grouping_cols (optional)
    +
    TEXT, default: NULL. A single column or a list of comma-separated columns that divides the input data into discrete groups, which are treated independently as separate graphs. When this value is NULL, no grouping is used and weakly connected components are generated for all data (single graph).
    Note
    Expressions are not currently supported for 'grouping_cols'.
    +
    +
    iteration_limit (optional)
    +

    INTEGER, default: NULL. Maximum number of iterations to run wcc. This parameter is used to stop wcc early to limit the number of subtransactions created by wcc. For such subtx issues, it is advised to set this parameter to

      +
    1. A wcc run that stopped early by this parameter can resume its progress by using the warm_start parameter. An additional table named <out_table>_message is also created. This table is necessary in case the iteration_limit is reached and there are still vertices to update. It gets used when the wcc continues the process via warm_start and gets dropped when the wcc determines there are no more updates necessary. The user might determine if the wcc is completed or not by checking the nodes_to_update column of <out_table>_summary table where 0 means wcc is complete.
      2. +
    +

    +
    +
    warm_start (optional)
    +

    BOOLEAN, default: NULL. If True, wcc will look for the <out_table>_message table and continue using it and the partial output from <out_table> to continue the wcc process.

    +

    +
    +
    +
    Note
    On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance. In addition, the user should note that this function creates a duplicate of the edge table (on Greenplum cluster) for better performance.
    +

    Retrieve Largest Connected Component
    +

    The largest connected component retrieval function finds the largest weakly connected component(s) in a graph. If weakly connected components was run with grouping, the largest connected components are computed for each group.

    +
    +graph_wcc_largest_cpt( wcc_table,
+                      largest_cpt_table
+                     )
+

    Arguments

    +
    wcc_table
    +

    TEXT. Name of the table that contains the output of weakly connected components.

    +

    +
    +
    largest_cpt_table
    +
    TEXT. Name of the output table that contains the largest component's information. It contains one or more rows for every group and has the following columns:
      +
    • grouping_cols: The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created.
      • +
    • component_id: The ID of the largest component. Recall that we use the convention where 'component_id' is the id of the first vertex in a particular group. It means that component ids are generally not contiguous. If there are multiple components of the same size, a row is created for each component. If grouping_cols is specified, the largest component is computed for each group.
      • +
    • num_vertices: Number of vertices in the largest component.
      • +
    +
    +
    +

    Retrieve Histogram of Vertices Per Connected Component
    +

    This function creates a histogram of the number of vertices per connected component.

    +
    +graph_wcc_histogram( wcc_table,
+                    histogram_table
+                   )
+

    Arguments

    +
    wcc_table
    +

    TEXT. Name of the table that contains the output of weakly connected components.

    +

    +
    +
    histogram_table
    +

    TEXT. Name of the output table that contains the number of vertices per component. A row is created for every comoponent in every group if grouping_cols was specified when running weakly connected components. The output table has the following columns:

      +
    • grouping_cols: The grouping columns given during the creation of the wcc_table. If there are no grouping columns, this column is not created.
      • +
    • component_id: The ID of the component.
      • +
    • num_vertices: Number of vertices in the component specified by the component_id column.
      • +
    +

    +
    +
    +

    Check if Two Vertices Belong to the Same Component
    +

    This function determines if two vertices belong to the same component.

    +
    +graph_wcc_vertex_check( wcc_table,
+                       vertex_pair,
+                       pair_table
+                      )
+

    Arguments

    +
    wcc_table
    +

    TEXT. Name of the table that contains the output of weakly connected components.

    +

    +
    +
    vertex_pair
    +

    BIGINT[]. A pair of vertex IDs separated by a comma. If multiple columns are used for identifying vertices, a 2D array will be required for this parameter.

    +

    +
    +
    pair_table
    +

    TEXT. Name of the output table that specifies if the two vertices in vertex_pair belong to the same component. If wcc_table was generated using grouping_cols, all the components in all groups are considered. The output table has the following columns:

      +
    • component_id: Component ID that contains both the vertices in vertex_pair.
      • +
    • grouping_cols: The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created.
      • +
    +

    +
    +
    +

    Retrieve All Vertices Reachable from a Vertex
    +

    This function finds all the vertices that can be reached from a given vertex via weakly connected paths.

    +
    +graph_wcc_reachable_vertices( wcc_table,
+                             src,
+                             reachable_vertices_table
+                            )
+

    Arguments

    +
    wcc_table
    +

    TEXT. Name of the table that contains the output of weakly connected components.

    +

    +
    +
    src
    +

    BIGINT or BIGINT[]. The vertex ID from which all reachable vertices have to be found.

    +

    +
    +
    reachable_vertices_table
    +

    TEXT. Name of the output table that contains the list of vertices that are reachable from the src vertex. The output table has the following columns:

      +
    • grouping_cols : The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created.
      • +
    • component_id : The ID of the component that both the src and dest vertices belong to.
      • +
    • dest : Vertex ID that is reachable from the src vertex. Reachability is computed with regard to a component.
      • +
    +

    +
    +
    +

    Count of Connected Components
    +

    This function finds the total number of components in the input graph.

    +
    +graph_wcc_num_cpts( wcc_table,
+                   count_table
+                  )
+

    Arguments

    +
    wcc_table
    +

    TEXT. Name of the table that contains the output of weakly connected components.

    +

    +
    +
    count_table
    +

    TEXT. Name of the output table that contains the total number of components per group in the graph, if there are any grouping_cols in wcc_table. The output table has the following columns:

      +
    • grouping_cols : The grouping columns given in the creation of wcc_table. If there are no grouping columns, this column is not created, and count is with regard to the entire graph.
      • +
    • num_components : Count of weakly connected components in a graph, or the number of components within a group if grouping_cols is defined.
      • +
    +

    +
    +
    +

    Examples
    +

    Download the example sql file here.

    +
      +
    1. Create vertex and edge tables to represent the graph: 
      +DROP TABLE IF EXISTS vertex, edge;
+CREATE TABLE vertex(
+    node_id INTEGER
+);
+CREATE TABLE edge(
+    conn_src INTEGER,
+    conn_dest INTEGER,
+    user_id INTEGER
+);
+INSERT INTO vertex VALUES
+(0),
+(1),
+(2),
+(3),
+(4),
+(5),
+(6),
+(10),
+(11),
+(12),
+(13),
+(14),
+(15),
+(16);
+INSERT INTO edge VALUES
+(0, 1, 1),
+(0, 2, 1),
+(1, 2, 1),
+(1, 3, 1),
+(2, 3, 1),
+(2, 5, 1),
+(2, 6, 1),
+(3, 0, 1),
+(5, 6, 1),
+(6, 3, 1),
+(10, 11, 2),
+(10, 12, 2),
+(11, 12, 2),
+(11, 13, 2),
+(12, 13, 2),
+(13, 10, 2),
+(15, 16, 2),
+(15, 14, 2);
+
      2. +
    2. Find all the weakly connected components in the graph: 
      +DROP TABLE IF EXISTS wcc_out, wcc_out_summary;
+SELECT madlib.weakly_connected_components(
+    'vertex',                        -- Vertex table
+    'node_id',                       -- Vertex id column
+    'edge',                          -- Edge table
+    'src=conn_src, dest=conn_dest',  -- Comma delimted string of edge arguments
+    'wcc_out');                      -- Output table of weakly connected components
+SELECT * FROM wcc_out ORDER BY component_id, node_id;
+
      + node_id | component_id
+---------+--------------
+       0 |            0
+       1 |            0
+       2 |            0
+       3 |            0
+       5 |            0
+       6 |            0
+       4 |            4
+      10 |           10
+      11 |           10
+      12 |           10
+      13 |           10
+      14 |           14
+      15 |           14
+      16 |           14
+(14 rows)
+
      3. +
    3. Now get the weakly connected components associated with each 'user_id' using the grouping feature: 
      +DROP TABLE IF EXISTS wcc_out, wcc_out_summary;
+SELECT madlib.weakly_connected_components(
+    'vertex',                       -- Vertex table
+    'node_id',                      -- Vertex id column
+    'edge',                         -- Edge table
+    'src=conn_src, dest=conn_dest', -- Comma delimted string of edge arguments
+    'wcc_out',                      -- Output table of weakly connected components
+    'user_id');                     -- Grouping column name
+SELECT * FROM wcc_out ORDER BY user_id, component_id, node_id;
+
      + node_id | component_id | user_id
+---------+--------------+---------
+       0 |            0 |       1
+       1 |            0 |       1
+       2 |            0 |       1
+       3 |            0 |       1
+       5 |            0 |       1
+       6 |            0 |       1
+      10 |           10 |       2
+      11 |           10 |       2
+      12 |           10 |       2
+      13 |           10 |       2
+      14 |           14 |       2
+      15 |           14 |       2
+      16 |           14 |       2
+(13 rows)
+
      Note that vertex 4 is not identified as a separate component above. This is because there is no entry in the edge table for vertex 4 indicating which group it belongs to (though you could do that if you wanted to).
      4. +
    4. Retrieve the largest connected component: 
      +DROP TABLE IF EXISTS largest_cpt_table;
+SELECT madlib.graph_wcc_largest_cpt(
+                         'wcc_out',             -- WCC output table
+                         'largest_cpt_table');  -- output table containing largest component ID
+SELECT * FROM largest_cpt_table ORDER BY component_id;
+
      + user_id | component_id | num_vertices
+---------+--------------+--------------
+       1 |            0 |            6
+       2 |           10 |            4
+(2 rows)
+
      5. +
    5. Retrieve histogram of the number of vertices per connected component: 
      +DROP TABLE IF EXISTS histogram_table;
+SELECT madlib.graph_wcc_histogram(
+                         'wcc_out',           -- WCC output table
+                         'histogram_table');  -- output table containing the histogram of vertices
+SELECT * FROM histogram_table ORDER BY component_id;
+
      + user_id | component_id | num_vertices
+---------+--------------+--------------
+       1 |            0 |            6
+       2 |           10 |            4
+       2 |           14 |            3
+(3 rows)
+
      6. +
    6. Check if two vertices belong to the same component: 
      +DROP TABLE IF EXISTS vc_table;
+SELECT madlib.graph_wcc_vertex_check(
+                         'wcc_out',    -- WCC output table
+                         '14,15',      -- Pair of vertex IDs
+                         'vc_table');  -- output table containing components that contain the two vertices
+SELECT * FROM vc_table ORDER BY component_id;
+
      + user_id | component_id
+---------+--------------
+       2 |           14
+(1 row)
+
      7. +
    7. Retrieve all vertices reachable from a vertex 
      +DROP TABLE IF EXISTS reach_table;
+SELECT madlib.graph_wcc_reachable_vertices(
+                         'wcc_out',         -- WCC output table
+                         '0',               -- source vertex
+                         'reach_table');    -- output table containing all vertices reachable from source vertex
+SELECT * FROM reach_table ORDER BY component_id, dest;
+
      + user_id | component_id | dest
+---------+--------------+------
+       1 |            0 |    1
+       1 |            0 |    2
+       1 |            0 |    3
+       1 |            0 |    5
+       1 |            0 |    6
+(5 rows)
+
      8. +
    8. Count of connected components: 
      +DROP TABLE IF EXISTS count_table;
+SELECT madlib.graph_wcc_num_cpts(
+                         'wcc_out',       -- WCC output table
+                         'count_table');  -- output table containing number of components per group
+SELECT * FROM count_table;
+
      + user_id | num_components
+---------+----------------
+       1 |              1
+       2 |              2
+(2 rows)
+
      9. +
    9. Create vertex and edge tables with multiple column ids to represent the graph: 
      +DROP TABLE IF EXISTS vertex_multicol_wcc, edge_multicol_wcc;
+CREATE TABLE vertex_multicol_wcc(
+    node_id_major BIGINT,
+    node_id_minor BIGINT
+);
+CREATE TABLE edge_multicol_wcc(
+    conn_src_major BIGINT,
+    conn_dest_major BIGINT,
+    user_id_major BIGINT,
+    conn_src_minor BIGINT,
+    conn_dest_minor BIGINT,
+    user_id_minor BIGINT
+);
+INSERT INTO vertex_multicol_wcc VALUES
+(0, 0),
+(1, 1),
+(2, 2),
+(3, 3),
+(4, 4),
+(5, 5),
+(6, 6);
+INSERT INTO edge_multicol_wcc VALUES
+(0, 1, 1, 0, 1, 1),
+(0, 2, 1, 0, 2, 1),
+(0, 4, 1, 0, 4, 1),
+(1, 2, 1, 1, 2, 1),
+(1, 3, 1, 1, 3, 1),
+(2, 3, 1, 2, 3, 1),
+(2, 5, 1, 2, 5, 1),
+(2, 6, 1, 2, 6, 1),
+(3, 0, 1, 3, 0, 1),
+(4, 0, 1, 4, 0, 1),
+(5, 6, 1, 5, 6, 1),
+(6, 3, 1, 6, 3, 1),
+(0, 1, 2, 0, 1, 2),
+(0, 2, 2, 0, 2, 2),
+(0, 4, 2, 0, 4, 2),
+(1, 2, 2, 1, 2, 2),
+(1, 3, 2, 1, 3, 2),
+(2, 3, 2, 2, 3, 2),
+(3, 0, 2, 3, 0, 2),
+(4, 0, 2, 4, 0, 2),
+(5, 6, 2, 5, 6, 2),
+(6, 3, 2, 6, 3, 2);
+
      10. +
    10. Find all the weakly connected components in the graph: 
      +DROP TABLE IF EXISTS wcc_multicol_out, wcc_multicol_out_summary;
+SELECT madlib.weakly_connected_components(
+    'vertex_multicol_wcc',                                                          -- Vertex table
+    '[node_id_major,node_id_minor]',                                                -- Vertex id column
+    'edge_multicol_wcc',                                                            -- Edge table
+    'src=[conn_src_major,conn_src_minor], dest=[conn_dest_major,conn_dest_minor]',  -- Comma delimted string of edge arguments
+    'wcc_multicol_out',                                                             -- Output table of weakly connected components
+    'user_id_major,user_id_minor');                                                 -- Grouping column name
+SELECT * FROM wcc_multicol_out ORDER BY user_id_major, user_id_minor, component_id, id;
+
      +  id   | component_id | user_id_major | user_id_minor
+-------+--------------+---------------+---------------
+ {0,0} |            3 |             1 |             1
+ {1,1} |            3 |             1 |             1
+ {2,2} |            3 |             1 |             1
+ {3,3} |            3 |             1 |             1
+ {4,4} |            3 |             1 |             1
+ {5,5} |            3 |             1 |             1
+ {6,6} |            3 |             1 |             1
+ {0,0} |            3 |             2 |             2
+ {1,1} |            3 |             2 |             2
+ {2,2} |            3 |             2 |             2
+ {3,3} |            3 |             2 |             2
+ {4,4} |            3 |             2 |             2
+ {5,5} |            3 |             2 |             2
+ {6,6} |            3 |             2 |             2
+(14 rows)
+
      11. +
    +

    Notes
    +
      +
    1. On a Greenplum cluster, the edge table should be distributed by the source vertex id column for better performance.
      2. +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/group__grp__xgboost.html b/docs/docs/v2.1.0/group__grp__xgboost.html new file mode 100644 index 00000000..5263125f --- /dev/null +++ b/docs/docs/v2.1.0/group__grp__xgboost.html @@ -0,0 +1,519 @@ + + + + + + + + +MADlib: XGBoost + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    XGBoost
    Early Stage Development
    +
    +
    +
    Contents +

    XGBoost is an optimized distributed gradient boosting library. The MADlib implementation is designed to train multiple models with different parameters to achieve parallelism on Greenplum systems (PostgreSQL is also supported.)

    +

    The main use case supported is classification. Regression is not currently supported.

    +

    Please note that the XGBoost implementation has the following limitations:

      +
    • All of the dataset is collected in a single segment, compressed by zlib and stored in a single cells (one column of one row). PostgreSQL has a 1 GB limit for each cell which means the supported dataset size is limited.
      • +
    • The collected data is passed to the XGBoost in a single segment. This means, without grid search, the XGBoost is using only a single segment which might increase the run time.
      • +
    +

    XGBoost requires the following python libraries available in every host machine:

      +
    • pandas v0.42
      • +
    • scikit-learn v0.19
      • +
    • xgboost v0.82
      • +
    +

    Versions are provided to ensure a python2 supported libraries can be obtained. Other versions of these libraries might work just as well.

    +

    Training Function
    +SELECT xgboost(
+    source_table,
+    output_table,
+    id_column,
+    dependent_variable,
+    list_of_features,
+    list_of_features_to_exclude,
+    params_str,
+    sample_weights,
+    train_set_size,
+    train_set_split_var
+)
+
    +

    Arguments

    +
    source_table
    +

    TEXT. Name of the table containing the training data.

    +

    +
    +
    output_table
    +

    TEXT. Name of the generated table containing the model. If a table with the same name already exists, an error will be returned. A summary table named <output_table>_summary is also created.

    +

    +
    +
    id_column
    +

    TEXT. Name of the column containing id information in the training data. This is a mandatory argument and the values are expected to be unique for each row. Suggested column types are INTEGER, BIGINT, and VARCHAR.

    +

    +
    +
    dependent_variable
    +

    TEXT. Name of the column that contains the output (response) for training. Boolean, integer and text types are accepted for classification.

    +

    +
    +
    list_of_features
    +

    TEXT. Comma-separated string of column names or expressions to use as predictors. Can also be a '*' implying all columns are to be used as predictors (except for the ones included in the next argument that lists exclusions).

    +

    +
    +
    list_of_features_to_exclude (optional)
    +

    TEXT[]. Text array of column names to exclude from the predictors list. The names in this parameter should be identical to the names used in the table and quoted appropriately. The id_column and dependent_variable are excluded by default.

    +

    +
    +
    params_str (optional)
    +

    TEXT. Comma-separated string of key-value pairs used for initializing XGBClassifier. Each parameter can be assigned an array of values. These values are expanded into multiple parameter sets for grid search.

    +

    Note that these key-value pairs are passed to the xgboost as is and xgboost accepts any parameter thanks to kwargs. If there is a typo in the list, it might get ignored by xgboost.

    +

    eval_metric is a unique key for this dictionary. In XGBoost v0.82, this parameter is passed to the fit function and not the initializer like the rest. After v1.6.0, it was moved to the initializer. MADlib interface keeps these parameters together to ensure that when we upgrade the supported version of the XGBoost, we will be able to maintain same the interface.

    +

    Default values set by MADlib: learning_rate: 0.3 max_depth: 6 n_estimators: 100 eval_metric: 'auc'

    +

    +

    +
    +
    sample_weights (optional)
    +

    TEXT. Column name containing numerical weights for sample_weights parameter of XGBClassifier fit function.

    +

    +
    +
    train_set_size (optional)
    +

    DOUBLE PRECISION. The proportion of the dataset to be used in training.

    +

    +
    +
    train_set_split_var (optional)
    +
    TEXT. Column name containing information on whether the associated row will be used for training or testing. If this parameter is set, train_set_size will be ignored.
    +
    +

    Output

    +
    +

    The model table produced by the training function contains the following columns:

    + + + + + + + +
    model BYTEA8. Trained XGBoost model stored in binary format (not human readable).
    features TEXT[]. Ordered levels (values) of categorical variables corresponding to the categorical features. Used to help interpret the trained model.
    params_index

    INTEGER. The index of the model. During grid search, each parameter set is given an index to distinguish different models.

    +

    +
    +

    A summary table named <output_table>_summary is also created at the same time, which has the following columns:

    + + + + + + + + + + + + + + + + + + + + + + + +
    mdl_train_ts TEXT. The timestamp for the initiation of the xgboost command.
    mdl_name TEXT. The name of the model set to <source_table>_xgboost.
    features TEXT[]. The list of features inputed to the XGBoost.
    params TEXT. The XGBClassifier parameters used for this particular model.
    fnames TEXT. The list of features in sorted order. This column is used for importance
    importance DOUBLE PRECISION[]. Importance values for each feature in the sorted order.
    recall DOUBLE PRECISION[]. Recall values for each class.
    fscore DOUBLE PRECISION[]. fscore values for each class.
    support DOUBLE PRECISION[]. support values for each class.
    test_ids INTEGER[]. The ids of the rows used for this particular model.
    params_index INTEGER. The index of the parameter set used for this model.
    +

    Prediction Function
    +
    +SELECT xgboost_predict(
+    test_table,
+    model_table,
+    predict_output_table,
+    id_column,
+    class_label,
+    model_filters
+);
+

    Arguments

    +
    test_table
    +

    TEXT. Name of the table containing the test data.

    +

    +
    +
    model_table
    +

    TEXT. Name of the table containing the xgboost train output.

    +

    +
    +
    predict_output_table
    +

    TEXT. Name of the generated table containing the prediction. If a table with the same name already exists, an error will be returned. A metrics table named <output_table_name>_metrics and an roc curve table named <output_table_name>_roc_curve are also created if class_label is not NULL.

    +

    +
    +
    id_column
    +

    TEXT. Name of the column containing id information in the test data. This is a mandatory argument and the values are expected to be unique for each row.

    +

    +
    +
    class_label (optional)
    +

    TEXT. Name of the column containing class_label for the metrics and roc_curve calculations.

    +

    +
    +
    model_filters (optional)
    +
    TEXT. The filter for the model_table in case the user wants to use a subset of the models from the grid search.
    +
    +

    Output

    +

    XGBoost prediction function creates three tables: <predict_output_table>, <predict_output_table>_metrics and <predict_output_table>_roc_curve. Some fields of the metrics table as well as the roc_curve table are available only if a class_label column is provided.

    +

    <predict_output_table>

    +
    + + + + + + + +
    id_column INTEGER. Name of the column containing id information in the test data.
    class_label_predicted TEXT. The predicted value for the given data id.
    class_label_proba_predicted DOUBLE PRECISION[]. The prediction probabilities for the given data id.
    +

    <predict_output_table>_metrics

    + + + + + + + + + + + + + + +
    precision DOUBLE PRECISION[]. Precision values for each class in the sorted order.
    recall DOUBLE PRECISION[]. Recall values for each class.
    fscore DOUBLE PRECISION[]. fscore values for each class.
    support DOUBLE PRECISION[]. support values for each class.
    roc_auc_scores DOUBLE PRECISION[]. roc_auc scores for each class.
    feature_names TEXT[]. The list of features in sorted order. This column is used for importance
    feature_importance_scores DOUBLE PRECISION[]. Importance values for each feature in the sorted order.
    +

    <predict_output_table>_roc_curve

    + + + + + + +
    fpr DOUBLE PRECISION[]. False positive rate for the roc curve.
    tpr DOUBLE PRECISION[]. True positive rate for the roc curve.
    thresholds DOUBLE PRECISION[]. Threshold values for the roc curve.
    +

    Examples
    +

    Download the example sql file here.

    +
      +
    1. Show the input data set. 
      +SELECT * FROM abalone LIMIT 10;
+
      + id | sex | length | diameter | height | whole_weight | shucked_weight | viscera_weight | shell_weight | rings
+----+-----+--------+----------+--------+--------------+----------------+----------------+--------------+-------
+  1 | M   |  0.455 |    0.365 |  0.095 |        0.514 |         0.2245 |          0.101 |         0.15 |    15
+ 12 | M   |   0.43 |     0.35 |   0.11 |        0.406 |         0.1675 |          0.081 |        0.135 |    10
+ 15 | F   |   0.47 |    0.355 |    0.1 |       0.4755 |         0.1675 |         0.0805 |        0.185 |    10
+ 20 | M   |   0.45 |     0.32 |    0.1 |        0.381 |         0.1705 |          0.075 |        0.115 |     9
+ 23 | F   |  0.565 |     0.44 |  0.155 |       0.9395 |         0.4275 |          0.214 |         0.27 |    12
+ 26 | F   |   0.56 |     0.44 |   0.14 |       0.9285 |         0.3825 |          0.188 |          0.3 |    11
+ 30 | M   |  0.575 |    0.425 |   0.14 |       0.8635 |          0.393 |          0.227 |          0.2 |    11
+ 31 | M   |   0.58 |     0.47 |  0.165 |       0.9975 |         0.3935 |          0.242 |         0.33 |    10
+ 35 | F   |  0.705 |     0.55 |    0.2 |       1.7095 |          0.633 |         0.4115 |         0.49 |    13
+ 36 | M   |  0.465 |    0.355 |  0.105 |       0.4795 |          0.227 |          0.124 |        0.125 |     8
+
      2. +
    2. Run XGBoost for a single parameter set and show the summary table 
      +DROP TABLE IF EXISTS xgb_out, xgb_out_summary;
+SELECT xgboost(
+    'abalone',  -- Training table
+    'id',       -- Id column
+    'sex',      -- Class label column
+    '*',        -- Independent variables
+    NULL,       -- Columns to exclude from features
+    $$
+    {
+        'learning_rate': [0.01], #Regularization on weights (eta). For smaller values, increase n_estimators
+        'max_depth': [9],#Larger values could lead to overfitting
+        'subsample': [0.85],#introduce randomness in samples picked to prevent overfitting
+        'colsample_bytree': [0.85],#introduce randomness in features picked to prevent overfitting
+        'min_child_weight': [10],#larger values will prevent over-fitting
+        'n_estimators':[100] #More estimators, lesser variance (better fit on test set)
+    }
+    $$,         -- XGBoost grid search parameters
+    'xgb_out',  -- Grid search results table.
+    '',         -- Class weights
+    0.8,        -- Training set size ratio
+    NULL        -- Variable used to do the test/train split.
+);
+\x on
+SELECT * FROM xgb_out_summary;
+
      +-[ RECORD 1 ]+---------------------------------------------
+mdl_train_ts | 2022-05-16 17:42:45.033789+03
+mdl_name     | abalone_xgboost
+features     | {length,diameter,height,whole_weight,shucked_weight,viscera_weight,shell_weight,rings}
+params       | ('colsample_bytree=0.85', 'learning_rate=0.01', 'min_child_weight=10', 'n_estimators=100', 'subsample=0.85', 'max_depth=9')
+fnames       | {viscera_weight,whole_weight,shucked_weight,shell_weight,length,rings,diameter,height}
+importance   | {1206,1189,1184,867,766,622,589,526}
+precision    | {0.4295774647887324,0.6858006042296072,0.4318181818181818}
+recall       | {0.46387832699619774,0.8021201413427562,0.328719723183391}
+fscore       | {0.4460694698354662,0.739413680781759,0.3732809430255403}
+support      | {263.0,283.0,289.0}
+test_ids     | {486,3627,432,2766,132,2397,3313,2346...}
+
      3. +
    3. Run XGBoost prediction. For this example we are using the same abalone table for prediction as well. 
      +DROP TABLE IF EXISTS xgb_score_out, xgb_score_out_metrics, xgb_score_out_roc_curve;
+SELECT xgboost_predict(
+    'abalone',          -- test_table
+    'xgb_out',          -- model_table
+    'xgb_score_out',    -- predict_output_table
+    'id',               -- id_column
+    'sex'               -- class_label
+);
+\x off
+SELECT * FROM xgb_score_out LIMIT 10;
+
      + id | sex_predicted |              sex_proba_predicted
+----+---------------+------------------------------------------------
+  5 | I             | {0.168330997229,0.632858633995,0.198810324073}
+  6 | I             | {0.202547758818,0.574552714825,0.222899526358}
+  9 | I             | {0.255484640598,0.44379144907,0.300723910332}
+ 10 | M             | {0.347418963909,0.242429286242,0.410151779652}
+ 11 | F             | {0.4157371521,0.316571623087,0.267691165209}
+ 13 | F             | {0.338543832302,0.32665386796,0.334802359343}
+ 14 | F             | {0.400314897299,0.293721526861,0.305963635445}
+ 17 | I             | {0.175603896379,0.608917593956,0.215478509665}
+ 21 | M             | {0.280931055546,0.333337903023,0.385731071234}
+ 25 | F             | {0.498989373446,0.185877665877,0.315133005381}
+
      4. +
    4. Show roc curve and metrics tables 
      +SELECT * FROM xgb_score_out_roc_curve limit 10;
      +            fpr            |            tpr            |        thresholds
+---------------------------+---------------------------+---------------------------
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+ {0.00000,0.00000,0.00000} | {0.00077,0.00075,0.00065} | {0.54791,0.65354,0.49352}
+
      +\x on
+SELECT * FROM xgb_score_out_metrics;
+
      +-[ RECORD 1 ]-------------+---------------------------------------------------------------------------------------
+precision                 | {0.549047282992237,0.70062893081761,0.598290598290598}
+recall                    | {0.595256312165264,0.830104321907601,0.458115183246073}
+fscore                    | {0.571218795888399,0.759890859481583,0.518902891030393}
+support                   | {1307,1342,1528}
+roc_auc_scores            | {0.77659,0.9091,0.74816}
+feature_names             | {viscera_weight,whole_weight,shucked_weight,shell_weight,length,rings,diameter,height}
+feature_importance_scores | {1206,1189,1184,867,766,622,589,526}
+
      5. +
    5. Run XGBoost grid search with parameter options 
      +DROP TABLE IF EXISTS xgb_out, xgb_out_summary;
+SELECT xgboost(
+    'abalone',  -- Training table
+    'id',       -- Id column
+    'sex',      -- Class label column
+    '*',        -- Independent variables
+    NULL,       -- Columns to exclude from features
+    $$
+    {
+        'learning_rate': [0.01,0.1], #Regularization on weights (eta). For smaller values, increase n_estimators
+        'max_depth': [9,12],#Larger values could lead to overfitting
+        'subsample': [0.85],#introduce randomness in samples picked to prevent overfitting
+        'colsample_bytree': [0.85],#introduce randomness in features picked to prevent overfitting
+        'min_child_weight': [10],#larger values will prevent over-fitting
+        'n_estimators':[100] #More estimators, lesser variance (better fit on test set)
+    }
+    $$,         -- XGBoost grid search parameters
+    'xgb_out',  -- Grid search results table.
+    '',         -- Class weights
+    0.8,        -- Training set size ratio
+    NULL        -- Variable used to do the test/train split.
+);
+\x on
+SELECT * FROM xgb_out_summary;
+
      +-[ RECORD 1 ]+---------------------------------------------
+mdl_train_ts | 2022-05-16 17:56:11.488767+03
+mdl_name     | abalone_xgboost
+features     | {length,diameter,height,whole_weight,shucked_weight,viscera_weight,shell_weight,rings}
+params       | ('colsample_bytree=0.85', 'learning_rate=0.01', 'min_child_weight=10', 'n_estimators=100', 'subsample=0.85', 'max_depth=12')
+fnames       | {viscera_weight,whole_weight,shucked_weight,shell_weight,length,rings,diameter,height}
+importance   | {1276,1205,1200,906,864,822,580,415}
+precision    | {0.4090909090909091,0.752411575562701,0.5}
+recall       | {0.45188284518828453,0.8153310104529616,0.42071197411003236}
+fscore       | {0.42942345924453285,0.782608695652174,0.45694200351493847}
+support      | {239.0,287.0,309.0}
+test_ids     | {3975,35,1759,1469,3437,3951...}
+-[ RECORD 2 ]+---------------------------------------------
+mdl_train_ts | 2022-05-16 17:56:11.488767+03
+mdl_name     | abalone_xgboost
+features     | {length,diameter,height,whole_weight,shucked_weight,viscera_weight,shell_weight,rings}
+params       | ('colsample_bytree=0.85', 'learning_rate=0.01', 'min_child_weight=10', 'n_estimators=100', 'subsample=0.85', 'max_depth=9')
+fnames       | {viscera_weight,whole_weight,shucked_weight,shell_weight,length,rings,diameter,height}
+importance   | {1268,1196,1182,860,832,668,595,461}
+precision    | {0.46096654275092935,0.6566265060240963,0.5213675213675214}
+recall       | {0.4901185770750988,0.8288973384030418,0.3824451410658307}
+fscore       | {0.475095785440613,0.7327731092436974,0.4412296564195299}
+support      | {253.0,263.0,319.0}
+test_ids     | {2988,2303,2034,3085,2465,2887...}
+-[ RECORD 3 ]+---------------------------------------------
+mdl_train_ts | 2022-05-16 17:56:11.488767+03
+mdl_name     | abalone_xgboost
+features     | {length,diameter,height,whole_weight,shucked_weight,viscera_weight,shell_weight,rings}
+params       | ('colsample_bytree=0.85', 'learning_rate=0.1', 'min_child_weight=10', 'n_estimators=100', 'subsample=0.85', 'max_depth=9')
+fnames       | {shucked_weight,whole_weight,viscera_weight,shell_weight,length,diameter,height,rings}
+importance   | {998,948,862,765,629,489,441,383}
+precision    | {0.4635036496350365,0.6986301369863014,0.45724907063197023}
+recall       | {0.4847328244274809,0.75,0.40863787375415284}
+fscore       | {0.47388059701492535,0.7234042553191489,0.43157894736842106}
+support      | {262.0,272.0,301.0}
+test_ids     | {396,2150,809,2846,1108,1841...}
+-[ RECORD 3 ]+---------------------------------------------
+mdl_train_ts | 2022-05-16 17:56:11.488767+03
+mdl_name     | abalone_xgboost
+features     | {length,diameter,height,whole_weight,shucked_weight,viscera_weight,shell_weight,rings}
+params       | ('colsample_bytree=0.85', 'learning_rate=0.1', 'min_child_weight=10', 'n_estimators=100', 'subsample=0.85', 'max_depth=12')
+fnames       | {shucked_weight,viscera_weight,whole_weight,shell_weight,length,diameter,height,rings}
+importance   | {1101,1056,1045,958,680,621,458,458}
+precision    | {0.40484429065743943,0.7016949152542373,0.43824701195219123}
+recall       | {0.4517374517374517,0.75,0.36666666666666664}
+fscore       | {0.42700729927007297,0.7250437828371278,0.3992740471869329}
+support      | {259.0,276.0,300.0}
+test_ids     | {1740,2777,1907,581,3525,1022...}
+
      6. +
    6. Run XGBoost prediction using params_index=2 
      +DROP TABLE IF EXISTS xgb_score_out, xgb_score_out_metrics, xgb_score_out_roc_curve;
+SELECT xgboost_predict(
+    'abalone',          -- test_table
+    'xgb_out',          -- model_table
+    'xgb_score_out',    -- predict_output_table
+    'id',               -- id_column
+    'sex',              -- class_label
+    2                   -- params_index
+);
+\x off
+SELECT * FROM xgb_score_out LIMIT 10;
+
      + id | sex_predicted |              sex_proba_predicted
+----+---------------+------------------------------------------------
+  5 | I             | {0.178420484066,0.599636971951,0.221942588687}
+  6 | I             | {0.185853347182,0.602131128311,0.212015494704}
+  9 | I             | {0.253592431545,0.440728843212,0.30567869544}
+ 10 | M             | {0.374555230141,0.249226689339,0.376218110323}
+ 11 | F             | {0.402999937534,0.336779236794,0.260220855474}
+ 13 | I             | {0.338803291321,0.36541134119,0.295785397291}
+ 14 | F             | {0.377499818802,0.301990658045,0.320509523153}
+ 17 | I             | {0.179169252515,0.602536559105,0.218294218183}
+ 21 | M             | {0.27216938138,0.33275142312,0.395079195499}
+ 25 | F             | {0.449239164591,0.187060594559,0.36370024085}
+
      7. +
    +

    Literature
    +

    [1] Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 785–794). New York, NY, USA: ACM. https://doi.org/10.1145/2939672.2939785

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/hits_8sql__in.html b/docs/docs/v2.1.0/hits_8sql__in.html new file mode 100644 index 00000000..e97e9be1 --- /dev/null +++ b/docs/docs/v2.1.0/hits_8sql__in.html @@ -0,0 +1,394 @@ + + + + + + + + +MADlib: hits.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
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    + + +
    + +
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    +
    +Functions
    +
    +
    hits.sql_in File Reference
    +
    +
    + + + + + + + + + + + + + + +

    +Functions

    void hits (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, integer max_iter, float8 threshold, varchar grouping_cols)
     
    void hits (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, integer max_iter, float8 threshold)
     
    void hits (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, integer max_iter)
     
    void hits (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table)
     
    varchar hits (varchar message)
     
    varchar hits ()
     
    +

    Function Documentation

    + +

    ◆ hits() [1/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void hits (text vertex_table,
    text vertex_id,
    text edge_table,
    text edge_args,
    text out_table,
    integer max_iter,
    float8 threshold,
    varchar grouping_cols 
    )
    +
    + +
    +
    + +

    ◆ hits() [2/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void hits (text vertex_table,
    text vertex_id,
    text edge_table,
    text edge_args,
    text out_table,
    integer max_iter,
    float8 threshold 
    )
    +
    + +
    +
    + +

    ◆ hits() [3/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void hits (text vertex_table,
    text vertex_id,
    text edge_table,
    text edge_args,
    text out_table,
    integer max_iter 
    )
    +
    + +
    +
    + +

    ◆ hits() [4/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void hits (text vertex_table,
    text vertex_id,
    text edge_table,
    text edge_args,
    text out_table 
    )
    +
    + +
    +
    + +

    ◆ hits() [5/6]

    + +
    +
    + + + + + + + + +
    varchar hits (varchar message)
    +
    + +
    +
    + +

    ◆ hits() [6/6]

    + +
    +
    + + + + + + + +
    varchar hits ()
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/hypothesis__tests_8sql__in.html b/docs/docs/v2.1.0/hypothesis__tests_8sql__in.html new file mode 100644 index 00000000..764e17cd --- /dev/null +++ b/docs/docs/v2.1.0/hypothesis__tests_8sql__in.html @@ -0,0 +1,1246 @@ + + + + + + + + +MADlib: hypothesis_tests.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
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    +
    +
    + +
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    + + +
    + +
    + +
    +
    +Functions
    +
    +
    hypothesis_tests.sql_in File Reference
    +
    +
    + +

    SQL functions for statistical hypothesis tests. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    float8 [] t_test_one_transition (float8[] state, float8 value)
     
    float8 [] t_test_merge_states (float8[] state1, float8[] state2)
     
    t_test_result t_test_one_final (float8[] state)
     
    f_test_result f_test_final (float8[] state)
     
    aggregate float8 [] t_test_one (float8 value)
     Perform one-sample or dependent paired Student t-test. More...
     
    float8 [] t_test_two_transition (float8[] state, boolean first, float8 value)
     
    t_test_result t_test_two_pooled_final (float8[] state)
     
    aggregate float8 [] t_test_two_pooled (boolean first, float8 value)
     Perform two-sample pooled (i.e., equal variances) Student t-test. More...
     
    t_test_result t_test_two_unpooled_final (float8[] state)
     
    aggregate float8 [] t_test_two_unpooled (boolean first, float8 value)
     Perform unpooled (i.e., unequal variances) t-test (also known as Welch's t-test) More...
     
    aggregate float8 [] f_test (boolean first, float8 value)
     Perform Fisher F-test. More...
     
    float8 [] chi2_gof_test_transition (float8[] state, bigint observed, float8 expected, bigint df)
     
    float8 [] chi2_gof_test_transition (float8[] state, bigint observed, float8 expected)
     
    float8 [] chi2_gof_test_transition (float8[] state, bigint observed)
     
    float8 [] chi2_gof_test_merge_states (float8[] state1, float8[] state2)
     
    chi2_test_result chi2_gof_test_final (float8[] state)
     
    aggregate float8 [] chi2_gof_test (bigint observed, float8 expected=1, bigint df=0)
     Perform Pearson's chi-squared goodness-of-fit test. More...
     
    aggregate float8 [] chi2_gof_test (bigint observed, float8 expected)
     
    aggregate float8 [] chi2_gof_test (bigint observed)
     
    float8 [] ks_test_transition (float8[] state, boolean first, float8 value, bigint numFirst, bigint numSecond)
     
    ks_test_result ks_test_final (float8[] state)
     
    float8 [] mw_test_transition (float8[] state, boolean first, float8 value)
     Perform Kolmogorov-Smirnov test. More...
     
    mw_test_result mw_test_final (float8[] state)
     
    float8 [] wsr_test_transition (float8[] state, float8 value, float8 precision)
     Perform Mann-Whitney test. More...
     
    float8 [] wsr_test_transition (float8[] state, float8 value)
     
    wsr_test_result wsr_test_final (float8[] state)
     
    float8 [] one_way_anova_transition (float8[] state, integer group, float8 value)
     Perform Wilcoxon-Signed-Rank test. More...
     
    float8 [] one_way_anova_merge_states (float8[] state1, float8[] state2)
     
    one_way_anova_result one_way_anova_final (float8[] state)
     
    aggregate float8 [] one_way_anova (integer group, float8 value)
     Perform one-way analysis of variance. More...
     
    +

    Detailed Description

    +
    See also
    For an overview of hypthesis-test functions, see the module description Hypothesis Tests.
    +

    Function Documentation

    + +

    ◆ chi2_gof_test() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] chi2_gof_test (bigint observed,
    float8 expected = 1,
    bigint df = 0 
    )
    +
    +

    Let \( n_1, \dots, n_k \) be a realization of a (vector) random variable \( N = (N_1, \dots, N_k) \) that follows the multinomial distribution with parameters \( k \) and \( p = (p_1, \dots, p_k) \). Test the null hypothesis \( H_0 : p = p^0 \).

    +
    Parameters
    + + + + +
    observedNumber \( n_i \) of observations of the current event/row
    expectedExpected number of observations of current event/row. This number is not required to be normalized. That is, \( p^0_i \) will be taken as expected divided by sum(expected). Hence, if this parameter is not specified, chi2_test() will by default use \( p^0 = (\frac 1k, \dots, \frac 1k) \), i.e., test that \( p \) is a discrete uniform distribution.
    dfDegrees of freedom. This is the number of events reduced by the degree of freedom lost by using the observed numbers for defining the expected number of observations. If this parameter is 0, the degree of freedom is taken as \( (k - 1) \).
    +
    +
    +
    Returns
    A composite value as follows. Let \( n = \sum_{i=1}^n n_i \).
      +
    • statistic FLOAT8 - Statistic

      +\[ \chi^2 = \sum_{i=1}^k \frac{(n_i - np_i)^2}{np_i} \] +

      + The corresponding random variable is approximately chi-squared distributed with df degrees of freedom.
      • +
    • df BIGINT - Degrees of freedom
      • +
    • p_value FLOAT8 - Approximate p-value, i.e., \( \Pr[X^2 \geq \chi^2 \mid p = p^0] \). Computed as (1.0 - chi_squared_cdf(statistic)).
      • +
    • phi FLOAT8 - Phi coefficient, i.e., \( \phi = \sqrt{\frac{\chi^2}{n}} \)
      • +
    • contingency_coef FLOAT8 - Contingency coefficient, i.e., \( \sqrt{\frac{\chi^2}{n + \chi^2}} \)
      • +
    +
    +
    Usage
      +
    • Test null hypothesis that all possible outcomes of a categorical variable are equally likely: 
      SELECT (chi2_gof_test(observed, 1, NULL)).* FROM source
      • +
    • Test null hypothesis that two categorical variables are independent. Such data is often shown in a contingency table (also known as crosstab). A crosstab is a matrix where possible values for the first variable correspond to rows and values for the second variable to columns. The matrix elements are the observation frequencies of the joint occurrence of the respective values. chi2_gof_test() assumes that the crosstab is stored in normalized form, i.e., there are three columns var1, var2, observed. 
      SELECT (chi2_gof_test(observed, expected, deg_freedom)).*
+FROM (
+    SELECT
+        observed,
+        sum(observed) OVER (PARTITION BY var1)::DOUBLE PRECISION
+            * sum(observed) OVER (PARTITION BY var2) AS expected
+    FROM source
+) p, (
+   SELECT
+        (count(DISTINCT var1) - 1) * (count(DISTINCT var2) - 1) AS deg_freedom
+    FROM source
+) q;
      • +
    +
    + +
    +
    + +

    ◆ chi2_gof_test() [2/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] chi2_gof_test (bigint observed,
    float8 expected 
    )
    +
    + +
    +
    + +

    ◆ chi2_gof_test() [3/3]

    + +
    +
    + + + + + + + + +
    aggregate float8 [] chi2_gof_test (bigint observed)
    +
    + +
    +
    + +

    ◆ chi2_gof_test_final()

    + +
    +
    + + + + + + + + +
    chi2_test_result chi2_gof_test_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ chi2_gof_test_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] chi2_gof_test_merge_states (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ chi2_gof_test_transition() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] chi2_gof_test_transition (float8 [] state,
    bigint observed,
    float8 expected,
    bigint df 
    )
    +
    + +
    +
    + +

    ◆ chi2_gof_test_transition() [2/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] chi2_gof_test_transition (float8 [] state,
    bigint observed,
    float8 expected 
    )
    +
    + +
    +
    + +

    ◆ chi2_gof_test_transition() [3/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] chi2_gof_test_transition (float8 [] state,
    bigint observed 
    )
    +
    + +
    +
    + +

    ◆ f_test()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] f_test (boolean first,
    float8 value 
    )
    +
    +

    Given realizations \( x_1, \dots, x_m \) and \( y_1, \dots, y_n \) of i.i.d. random variables \( X_1, \dots, X_m \sim N(\mu_X, \sigma^2) \) and \( Y_1, \dots, Y_n \sim N(\mu_Y, \sigma^2) \) with unknown parameters \( \mu_X, \mu_Y, \) and \( \sigma^2 \), test the null hypotheses \( H_0 : \sigma_X < \sigma_Y \) and \( H_0 : \sigma_X = \sigma_Y \).

    +
    Parameters
    + + + +
    firstIndicator whether value is from first sample \( x_1, \dots, x_m \) (if TRUE) or from second sample \( y_1, \dots, y_n \) (if FALSE)
    valueValue of random variate \( x_i \) or \( y_i \)
    +
    +
    +
    Returns
    A composite value as follows. We denote by \( \bar x, \bar y \) the sample means and by \( s_X^2, s_Y^2 \) the sample variances.
      +
    • statistic FLOAT8 - Statistic

      +\[ f = \frac{s_Y^2}{s_X^2} \] +

      + The corresponding random variable is F-distributed with \( (n - 1) \) degrees of freedom in the numerator and \( (m - 1) \) degrees of freedom in the denominator.
      • +
    • df1 BIGINT - Degrees of freedom in the numerator \( (n - 1) \)
      • +
    • df2 BIGINT - Degrees of freedom in the denominator \( (m - 1) \)
      • +
    • p_value_one_sided FLOAT8 - Lower bound on one-sided p-value. In detail, the result is \( \Pr[F \geq f \mid \sigma_X = \sigma_Y] \), which is a lower bound on \( \Pr[F \geq f \mid \sigma_X \leq \sigma_Y] \). Computed as (1.0 - fisher_f_cdf(statistic)).
      • +
    • p_value_two_sided FLOAT8 - Two-sided p-value, i.e., \( 2 \cdot \min \{ p, 1 - p \} \) where \( p = \Pr[ F \geq f \mid \sigma_X = \sigma_Y] \). Computed as (min(p_value_one_sided, 1. - p_value_one_sided)).
      • +
    +
    +
    Usage
      +
    • Test null hypothesis that the variance of the first sample is at most (or equal to, respectively) the variance of the second sample: 
      SELECT (f_test(first, value)).* FROM source
      • +
    +
    + +
    +
    + +

    ◆ f_test_final()

    + +
    +
    + + + + + + + + +
    f_test_result f_test_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ ks_test_final()

    + +
    +
    + + + + + + + + +
    ks_test_result ks_test_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ ks_test_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] ks_test_transition (float8 [] state,
    boolean first,
    float8 value,
    bigint numFirst,
    bigint numSecond 
    )
    +
    + +
    +
    + +

    ◆ mw_test_final()

    + +
    +
    + + + + + + + + +
    mw_test_result mw_test_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ mw_test_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] mw_test_transition (float8 [] state,
    boolean first,
    float8 value 
    )
    +
    +

    Given realizations \( x_1, \dots, x_m \) and \( y_1, \dots, y_m \) of i.i.d. random variables \( X_1, \dots, X_m \) and i.i.d. \( Y_1, \dots, Y_n \), respectively, test the null hypothesis that the underlying distributions function \( F_X, F_Y \) are identical, i.e., \( H_0 : F_X = F_Y \).

    +
    Parameters
    + + + + + +
    firstDetermines whether the value belongs to the first (if TRUE) or the second sample (if FALSE)
    valueValue of random variate \( x_i \) or \( y_i \)
    mSize \( m \) of the first sample. See usage instructions below.
    nSize of the second sample. See usage instructions below.
    +
    +
    +
    Returns
    A composite value.
      +
    • statistic FLOAT8 - Kolmogorov–Smirnov statistic

      +\[ d = \max_{t \in \mathbb R} |F_x(t) - F_y(t)| \] +

      + where \( F_x(t) := \frac 1m |\{ i \mid x_i \leq t \}| \) and \( F_y \) (defined likewise) are the empirical distribution functions.
      • +
    • k_statistic FLOAT8 - Kolmogorov statistic \( k = (r + 0.12 + \frac{0.11}{r}) \cdot d \) where \( r = \sqrt{\frac{m n}{m+n}}. \) and \( d \) is the statistic. Then \( k \) is approximately Kolmogorov distributed.
      • +
    • p_value FLOAT8 - Approximate p-value, i.e., an approximate value for \( \Pr[D \geq d \mid F_X = F_Y] \). Computed as (1.0 - kolmogorov_cdf(k_statistic)).
      • +
    +
    +
    Usage
      +
    • Test null hypothesis that two samples stem from the same distribution: 
      SELECT (ks_test(first, value,
+    (SELECT count(value) FROM source WHERE first),
+    (SELECT count(value) FROM source WHERE NOT first)
+    ORDER BY value
+)).* FROM source
      • +
    +
    +
    Note
    This aggregate must be used as an ordered aggregate (ORDER BY value) and will raise an exception if values are not ordered.
    + +
    +
    + +

    ◆ one_way_anova()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] one_way_anova (integer group,
    float8 value 
    )
    +
    +

    Given realizations \( x_{1,1}, \dots, x_{1, n_1}, x_{2,1}, \dots, x_{2,n_2}, \dots, x_{k,n_k} \) of i.i.d. random variables \( X_{i,j} \sim N(\mu_i, \sigma^2) \) with unknown parameters \( \mu_1, \dots, \mu_k \) and \( \sigma^2 \), test the null hypotheses \( H_0 : \mu_1 = \dots = \mu_k \).

    +
    Parameters
    + + + +
    groupGroup which value is from. Note that group can assume arbitary value not limited to a continguous range of integers.
    valueValue of random variate \( x_{i,j} \)
    +
    +
    +
    Returns
    A composite value as follows. Let \( n := \sum_{i=1}^k n_i \) be the total size of all samples. Denote by \( \bar x \) the grand mean, by \( \overline{x_i} \) the group sample means, and by \( s_i^2 \) the group sample variances.
      +
    • sum_squares_between DOUBLE PRECISION - sum of squares between the group means, i.e., \( \mathit{SS}_b = \sum_{i=1}^k n_i (\overline{x_i} - \bar x)^2. \)
      • +
    • sum_squares_within DOUBLE PRECISION - sum of squares within the groups, i.e., \( \mathit{SS}_w = \sum_{i=1}^k (n_i - 1) s_i^2. \)
      • +
    • df_between BIGINT - degree of freedom for between-group variation \( (k-1) \)
      • +
    • df_within BIGINT - degree of freedom for within-group variation \( (n-k) \)
      • +
    • mean_squares_between DOUBLE PRECISION - mean square between groups, i.e., \( s_b^2 := \frac{\mathit{SS}_b}{k-1} \)
      • +
    • mean_squares_within DOUBLE PRECISION - mean square within groups, i.e., \( s_w^2 := \frac{\mathit{SS}_w}{n-k} \)
      • +
    • statistic DOUBLE PRECISION - Statistic computed as

      +\[ f = \frac{s_b^2}{s_w^2}. \] +

      + This statistic is Fisher F-distributed with \( (k-1) \) degrees of freedom in the numerator and \( (n-k) \) degrees of freedom in the denominator.
      • +
    • p_value DOUBLE PRECISION - p-value, i.e., \( \Pr[ F \geq f \mid H_0] \).
      • +
    +
    +
    Usage
      +
    • Test null hypothesis that the mean of the all samples is equal: 
      SELECT (one_way_anova(group, value)).* FROM source
      • +
    +
    + +
    +
    + +

    ◆ one_way_anova_final()

    + +
    +
    + + + + + + + + +
    one_way_anova_result one_way_anova_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ one_way_anova_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] one_way_anova_merge_states (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ one_way_anova_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] one_way_anova_transition (float8 [] state,
    integer group,
    float8 value 
    )
    +
    +

    Given realizations \( x_1, \dots, x_n \) of i.i.d. random variables \( X_1, \dots, X_n \) with unknown mean \( \mu \), test the null hypotheses \( H_0 : \mu \leq 0 \) and \( H_0 : \mu = 0 \).

    +
    Parameters
    + + + +
    valueValue of random variate \( x_i \) or \( y_i \). Values of 0 are ignored (i.e., they do not count towards \( n \)).
    precisionThe precision \( \epsilon_i \) with which value is known. The precision determines the handling of ties. The current value \( v_i \) is regarded a tie with the previous value \( v_{i-1} \) if \( v_i - \epsilon_i \leq \max_{j=1, \dots, i-1} v_j + \epsilon_j \). If precision is negative, then it will be treated as value * 2^(-52). (Note that \( 2^{-52} \) is the machine epsilon for type DOUBLE PRECISION.)
    +
    +
    +
    Returns
    A composite value:
      +
    • statistic FLOAT8 - statistic computed as follows. Let \( w^+ = \sum_{i \mid x_i > 0} r_i \) and \( w^- = \sum_{i \mid x_i < 0} r_i \) be the signed rank sums where

      +\[ r_i = \{ j \mid |x_j| < |x_i| \} + \frac{\{ j \mid |x_j| = |x_i| \} + 1}{2}. \] +

      + The Wilcoxon signed-rank statistic is \( w = \min \{ w^+, w^- \} \).
      • +
    • rank_sum_pos FLOAT8 - rank sum of all positive values, i.e., \( w^+ \)
      • +
    • rank_sum_neg FLOAT8 - rank sum of all negative values, i.e., \( w^- \)
      • +
    • num BIGINT - number \( n \) of non-zero values
      • +
    • z_statistic FLOAT8 - z-statistic

      +\[ z = \frac{w^+ - \frac{n(n+1)}{4}} {\sqrt{\frac{n(n+1)(2n+1)}{24} - \sum_{i=1}^n \frac{t_i^2 - 1}{48}}} \] +

      + where \( t_i \) is the number of values with absolute value equal to \( |x_i| \). The corresponding random variable is approximately standard normally distributed.
      • +
    • p_value_one_sided FLOAT8 - One-sided p-value i.e., \( \Pr[Z \geq z \mid \mu \leq 0] \). Computed as (1.0 - normal_cdf(z_statistic)).
      • +
    • p_value_two_sided FLOAT8 - Two-sided p-value, i.e., \( \Pr[ |Z| \geq |z| \mid \mu = 0] \). Computed as (2 * normal_cdf(-abs(z_statistic))).
      • +
    +
    +
    Usage
      +
    • One-sample test: Test null hypothesis that the mean of a sample is at most (or equal to, respectively) \( \mu_0 \): 
      SELECT (wsr_test(value - mu_0 ORDER BY abs(value))).* FROM source
      • +
    • Dependent paired test: Test null hypothesis that the mean difference between the first and second value in a pair is at most (or equal to, respectively) \( \mu_0 \): 
      SELECT (wsr_test(first - second - mu_0 ORDER BY abs(first - second))).* FROM source
      If correctly determining ties is important (e.g., you may want to do so when comparing to software products that take first, second, and mu_0 as individual parameters), supply the precision parameter. This can be done as follows: 
      SELECT (wsr_test(
+    first - second - mu_0,
+    3 * 2^(-52) * greatest(first, second, mu_0)
+    ORDER BY abs(first - second)
+)).* FROM source
      Here \( 2^{-52} \) is the machine epsilon, which we scale to the magnitude of the input data and multiply with 3 because we have a sum with three terms.
      • +
    +
    +
    Note
    This aggregate must be used as an ordered aggregate (ORDER BY abs(value)) and will raise an exception if the absolute values are not ordered.
    + +
    +
    + +

    ◆ t_test_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] t_test_merge_states (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ t_test_one()

    + +
    +
    + + + + + + + + +
    aggregate float8 [] t_test_one (float8 value)
    +
    +

    Given realizations \( x_1, \dots, x_n \) of i.i.d. random variables \( X_1, \dots, X_n \sim N(\mu, \sigma^2) \) with unknown parameters \( \mu \) and \( \sigma^2 \), test the null hypotheses \( H_0 : \mu \leq 0 \) and \( H_0 : \mu = 0 \).

    +
    Parameters
    + + +
    valueValue of random variate \( x_i \)
    +
    +
    +
    Returns
    A composite value as follows. We denote by \( \bar x \) the sample mean and by \( s^2 \) the sample variance.
      +
    • statistic FLOAT8 - Statistic

      +\[ t = \frac{\sqrt n \cdot \bar x}{s} \] +

      + The corresponding random variable is Student-t distributed with \( (n - 1) \) degrees of freedom.
      • +
    • df FLOAT8 - Degrees of freedom \( (n - 1) \)
      • +
    • p_value_one_sided FLOAT8 - Lower bound on one-sided p-value. In detail, the result is \( \Pr[\bar X \geq \bar x \mid \mu = 0] \), which is a lower bound on \( \Pr[\bar X \geq \bar x \mid \mu \leq 0] \). Computed as (1.0 - students_t_cdf(statistic)).
      • +
    • p_value_two_sided FLOAT8 - Two-sided p-value, i.e., \( \Pr[ |\bar X| \geq |\bar x| \mid \mu = 0] \). Computed as (2 * students_t_cdf(-abs(statistic))).
      • +
    +
    +
    Usage
      +
    • One-sample t-test: Test null hypothesis that the mean of a sample is at most (or equal to, respectively) \( \mu_0 \): 
      SELECT (t_test_one(value - mu_0)).* FROM source
      • +
    • Dependent paired t-test: Test null hypothesis that the mean difference between the first and second value in each pair is at most (or equal to, respectively) \( \mu_0 \): 
      SELECT (t_test_one(first - second - mu_0)).*
+              FROM source
      • +
    +
    + +
    +
    + +

    ◆ t_test_one_final()

    + +
    +
    + + + + + + + + +
    t_test_result t_test_one_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ t_test_one_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] t_test_one_transition (float8 [] state,
    float8 value 
    )
    +
    + +
    +
    + +

    ◆ t_test_two_pooled()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] t_test_two_pooled (boolean first,
    float8 value 
    )
    +
    +

    Given realizations \( x_1, \dots, x_n \) and \( y_1, \dots, y_m \) of i.i.d. random variables \( X_1, \dots, X_n \sim N(\mu_X, \sigma^2) \) and \( Y_1, \dots, Y_m \sim N(\mu_Y, \sigma^2) \) with unknown parameters \( \mu_X, \mu_Y, \) and \( \sigma^2 \), test the null hypotheses \( H_0 : \mu_X \leq \mu_Y \) and \( H_0 : \mu_X = \mu_Y \).

    +
    Parameters
    + + + +
    firstIndicator whether value is from first sample \( x_1, \dots, x_n \) (if TRUE) or from second sample \( y_1, \dots, y_m \) (if FALSE)
    valueValue of random variate \( x_i \) or \( y_i \)
    +
    +
    +
    Returns
    A composite value as follows. We denote by \( \bar x, \bar y \) the sample means and by \( s_X^2, s_Y^2 \) the sample variances.
      +
    • statistic FLOAT8 - Statistic

      +\[ t = \frac{\bar x - \bar y}{s_p \sqrt{1/n + 1/m}} \] +

      + where

      +\[ s_p^2 = \frac{\sum_{i=1}^n (x_i - \bar x)^2 + \sum_{i=1}^m (y_i - \bar y)^2} {n + m - 2} \] +

      + is the pooled variance. The corresponding random variable is Student-t distributed with \( (n + m - 2) \) degrees of freedom.
      • +
    • df FLOAT8 - Degrees of freedom \( (n + m - 2) \)
      • +
    • p_value_one_sided FLOAT8 - Lower bound on one-sided p-value. In detail, the result is \( \Pr[\bar X - \bar Y \geq \bar x - \bar y \mid \mu_X = \mu_Y] \), which is a lower bound on \( \Pr[\bar X - \bar Y \geq \bar x - \bar y \mid \mu_X \leq \mu_Y] \). Computed as (1.0 - students_t_cdf(statistic)).
      • +
    • p_value_two_sided FLOAT8 - Two-sided p-value, i.e., \( \Pr[ |\bar X - \bar Y| \geq |\bar x - \bar y| \mid \mu_X = \mu_Y] \). Computed as (2 * students_t_cdf(-abs(statistic))).
      • +
    +
    +
    Usage
      +
    • Two-sample pooled t-test: Test null hypothesis that the mean of the first sample is at most (or equal to, respectively) the mean of the second sample: 
      SELECT (t_test_pooled(first, value)).* FROM source
      • +
    +
    + +
    +
    + +

    ◆ t_test_two_pooled_final()

    + +
    +
    + + + + + + + + +
    t_test_result t_test_two_pooled_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ t_test_two_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] t_test_two_transition (float8 [] state,
    boolean first,
    float8 value 
    )
    +
    + +
    +
    + +

    ◆ t_test_two_unpooled()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] t_test_two_unpooled (boolean first,
    float8 value 
    )
    +
    +

    Given realizations \( x_1, \dots, x_n \) and \( y_1, \dots, y_m \) of i.i.d. random variables \( X_1, \dots, X_n \sim N(\mu_X, \sigma_X^2) \) and \( Y_1, \dots, Y_m \sim N(\mu_Y, \sigma_Y^2) \) with unknown parameters \( \mu_X, \mu_Y, \sigma_X^2, \) and \( \sigma_Y^2 \), test the null hypotheses \( H_0 : \mu_X \leq \mu_Y \) and \( H_0 : \mu_X = \mu_Y \).

    +
    Parameters
    + + + +
    firstIndicator whether value is from first sample \( x_1, \dots, x_n \) (if TRUE) or from second sample \( y_1, \dots, y_m \) (if FALSE)
    valueValue of random variate \( x_i \) or \( y_i \)
    +
    +
    +
    Returns
    A composite value as follows. We denote by \( \bar x, \bar y \) the sample means and by \( s_X^2, s_Y^2 \) the sample variances.
      +
    • statistic FLOAT8 - Statistic

      +\[ t = \frac{\bar x - \bar y}{\sqrt{s_X^2/n + s_Y^2/m}} \] +

      + The corresponding random variable is approximately Student-t distributed with

      +\[ \frac{(s_X^2 / n + s_Y^2 / m)^2}{(s_X^2 / n)^2/(n-1) + (s_Y^2 / m)^2/(m-1)} \] +

      + degrees of freedom (Welch–Satterthwaite formula).
      • +
    • df FLOAT8 - Degrees of freedom (as above)
      • +
    • p_value_one_sided FLOAT8 - Lower bound on one-sided p-value. In detail, the result is \( \Pr[\bar X - \bar Y \geq \bar x - \bar y \mid \mu_X = \mu_Y] \), which is a lower bound on \( \Pr[\bar X - \bar Y \geq \bar x - \bar y \mid \mu_X \leq \mu_Y] \). Computed as (1.0 - students_t_cdf(statistic)).
      • +
    • p_value_two_sided FLOAT8 - Two-sided p-value, i.e., \( \Pr[ |\bar X - \bar Y| \geq |\bar x - \bar y| \mid \mu_X = \mu_Y] \). Computed as (2 * students_t_cdf(-abs(statistic))).
      • +
    +
    +
    Usage
      +
    • Two-sample unpooled t-test: Test null hypothesis that the mean of the first sample is at most (or equal to, respectively) the mean of the second sample: 
      SELECT (t_test_unpooled(first, value)).* FROM source
      • +
    +
    + +
    +
    + +

    ◆ t_test_two_unpooled_final()

    + +
    +
    + + + + + + + + +
    t_test_result t_test_two_unpooled_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ wsr_test_final()

    + +
    +
    + + + + + + + + +
    wsr_test_result wsr_test_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ wsr_test_transition() [1/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] wsr_test_transition (float8 [] state,
    float8 value,
    float8 precision 
    )
    +
    +

    Given realizations \( x_1, \dots, x_m \) and \( y_1, \dots, y_m \) of i.i.d. random variables \( X_1, \dots, X_m \) and i.i.d. \( Y_1, \dots, Y_n \), respectively, test the null hypothesis that the underlying distributions are equal, i.e., \( H_0 : \forall i,j: \Pr[X_i > Y_j] + \frac{\Pr[X_i = Y_j]}{2} = \frac 12 \).

    +
    Parameters
    + + + +
    firstDetermines whether the value belongs to the first (if TRUE) or the second sample (if FALSE)
    valueValue of random variate \( x_i \) or \( y_i \)
    +
    +
    +
    Returns
    A composite value.
      +
    • statistic FLOAT8 - Statistic

      +\[ z = \frac{u - \bar x}{\sqrt{\frac{mn(m+n+1)}{12}}} \] +

      + where \( u \) is the u-statistic computed as follows. The z-statistic is approximately standard normally distributed.
      • +
    • u_statistic FLOAT8 - Statistic \( u = \min \{ u_x, u_y \} \) where

      +\[ u_x = mn + \binom{m+1}{2} - \sum_{i=1}^m r_{x,i} \] +

      + where

      +\[ r_{x,i} = \{ j \mid x_j < x_i \} + \{ j \mid y_j < x_i \} + \frac{\{ j \mid x_j = x_i \} + \{ j \mid y_j = x_i \} + 1}{2} \] +

      + is defined as the rank of \( x_i \) in the combined list of all \( m+n \) observations. For ties, the average rank of all equal values is used.
      • +
    • p_value_one_sided FLOAT8 - Approximate one-sided p-value, i.e., an approximate value for \( \Pr[Z \geq z \mid H_0] \). Computed as (1.0 - normal_cdf(z_statistic)).
      • +
    • p_value_two_sided FLOAT8 - Approximate two-sided p-value, i.e., an approximate value for \( \Pr[|Z| \geq |z| \mid H_0] \). Computed as (2 * normal_cdf(-abs(z_statistic))).
      • +
    +
    +
    Usage
      +
    • Test null hypothesis that two samples stem from the same distribution: 
      SELECT (mw_test(first, value ORDER BY value)).* FROM source
      • +
    +
    +
    Note
    This aggregate must be used as an ordered aggregate (ORDER BY value) and will raise an exception if values are not ordered.
    + +
    +
    + +

    ◆ wsr_test_transition() [2/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] wsr_test_transition (float8 [] state,
    float8 value 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/index.html b/docs/docs/v2.1.0/index.html new file mode 100644 index 00000000..d0650779 --- /dev/null +++ b/docs/docs/v2.1.0/index.html @@ -0,0 +1,135 @@ + + + + + + + + +MADlib: Main Page + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +
    MADlib Documentation
    +
    +
    +

    Apache MADlib is an open-source library for scalable in-database analytics. It provides data-parallel implementations of mathematical, statistical, graph and machine learning methods for structured and unstructured data.

    +

    Useful links:

    +

    Please refer to the ReadMe file for information about incorporated third-party material. License information regarding MADlib and included third-party libraries can be found in the License directory.

    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/input__data__preprocessor_8sql__in.html b/docs/docs/v2.1.0/input__data__preprocessor_8sql__in.html new file mode 100644 index 00000000..f85635a3 --- /dev/null +++ b/docs/docs/v2.1.0/input__data__preprocessor_8sql__in.html @@ -0,0 +1,413 @@ + + + + + + + + +MADlib: input_data_preprocessor.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    input_data_preprocessor.sql_in File Reference
    +
    +
    + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    void validation_preprocessor_dl (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, varchar training_preprocessor_table, integer buffer_size=NULL, text distribution_rules=NULL)
     
    varchar validation_preprocessor_dl (varchar message="")
     
    void training_preprocessor_dl (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, integer buffer_size=NULL, real normalizing_const=1.0, integer[] num_classes=NULL, text distribution_rules=NULL)
     
    varchar training_preprocessor_dl (varchar message="")
     
    aggregate real [] agg_array_concat (real[])
     
    aggregate smallint [] agg_array_concat (smallint[])
     
    bytea convert_array_to_bytea (real[] var)
     
    bytea convert_array_to_bytea (smallint[] var)
     
    real [] convert_bytea_to_real_array (bytea var)
     
    smallint [] convert_bytea_to_smallint_array (bytea var)
     
    +

    Function Documentation

    + +

    ◆ agg_array_concat() [1/2]

    + +
    +
    + + + + + + + + +
    aggregate real [] agg_array_concat (real [])
    +
    + +
    +
    + +

    ◆ agg_array_concat() [2/2]

    + +
    +
    + + + + + + + + +
    aggregate smallint [] agg_array_concat (smallint [])
    +
    + +
    +
    + +

    ◆ convert_array_to_bytea() [1/2]

    + +
    +
    + + + + + + + + +
    bytea convert_array_to_bytea (real [] var)
    +
    + +
    +
    + +

    ◆ convert_array_to_bytea() [2/2]

    + +
    +
    + + + + + + + + +
    bytea convert_array_to_bytea (smallint [] var)
    +
    + +
    +
    + +

    ◆ convert_bytea_to_real_array()

    + +
    +
    + + + + + + + + +
    real [] convert_bytea_to_real_array (bytea var)
    +
    + +
    +
    + +

    ◆ convert_bytea_to_smallint_array()

    + +
    +
    + + + + + + + + +
    smallint [] convert_bytea_to_smallint_array (bytea var)
    +
    + +
    +
    + +

    ◆ training_preprocessor_dl() [1/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void training_preprocessor_dl (varchar source_table,
    varchar output_table,
    varchar dependent_varname,
    varchar independent_varname,
    integer buffer_size = NULL,
    real normalizing_const = 1.0,
    integer [] num_classes = NULL,
    text distribution_rules = NULL 
    )
    +
    + +
    +
    + +

    ◆ training_preprocessor_dl() [2/2]

    + +
    +
    + + + + + + + + +
    varchar training_preprocessor_dl (varchar message = "")
    +
    + +
    +
    + +

    ◆ validation_preprocessor_dl() [1/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void validation_preprocessor_dl (varchar source_table,
    varchar output_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar training_preprocessor_table,
    integer buffer_size = NULL,
    text distribution_rules = NULL 
    )
    +
    + +
    +
    + +

    ◆ validation_preprocessor_dl() [2/2]

    + +
    +
    + + + + + + + + +
    varchar validation_preprocessor_dl (varchar message = "")
    +
    + +
    +
    +
    +
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0},disableSelection:function(){return this.bind((a.support.selectstart?"selectstart":"mousedown")+".ui-disableSelection",function(e){e.preventDefault()})},enableSelection:function(){return this.unbind(".ui-disableSelection")}});a.each(["Width","Height"],function(g,e){var f=e==="Width"?["Left","Right"]:["Top","Bottom"],h=e.toLowerCase(),k={innerWidth:a.fn.innerWidth,innerHeight:a.fn.innerHeight,outerWidth:a.fn.outerWidth,outerHeight:a.fn.outerHeight};function j(m,l,i,n){a.each(f,function(){l-=parseFloat(a.curCSS(m,"padding"+this,true))||0;if(i){l-=parseFloat(a.curCSS(m,"border"+this+"Width",true))||0}if(n){l-=parseFloat(a.curCSS(m,"margin"+this,true))||0}});return l}a.fn["inner"+e]=function(i){if(i===d){return k["inner"+e].call(this)}return this.each(function(){a(this).css(h,j(this,i)+"px")})};a.fn["outer"+e]=function(i,l){if(typeof i!=="number"){return k["outer"+e].call(this,i)}return this.each(function(){a(this).css(h,j(this,i,true,l)+"px")})}});function c(g,e){var j=g.nodeName.toLowerCase();if("area"===j){var i=g.parentNode,h=i.name,f;if(!g.href||!h||i.nodeName.toLowerCase()!=="map"){return false}f=a("img[usemap=#"+h+"]")[0];return !!f&&b(f)}return(/input|select|textarea|button|object/.test(j)?!g.disabled:"a"==j?g.href||e:e)&&b(g)}function b(e){return !a(e).parents().andSelf().filter(function(){return a.curCSS(this,"visibility")==="hidden"||a.expr.filters.hidden(this)}).length}a.extend(a.expr[":"],{data:function(g,f,e){return !!a.data(g,e[3])},focusable:function(e){return c(e,!isNaN(a.attr(e,"tabindex")))},tabbable:function(g){var e=a.attr(g,"tabindex"),f=isNaN(e);return(f||e>=0)&&c(g,!f)}});a(function(){var e=document.body,f=e.appendChild(f=document.createElement("div"));f.offsetHeight;a.extend(f.style,{minHeight:"100px",height:"auto",padding:0,borderWidth:0});a.support.minHeight=f.offsetHeight===100;a.support.selectstart="onselectstart" in f;e.removeChild(f).style.display="none"});a.extend(a.ui,{plugin:{add:function(f,g,j){var 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http://jquery.org/license + * + * http://docs.jquery.com/UI/Mouse + * + * Depends: + * jquery.ui.widget.js + */ +(function(b,c){var a=false;b(document).mouseup(function(d){a=false});b.widget("ui.mouse",{options:{cancel:":input,option",distance:1,delay:0},_mouseInit:function(){var d=this;this.element.bind("mousedown."+this.widgetName,function(e){return d._mouseDown(e)}).bind("click."+this.widgetName,function(e){if(true===b.data(e.target,d.widgetName+".preventClickEvent")){b.removeData(e.target,d.widgetName+".preventClickEvent");e.stopImmediatePropagation();return false}});this.started=false},_mouseDestroy:function(){this.element.unbind("."+this.widgetName)},_mouseDown:function(f){if(a){return}(this._mouseStarted&&this._mouseUp(f));this._mouseDownEvent=f;var e=this,g=(f.which==1),d=(typeof this.options.cancel=="string"&&f.target.nodeName?b(f.target).closest(this.options.cancel).length:false);if(!g||d||!this._mouseCapture(f)){return true}this.mouseDelayMet=!this.options.delay;if(!this.mouseDelayMet){this._mouseDelayTimer=setTimeout(function(){e.mouseDelayMet=true},this.options.delay)}if(this._mouseDistanceMet(f)&&this._mouseDelayMet(f)){this._mouseStarted=(this._mouseStart(f)!==false);if(!this._mouseStarted){f.preventDefault();return true}}if(true===b.data(f.target,this.widgetName+".preventClickEvent")){b.removeData(f.target,this.widgetName+".preventClickEvent")}this._mouseMoveDelegate=function(h){return e._mouseMove(h)};this._mouseUpDelegate=function(h){return e._mouseUp(h)};b(document).bind("mousemove."+this.widgetName,this._mouseMoveDelegate).bind("mouseup."+this.widgetName,this._mouseUpDelegate);f.preventDefault();a=true;return true},_mouseMove:function(d){if(b.browser.msie&&!(document.documentMode>=9)&&!d.button){return this._mouseUp(d)}if(this._mouseStarted){this._mouseDrag(d);return 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i=this.className.match(/ui-resizable-(se|sw|ne|nw|n|e|s|w)/i)}f.axis=i&&i[1]?i[1]:"se"}});if(k.autoHide){this._handles.hide();c(this.element).addClass("ui-resizable-autohide").hover(function(){if(k.disabled){return}c(this).removeClass("ui-resizable-autohide");f._handles.show()},function(){if(k.disabled){return}if(!f.resizing){c(this).addClass("ui-resizable-autohide");f._handles.hide()}})}this._mouseInit()},destroy:function(){this._mouseDestroy();var e=function(g){c(g).removeClass("ui-resizable ui-resizable-disabled ui-resizable-resizing").removeData("resizable").unbind(".resizable").find(".ui-resizable-handle").remove()};if(this.elementIsWrapper){e(this.element);var f=this.element;f.after(this.originalElement.css({position:f.css("position"),width:f.outerWidth(),height:f.outerHeight(),top:f.css("top"),left:f.css("left")})).remove()}this.originalElement.css("resize",this.originalResizeStyle);e(this.originalElement);return this},_mouseCapture:function(f){var g=false;for(var e in this.handles){if(c(this.handles[e])[0]==f.target){g=true}}return !this.options.disabled&&g},_mouseStart:function(g){var j=this.options,f=this.element.position(),e=this.element;this.resizing=true;this.documentScroll={top:c(document).scrollTop(),left:c(document).scrollLeft()};if(e.is(".ui-draggable")||(/absolute/).test(e.css("position"))){e.css({position:"absolute",top:f.top,left:f.left})}this._renderProxy();var k=b(this.helper.css("left")),h=b(this.helper.css("top"));if(j.containment){k+=c(j.containment).scrollLeft()||0;h+=c(j.containment).scrollTop()||0}this.offset=this.helper.offset();this.position={left:k,top:h};this.size=this._helper?{width:e.outerWidth(),height:e.outerHeight()}:{width:e.width(),height:e.height()};this.originalSize=this._helper?{width:e.outerWidth(),height:e.outerHeight()}:{width:e.width(),height:e.height()};this.originalPosition={left:k,top:h};this.sizeDiff={width:e.outerWidth()-e.width(),height:e.outerHeight()-e.height()};this.originalMousePosition={left:g.pageX,top:g.pageY};this.aspectRatio=(typeof j.aspectRatio=="number")?j.aspectRatio:((this.originalSize.width/this.originalSize.height)||1);var i=c(".ui-resizable-"+this.axis).css("cursor");c("body").css("cursor",i=="auto"?this.axis+"-resize":i);e.addClass("ui-resizable-resizing");this._propagate("start",g);return true},_mouseDrag:function(e){var h=this.helper,g=this.options,m={},q=this,j=this.originalMousePosition,n=this.axis;var r=(e.pageX-j.left)||0,p=(e.pageY-j.top)||0;var i=this._change[n];if(!i){return false}var l=i.apply(this,[e,r,p]),k=c.browser.msie&&c.browser.version<7,f=this.sizeDiff;this._updateVirtualBoundaries(e.shiftKey);if(this._aspectRatio||e.shiftKey){l=this._updateRatio(l,e)}l=this._respectSize(l,e);this._propagate("resize",e);h.css({top:this.position.top+"px",left:this.position.left+"px",width:this.size.width+"px",height:this.size.height+"px"});if(!this._helper&&this._proportionallyResizeElements.length){this._proportionallyResize()}this._updateCache(l);this._trigger("resize",e,this.ui());return false},_mouseStop:function(h){this.resizing=false;var i=this.options,m=this;if(this._helper){var g=this._proportionallyResizeElements,e=g.length&&(/textarea/i).test(g[0].nodeName),f=e&&c.ui.hasScroll(g[0],"left")?0:m.sizeDiff.height,k=e?0:m.sizeDiff.width;var n={width:(m.helper.width()-k),height:(m.helper.height()-f)},j=(parseInt(m.element.css("left"),10)+(m.position.left-m.originalPosition.left))||null,l=(parseInt(m.element.css("top"),10)+(m.position.top-m.originalPosition.top))||null;if(!i.animate){this.element.css(c.extend(n,{top:l,left:j}))}m.helper.height(m.size.height);m.helper.width(m.size.width);if(this._helper&&!i.animate){this._proportionallyResize()}}c("body").css("cursor","auto");this.element.removeClass("ui-resizable-resizing");this._propagate("stop",h);if(this._helper){this.helper.remove()}return false},_updateVirtualBoundaries:function(g){var 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g=Math.round((k.width-i.width)/(h.grid[0]||1))*(h.grid[0]||1),f=Math.round((k.height-i.height)/(h.grid[1]||1))*(h.grid[1]||1);if(/^(se|s|e)$/.test(n)){p.size.width=i.width+g;p.size.height=i.height+f}else{if(/^(ne)$/.test(n)){p.size.width=i.width+g;p.size.height=i.height+f;p.position.top=j.top-f}else{if(/^(sw)$/.test(n)){p.size.width=i.width+g;p.size.height=i.height+f;p.position.left=j.left-g}else{p.size.width=i.width+g;p.size.height=i.height+f;p.position.top=j.top-f;p.position.left=j.left-g}}}}});var b=function(e){return parseInt(e,10)||0};var a=function(e){return !isNaN(parseInt(e,10))}})(jQuery);/*! + * jQuery hashchange event - v1.3 - 7/21/2010 + * http://benalman.com/projects/jquery-hashchange-plugin/ + * + * Copyright (c) 2010 "Cowboy" Ben Alman + * Dual licensed under the MIT and GPL licenses. + * http://benalman.com/about/license/ + */ +(function($,e,b){var c="hashchange",h=document,f,g=$.event.special,i=h.documentMode,d="on"+c in e&&(i===b||i>7);function a(j){j=j||location.href;return"#"+j.replace(/^[^#]*#?(.*)$/,"$1")}$.fn[c]=function(j){return j?this.bind(c,j):this.trigger(c)};$.fn[c].delay=50;g[c]=$.extend(g[c],{setup:function(){if(d){return false}$(f.start)},teardown:function(){if(d){return false}$(f.stop)}});f=(function(){var j={},p,m=a(),k=function(q){return q},l=k,o=k;j.start=function(){p||n()};j.stop=function(){p&&clearTimeout(p);p=b};function n(){var r=a(),q=o(m);if(r!==m){l(m=r,q);$(e).trigger(c)}else{if(q!==m){location.href=location.href.replace(/#.*/,"")+q}}p=setTimeout(n,$.fn[c].delay)}$.browser.msie&&!d&&(function(){var q,r;j.start=function(){if(!q){r=$.fn[c].src;r=r&&r+a();q=$(' + + +
    +
    +Functions
    +
    +
    keras_model_arch_table.sql_in File Reference
    +
    +
    +
    + + + + + + + + + + + + + + + + + + + +

    +Functions

    void load_keras_model (varchar keras_model_arch_table, json model_arch, bytea model_weights, text name, text description)
     
    void load_keras_model (varchar keras_model_arch_table, json model_arch)
     
    void load_keras_model (varchar keras_model_arch_table, json model_arch, bytea model_weights)
     
    void load_keras_model (varchar keras_model_arch_table, json model_arch, bytea model_weights, text name)
     
    varchar load_keras_model (varchar message)
     
    varchar load_keras_model ()
     
    void delete_keras_model (varchar keras_model_arch_table, integer model_id)
     
    varchar delete_keras_model (varchar message)
     
    varchar delete_keras_model ()
     
    +

    Function Documentation

    + +

    ◆ delete_keras_model() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    void delete_keras_model (varchar keras_model_arch_table,
    integer model_id 
    )
    +
    + +
    +
    + +

    ◆ delete_keras_model() [2/3]

    + +
    +
    + + + + + + + + +
    varchar delete_keras_model (varchar message)
    +
    + +
    +
    + +

    ◆ delete_keras_model() [3/3]

    + +
    +
    + + + + + + + +
    varchar delete_keras_model ()
    +
    + +
    +
    + +

    ◆ load_keras_model() [1/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_keras_model (varchar keras_model_arch_table,
    json model_arch,
    bytea model_weights,
    text name,
    text description 
    )
    +
    + +
    +
    + +

    ◆ load_keras_model() [2/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    void load_keras_model (varchar keras_model_arch_table,
    json model_arch 
    )
    +
    + +
    +
    + +

    ◆ load_keras_model() [3/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_keras_model (varchar keras_model_arch_table,
    json model_arch,
    bytea model_weights 
    )
    +
    + +
    +
    + +

    ◆ load_keras_model() [4/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_keras_model (varchar keras_model_arch_table,
    json model_arch,
    bytea model_weights,
    text name 
    )
    +
    + +
    +
    + +

    ◆ load_keras_model() [5/6]

    + +
    +
    + + + + + + + + +
    varchar load_keras_model (varchar message)
    +
    + +
    +
    + +

    ◆ load_keras_model() [6/6]

    + +
    +
    + + + + + + + +
    varchar load_keras_model ()
    +
    + +
    +
    + + + + + + diff --git a/docs/docs/v2.1.0/kmeans_8sql__in.html b/docs/docs/v2.1.0/kmeans_8sql__in.html new file mode 100644 index 00000000..1f980883 --- /dev/null +++ b/docs/docs/v2.1.0/kmeans_8sql__in.html @@ -0,0 +1,284 @@ + + + + + + + + +MADlib: kmeans.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    kmeans.sql_in File Reference
    +
    +
    + +

    Set of functions for k-means clustering. +More...

    + + + + + + + + + + +

    +Functions

    void internal_execute_using_kmeans_args (varchar sql, float8[][], regproc, integer, float8, varchar)
     
    integer internal_compute_kmeans (varchar rel_args, varchar rel_state, varchar rel_source, varchar expr_point, varchar agg_centroid)
     
    void __kmeans_validate_src (varchar rel_source)
     
    boolean __kmeans_validate_expr (varchar rel_source, varchar expr_point)
     
    +

    Detailed Description

    +
    See also
    For a brief introduction to k-means clustering, see the module description k-Means Clustering.
    +

    Function Documentation

    + +

    ◆ __kmeans_validate_expr()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    boolean __kmeans_validate_expr (varchar rel_source,
    varchar expr_point 
    )
    +
    + +
    +
    + +

    ◆ __kmeans_validate_src()

    + +
    +
    + + + + + + + + +
    void __kmeans_validate_src (varchar rel_source)
    +
    + +
    +
    + +

    ◆ internal_compute_kmeans()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer internal_compute_kmeans (varchar rel_args,
    varchar rel_state,
    varchar rel_source,
    varchar expr_point,
    varchar agg_centroid 
    )
    +
    + +
    +
    + +

    ◆ internal_execute_using_kmeans_args()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void internal_execute_using_kmeans_args (varchar sql,
    float8 [][],
    regproc ,
    integer ,
    float8 ,
    varchar  
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/knn_8sql__in.html b/docs/docs/v2.1.0/knn_8sql__in.html new file mode 100644 index 00000000..b3774c13 --- /dev/null +++ b/docs/docs/v2.1.0/knn_8sql__in.html @@ -0,0 +1,840 @@ + + + + + + + + +MADlib: knn.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    knn.sql_in File Reference
    +
    +
    + +

    Set of functions for k-nearest neighbors. +More...

    + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    integer __knn_validate_src (varchar point_source, varchar point_column_name, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k, boolean output_neighbors, varchar fn_dist)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k, boolean output_neighbors, text fn_dist, boolean weighted_avg, varchar algorithm, varchar algorithm_params)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k, boolean output_neighbors, text fn_dist, boolean weighted_avg, varchar algorithm)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k, boolean output_neighbors, text fn_dist, boolean weighted_avg)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k, boolean output_neighbors, text fn_dist)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k, boolean output_neighbors)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table, integer k)
     
    varchar knn (varchar point_source, varchar point_column_name, varchar point_id, varchar label_column_name, varchar test_source, varchar test_column_name, varchar test_id, varchar output_table)
     
    varchar knn (varchar message)
     
    varchar knn ()
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    See also
    For a brief introduction to k-nearest neighbors algorithm for regression and classification, see the module description k-Nearest Neighbors.
    +

    Function Documentation

    + +

    ◆ __knn_validate_src()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer __knn_validate_src (varchar point_source,
    varchar point_column_name,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k,
    boolean output_neighbors,
    varchar fn_dist 
    )
    +
    + +
    +
    + +

    ◆ knn() [1/9]

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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k,
    boolean output_neighbors,
    text fn_dist,
    boolean weighted_avg,
    varchar algorithm,
    varchar algorithm_params 
    )
    +
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    ◆ knn() [2/9]

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    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k,
    boolean output_neighbors,
    text fn_dist,
    boolean weighted_avg,
    varchar algorithm 
    )
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    ◆ knn() [3/9]

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    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k,
    boolean output_neighbors,
    text fn_dist,
    boolean weighted_avg 
    )
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    ◆ knn() [4/9]

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    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k,
    boolean output_neighbors,
    text fn_dist 
    )
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    ◆ knn() [5/9]

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    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k,
    boolean output_neighbors 
    )
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    ◆ knn() [6/9]

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    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table,
    integer k 
    )
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    ◆ knn() [7/9]

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    varchar knn (varchar point_source,
    varchar point_column_name,
    varchar point_id,
    varchar label_column_name,
    varchar test_source,
    varchar test_column_name,
    varchar test_id,
    varchar output_table 
    )
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    ◆ knn() [8/9]

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    varchar knn (varchar message)
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    ◆ knn() [9/9]

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    varchar knn ()
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    + + + + diff --git a/docs/docs/v2.1.0/lda_8sql__in.html b/docs/docs/v2.1.0/lda_8sql__in.html new file mode 100644 index 00000000..31709594 --- /dev/null +++ b/docs/docs/v2.1.0/lda_8sql__in.html @@ -0,0 +1,1556 @@ + + + + + + + + +MADlib: lda.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    +Functions
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    lda.sql_in File Reference
    +
    +
    + +

    SQL functions for Latent Dirichlet Allocation. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    set< lda_result > lda_train (text data_table, text model_table, text output_data_table, int4 voc_size, int4 topic_num, int4 iter_num, float8 alpha, float8 beta)
     This UDF provides an entry for the lda training process. More...
     
    set< lda_result > lda_train (text data_table, text model_table, text output_data_table, int4 voc_size, int4 topic_num, int4 iter_num, float8 alpha, float8 beta, int4 evaluate_every, float8 perplexity_tol)
     
    set< lda_result > lda_train (text data_table, text model_table, text output_data_table, int4 voc_size, int4 topic_num, int4 iter_num, float8 alpha, float8 beta, int4 evaluate_every)
     
    set< lda_result > lda_predict (text data_table, text model_table, text output_table)
     This UDF provides an entry for the lda predicton process. More...
     
    set< lda_result > lda_predict (text data_table, text model_table, text output_table, int4 iter_num)
     A overloaded version which allows users to specify iter_num. More...
     
    set< lda_result > lda_get_topic_word_count (text model_table, text output_table)
     This UDF computes the per-topic word counts. More...
     
    set< lda_result > lda_get_word_topic_count (text model_table, text output_table)
     This UDF computes the per-word topic counts. More...
     
    set< lda_result > lda_get_topic_desc (text model_table, text vocab_table, text desc_table, int4 top_k)
     This UDF gets the description for each topic (top-k words) More...
     
    set< lda_result > lda_get_word_topic_mapping (text lda_output_table, text mapping_table)
     This UDF gets the wordid - topicid mapping from the lda training output table. More...
     
    int4 [] __lda_random_assign (int4 word_count, int4 topic_num)
     This UDF assigns topics to words in a document randomly. More...
     
    int4 [] __lda_gibbs_sample (int4[] words, int4[] counts, int4[] doc_topic, int8[] model, float8 alpha, float8 beta, int4 voc_size, int4 topic_num, int4 iter_num)
     This UDF learns the topics of words in a document and is the main step of a Gibbs sampling iteration. The model parameter (including the per-word topic counts and corpus-level topic counts) is passed to this function in the first call and then transfered to the rest calls through fcinfo->flinfo->fn_extra to allow the immediate update. More...
     
    int8 [] __lda_count_topic_sfunc (int8[] state, int4[] words, int4[] counts, int4[] topic_assignment, int4 voc_size, int4 topic_num)
     This UDF is the sfunc for the aggregator computing the topic counts for each word and the topic count in the whole corpus. It scans the topic assignments in a document and updates the topic counts. More...
     
    int8 [] __lda_count_topic_prefunc (int8[] state1, int8[] state2)
     This UDF is the prefunc for the aggregator computing the per-word topic counts. More...
     
    aggregate int8 [] __lda_count_topic_agg (int4[], int4[], int4[], int4, int4)
     This uda computes the word topic counts by scanning and summing up topic assignments in each document. More...
     
    float8 lda_get_perplexity (text model_table, text output_data_table)
     This UDF computes the perplexity given the output data table and the model table. More...
     
    int8 [] __lda_perplexity_sfunc (int8[] state, int4[] words, int4[] counts, int4[] doc_topic, int8[] model, float8 alpha, float8 beta, int4 voc_size, int4 topic_num)
     This UDF is the sfunc for the aggregator computing the perpleixty. More...
     
    int8 [] __lda_perplexity_prefunc (int8[] state1, int8[] state2)
     This UDF is the prefunc for the aggregator computing the perplexity. More...
     
    float8 __lda_perplexity_ffunc (int8[] state)
     This UDF is the finalfunc for the aggregator computing the perplexity. More...
     
    aggregate int8 [] __lda_perplexity_agg (int4[], int4[], int4[], int8[], float8, float8, int4, int4)
     
    int4 [] __lda_check_count_ceiling (int8[] arr, int4 r, int4 c)
     
    set< int4[]> __lda_util_unnest (int8[] arr, int4 r, int4 c)
     Unnest a 2-D array into a set of 1-D arrays. More...
     
    set< int4[]> __lda_util_unnest_transpose (int8[] arr, int4 r, int4 c)
     
    int8 [][] __lda_util_transpose (int8[][] matrix)
     Transpose a 2-D array. More...
     
    float8 [] __lda_util_norm_with_smoothing (float8[] arr, float8 smooth)
     L1 normalization with smoothing. More...
     
    int4 [] __lda_util_index_sort (float8[] arr)
     This UDF returns the index of elements in a sorted order. More...
     
    set< lda_result > __lda_util_norm_vocab (text vocab_table, text output_vocab_table)
     This UDF checks the vocabulary and converts non-continous wordids into continuous integers ranging from 0 to voc_size - 1. More...
     
    set< lda_result > __lda_util_norm_dataset (text data_table, text norm_vocab_table, text output_data_table)
     This UDF converts the data table according to the normalized vocabulary, and all rows with non-positive count values will be removed. More...
     
    set< lda_result > __lda_util_conorm_data (text data_table, text vocab_table, text output_data_table, text output_vocab_table)
     This UDF extracts the list of wordids from the data table and joins it with the vocabulary table to get the list of common wordids, next it will normalize the vocabulary based on the common wordids and then normalize the data table based on the normalized vocabulary. More...
     
    _pivotalr_lda_model lda_parse_model (bigint[] lda_model, integer voc_size, integer topic_num)
     
    +

    Detailed Description

    +
    Date
    Dec 2012
    +
    See also
    For an introduction to Latent Dirichlet Allocation models, see the module description Latent Dirichlet Allocation.
    +

    Function Documentation

    + +

    ◆ __lda_check_count_ceiling()

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    int4 [] __lda_check_count_ceiling (int8 [] arr,
    int4 r,
    int4 c 
    )
    +
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    + +

    ◆ __lda_count_topic_agg()

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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate int8 [] __lda_count_topic_agg (int4 [],
    int4 [],
    int4 [],
    int4 ,
    int4  
    )
    +
    +
    Parameters
    + + + + + + +
    wordsThe unique words in the document
    countsThe counts of each unique words in the document
    topic_assignmentThe topic assignments in the document
    voc_sizeThe size of vocabulary
    topic_numThe number of topics
    +
    +
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    Returns
    The word topic counts (a 1-d array embeding a 2-d array)
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    ◆ __lda_count_topic_prefunc()

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    int8 [] __lda_count_topic_prefunc (int8 [] state1,
    int8 [] state2 
    )
    +
    +
    Parameters
    + + + +
    state1The local word topic counts
    state2The local word topic counts
    +
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    Returns
    The element-wise sum of two local states
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    ◆ __lda_count_topic_sfunc()

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    int8 [] __lda_count_topic_sfunc (int8 [] state,
    int4 [] words,
    int4 [] counts,
    int4 [] topic_assignment,
    int4 voc_size,
    int4 topic_num 
    )
    +
    +
    Parameters
    + + + + + + + +
    stateThe topic counts
    wordsThe unique words in the document
    countsThe counts of each unique words in the document (sum(counts) = word_count)
    topic_assignmentThe topic assignments in the document
    voc_sizeThe size of vocabulary
    topic_numThe number of topics
    +
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    Returns
    The updated state
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    ◆ __lda_gibbs_sample()

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    int4 [] __lda_gibbs_sample (int4 [] words,
    int4 [] counts,
    int4 [] doc_topic,
    int8 [] model,
    float8 alpha,
    float8 beta,
    int4 voc_size,
    int4 topic_num,
    int4 iter_num 
    )
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    +
    Parameters
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    wordsThe set of unique words in the document
    countsThe counts of each unique words in the document (sum(counts) = word_count)
    doc_topicThe current per-doc topic counts and topic assignments
    modelThe current model (including the per-word topic counts and the corpus-level topic counts)
    alphaThe Dirichlet parameter for per-document topic multinomial
    betaThe Dirichlet parameter for per-topic word multinomial
    voc_sizeThe size of vocabulary
    topic_numThe number of topics
    iter_numThe number of iterations
    +
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    Returns
    The learned topic counts and topic assignments
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    ◆ __lda_perplexity_agg()

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    aggregate int8 [] __lda_perplexity_agg (int4 [],
    int4 [],
    int4 [],
    int8 [],
    float8 ,
    float8 ,
    int4 ,
    int4  
    )
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    ◆ __lda_perplexity_ffunc()

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    float8 __lda_perplexity_ffunc (int8 [] state)
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    Parameters
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    stateThe merged state
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    Returns
    The perpleixty
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    ◆ __lda_perplexity_prefunc()

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    int8 [] __lda_perplexity_prefunc (int8 [] state1,
    int8 [] state2 
    )
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    Parameters
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    state1The local state
    state2The local state
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    Returns
    The merged state
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    ◆ __lda_perplexity_sfunc()

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    int8 [] __lda_perplexity_sfunc (int8 [] state,
    int4 [] words,
    int4 [] counts,
    int4 [] doc_topic,
    int8 [] model,
    float8 alpha,
    float8 beta,
    int4 voc_size,
    int4 topic_num 
    )
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    +
    Parameters
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    stateThe cached model plus perplexity
    wordsThe unique words in the document
    countsThe counts of each unique words in the document
    doc_topicThe topic counts in the document
    modelThe learned model
    alphaThe Dirichlet parameter for per-document topic multinomial
    betaThe Dirichlet parameter for per-topic word multinomial
    voc_sizeThe size of vocabulary
    topic_numThe number of topics
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    Returns
    The updated state
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    ◆ __lda_random_assign()

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    int4 [] __lda_random_assign (int4 word_count,
    int4 topic_num 
    )
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    Parameters
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    word_countThe number of words in the document
    topic_numThe number of topics (specified by the user)
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    Returns
    The topic counts and topic assignments
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    ◆ __lda_util_conorm_data()

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    set<lda_result> __lda_util_conorm_data (text data_table,
    text vocab_table,
    text output_data_table,
    text output_vocab_table 
    )
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    Parameters
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    data_tableThe data table to be normalized
    vocab_tableThe vocabulary table to be normalized
    output_data_tableThe normalized data table
    output_vocab_tableThe normalized vocabulary table
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    ◆ __lda_util_index_sort()

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    int4 [] __lda_util_index_sort (float8 [] arr)
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    Parameters
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    arrThe array to be sorted
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    Returns
    The index of elements
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    ◆ __lda_util_norm_dataset()

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    set<lda_result> __lda_util_norm_dataset (text data_table,
    text norm_vocab_table,
    text output_data_table 
    )
    +
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    Parameters
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    data_tableThe data table to be normalized
    vocab_tableThe normalized vocabulary table
    output_data_tableThe normalized data table
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    ◆ __lda_util_norm_vocab()

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    set<lda_result> __lda_util_norm_vocab (text vocab_table,
    text output_vocab_table 
    )
    +
    +
    Parameters
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    vocab_tableThe vocabulary table in the form of <wordid::int4, word::text>
    output_vocab_tableThe regularized vocabulary table
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    ◆ __lda_util_norm_with_smoothing()

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    float8 [] __lda_util_norm_with_smoothing (float8 [] arr,
    float8 smooth 
    )
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    Parameters
    + + + +
    arrThe array to be normalized
    smoothThe smoothing parameter
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    Returns
    The normalized vector
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    ◆ __lda_util_transpose()

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    int8 [][] __lda_util_transpose (int8 matrix[][])
    +
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    Parameters
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    matrixThe input 2-D array
    Thetransposed array
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    ◆ __lda_util_unnest()

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    set<int4[]> __lda_util_unnest (int8 [] arr,
    int4 r,
    int4 c 
    )
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    Parameters
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    arrThe 2-D array to be unnested
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    Returns
    The unnested 1-D arrays
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    ◆ __lda_util_unnest_transpose()

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    set<int4[]> __lda_util_unnest_transpose (int8 [] arr,
    int4 r,
    int4 c 
    )
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    ◆ lda_get_perplexity()

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    float8 lda_get_perplexity (text model_table,
    text output_data_table 
    )
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    +
    Parameters
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    model_tableThe model table generated by lda_train
    output_data_tableThe output data table generated by lda_predict
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    Returns
    The perplexity
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    ◆ lda_get_topic_desc()

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    set<lda_result> lda_get_topic_desc (text model_table,
    text vocab_table,
    text desc_table,
    int4 top_k 
    )
    +
    +
    Parameters
    + + + + + +
    model_tableThe model table generated by the training process
    vocab_tableThe vocabulary table (<wordid, word>)
    top_kThe number of top words for each topic description
    desc_tableThe output table for storing the per-topic description
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    ◆ lda_get_topic_word_count()

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    set<lda_result> lda_get_topic_word_count (text model_table,
    text output_table 
    )
    +
    +
    Parameters
    + + + +
    model_tableThe model table generated by the training process
    output_tableThe output table storing the per-topic word counts
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    ◆ lda_get_word_topic_count()

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    set<lda_result> lda_get_word_topic_count (text model_table,
    text output_table 
    )
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    Parameters
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    model_tableThe model table generated by the training process
    dist_tableThe output table storing the per-word topic counts
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    ◆ lda_get_word_topic_mapping()

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    set<lda_result> lda_get_word_topic_mapping (text lda_output_table,
    text mapping_table 
    )
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    +
    Parameters
    + + + +
    lda_output_tableThe output table from lda traning or predicting
    mapping_tableThe result table that saves the mapping info
    +
    +
    + +
    +
    + +

    ◆ lda_parse_model()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    _pivotalr_lda_model lda_parse_model (bigint [] lda_model,
    integer voc_size,
    integer topic_num 
    )
    +
    + +
    +
    + +

    ◆ lda_predict() [1/2]

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    set<lda_result> lda_predict (text data_table,
    text model_table,
    text output_table 
    )
    +
    +
    Parameters
    + + + + +
    data_tableTable storing the testing dataset, each row is in the form of <docid, wordid, count> where docid, wordid, and count are all non-negative integers.
    model_tableTable storing the learned models
    output_tableTable storing per-document topic counts and topic assignments
    +
    +
    +
    Note
    default iter_num = 20
    + +
    +
    + +

    ◆ lda_predict() [2/2]

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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    set<lda_result> lda_predict (text data_table,
    text model_table,
    text output_table,
    int4 iter_num 
    )
    +
    + +
    +
    + +

    ◆ lda_train() [1/3]

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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    set<lda_result> lda_train (text data_table,
    text model_table,
    text output_data_table,
    int4 voc_size,
    int4 topic_num,
    int4 iter_num,
    float8 alpha,
    float8 beta 
    )
    +
    +
    Parameters
    + + + + + + + + + +
    data_tableTable storing the training dataset, each row is in the form of <docid, wordid, count> where docid, wordid, and count are all non-negative integers.
    model_tableTable storing the learned models (voc_size, topic_num, alpha, beta, per-word topic counts, and corpus-level topic counts)
    output_data_tableTable storing the output data table in the form of <docid, wordcount, words, counts, topic_count, topic_assignment>
    voc_sizeSize of the vocabulary (Note that the wordid should be continous integers starting from 0 to voc_size -
      +
    1. A data validation rountine will be called to validate the dataset.)
      2. +
    +
    topic_numNumber of topics (e.g. 100)
    iter_numNumber of iterations (e.g. 60)
    alphaDirichlet parameter for the per-doc topic multinomial (e.g. 50/topic_num)
    betaDirichlet parameter for the per-topic word multinomial (e.g. 0.01)
    +
    +
    + +
    +
    + +

    ◆ lda_train() [2/3]

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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    set<lda_result> lda_train (text data_table,
    text model_table,
    text output_data_table,
    int4 voc_size,
    int4 topic_num,
    int4 iter_num,
    float8 alpha,
    float8 beta,
    int4 evaluate_every,
    float8 perplexity_tol 
    )
    +
    + +
    +
    + +

    ◆ lda_train() [3/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    set<lda_result> lda_train (text data_table,
    text model_table,
    text output_data_table,
    int4 voc_size,
    int4 topic_num,
    int4 iter_num,
    float8 alpha,
    float8 beta,
    int4 evaluate_every 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/linalg_8sql__in.html b/docs/docs/v2.1.0/linalg_8sql__in.html new file mode 100644 index 00000000..01c6a642 --- /dev/null +++ b/docs/docs/v2.1.0/linalg_8sql__in.html @@ -0,0 +1,1326 @@ + + + + + + + + +MADlib: linalg.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
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    + + + +
    +
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    + + +
    + +
    + +
    +
    +Functions
    +
    +
    linalg.sql_in File Reference
    +
    +
    + +

    SQL functions for linear algebra. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    float8 norm1 (float8[] x)
     1-norm of a vector More...
     
    float8 norm2 (float8[] x)
     2-norm of a vector More...
     
    float8 dist_inf_norm (float8[] x, float8[] y)
     Infinity-norm of the difference between two vectors. More...
     
    float8 dist_pnorm (float8[] x, float8[] y, float8 p)
     p-norm of the difference between two vectors More...
     
    float8 dist_norm1 (float8[] x, float8[] y)
     1-norm of the difference between two vectors More...
     
    float8 dist_norm2 (float8[] x, float8[] y)
     2-norm of the difference between two vectors More...
     
    float8 cosine_similarity (float8[] x, float8[] y)
     cosine similarity score between two vectors More...
     
    float8 squared_dist_norm2 (float8[] x, float8[] y)
     Squared 2-norm of the difference between two vectors. More...
     
    float8 dist_angle (float8[] x, float8[] y)
     Angle between two vectors. More...
     
    float8 dist_tanimoto (float8[] x, float8[] y)
     Tanimoto distance between two vectors. More...
     
    float8 dist_jaccard (text[] x, text[] y)
     Jaccard distance between two vectors (treated as sets) More...
     
    closest_column_result _closest_column (float8[] m, float8[] x, regproc dist, text dist_dn)
     
    closest_column_result closest_column (float8[] m, float8[] x, regproc dist="squared_dist_norm2")
     Given matrix \( M \) and vector \( \vec x \) compute the column of \( M \) that is closest to \( \vec x \). More...
     
    closest_column_result closest_column (float8[] m, float8[] x)
     
    closest_columns_result _closest_columns (float8[] m, float8[] x, integer num, regproc dist, text dist_dn)
     Given matrix \( M \) and vector \( \vec x \) compute the columns of \( M \) that are closest to \( \vec x \). More...
     
    closest_columns_result closest_columns (float8[] m, float8[] x, integer num, regproc dist)
     
    closest_columns_result closest_columns (float8[] m, float8[] x, integer num)
     
    float8 [] avg_vector_transition (float8[] state, float8[] x)
     
    float8 [] avg_vector_merge (float8[] state_left, float8[] state_right)
     
    float8 [] avg_vector_final (float8[] state)
     
    aggregate float8 [] avg (float8[] x)
     Compute the average of vectors. More...
     
    float8 [] normalized_avg_vector_transition (float8[] state, float8[] x)
     
    float8 [] normalized_avg_vector_final (float8[] state)
     
    aggregate float8 [] normalized_avg (float8[] x)
     Compute the normalized average of vectors. More...
     
    float8 [] matrix_agg_transition (float8[] state, float8[] x)
     
    float8 [] matrix_agg_final (float8[] state)
     
    aggregate float8 [] matrix_agg (float8[] x)
     Combine vectors to a matrix. More...
     
    float8 [] matrix_column (float8[] matrix, integer col)
     Return the column of a matrix. More...
     
    set< record > deconstruct_2d_array (float8[] in_array)
     Construct a M-column N-row table of 2-D array. More...
     
    set< record > __deconstruct_lower_triangle (float8[] in_array)
     Construct a M-column M-row table of using lower triangle of 2-D array. More...
     
    float8 [] array_to_1d (float8[] in_array)
     Return the input array as 1-D. More...
     
    float8 [] array_to_2d (float8[] in_array)
     Return A 2-D matrix that the number of rows is encoded as the first element of the input array and the number of cols second. More...
     
    float8 [] index_2d_array (float8[] in_2d_array, integer index)
     Return A 1-D form of the specified row of the given 2-D array. More...
     
    float8 [] get_row (float8[] in_2d_array, integer index)
     Get an indexed row of the given matrix (2-D array) More...
     
    float8 [] get_col (float8[] in_2d_array, integer index)
     Get an indexed col of the given matrix (2-D array) More...
     
    +

    Detailed Description

    +
    See also
    For an overview of linear-algebra functions, see the module description Norms and Distance Functions.
    +

    Function Documentation

    + +

    ◆ __deconstruct_lower_triangle()

    + +
    +
    + + + + + + + + +
    set<record> __deconstruct_lower_triangle (float8 [] in_array)
    +
    +
    Parameters
    + + +
    in_array2-D array
    +
    +
    + +
    +
    + +

    ◆ _closest_column()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    closest_column_result _closest_column (float8 [] m,
    float8 [] x,
    regproc dist,
    text dist_dn 
    )
    +
    + +
    +
    + +

    ◆ _closest_columns()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    closest_columns_result _closest_columns (float8 [] m,
    float8 [] x,
    integer num,
    regproc dist,
    text dist_dn 
    )
    +
    +

    This function does essentially the same as closest_column(), except that it allows to specify the number of closest columns to return. The return value is a composite value:

      +
    • columns_ids INTEGER[] - The 0-based indices of the num columns of \( M \) that are closest to \( x \). In case of ties, the first such indices are returned.
      • +
    • distances DOUBLE PRECISION[] - The distances between the columns of \( M \) with indices in columns_ids and \( x \). That is, distances[i] contains \( \operatorname{dist}(\vec{m_j}, \vec x) \), where \( j = \) columns_ids[i].
      • +
    + +
    +
    + +

    ◆ array_to_1d()

    + +
    +
    + + + + + + + + +
    float8 [] array_to_1d (float8 [] in_array)
    +
    +
    Parameters
    + + +
    in_array1-D or 2-D array
    +
    +
    + +
    +
    + +

    ◆ array_to_2d()

    + +
    +
    + + + + + + + + +
    float8 [] array_to_2d (float8 [] in_array)
    +
    +
    Parameters
    + + +
    in_arrayInput array with first 2 elements describing dimensions
    +
    +
    + +
    +
    + +

    ◆ avg()

    + +
    +
    + + + + + + + + +
    aggregate float8 [] avg (float8 [] x)
    +
    +

    Given vectors \( x_1, \dots, x_n \), compute the average \( \frac 1n \sum_{i=1}^n x_i \).

    +
    Parameters
    + + +
    xPoint \( x_i \)
    +
    +
    +
    Returns
    Average \( \frac 1n \sum_{i=1}^n x_i \)
    + +
    +
    + +

    ◆ avg_vector_final()

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    +
    + + + + + + + + +
    float8 [] avg_vector_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ avg_vector_merge()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] avg_vector_merge (float8 [] state_left,
    float8 [] state_right 
    )
    +
    + +
    +
    + +

    ◆ avg_vector_transition()

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    + + + + + + + + + + + + + + + + + + +
    float8 [] avg_vector_transition (float8 [] state,
    float8 [] x 
    )
    +
    + +
    +
    + +

    ◆ closest_column() [1/2]

    + +
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    + + + + + + + + + + + + + + + + + + + + + + + + +
    closest_column_result closest_column (float8 [] m,
    float8 [] x,
    regproc dist = "squared_dist_norm2" 
    )
    +
    +
    Parameters
    + + + + +
    MMatrix \( M = (\vec{m_0} \dots \vec{m_{l-1}}) \in \mathbb{R}^{k \times l} \)
    xVector \( \vec x \in \mathbb R^k \)
    distThe metric \( \operatorname{dist} \). This needs to be a function with signature DOUBLE PRECISION[] x DOUBLE PRECISION[] -> DOUBLE PRECISION.
    +
    +
    +
    Returns
    A composite value:
      +
    • columns_id INTEGER - The 0-based index of the column of \( M \) that is closest to \( x \). In case of ties, the first such index is returned. That is, columns_id is the minimum element in the set \( \arg\min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \).
      • +
    • distance DOUBLE PRECISION - The minimum distance between any column of \( M \) and \( x \). That is, \( \min_{i=0,\dots,l-1} \operatorname{dist}(\vec{m_i}, \vec x) \).
      • +
    +
    + +
    +
    + +

    ◆ closest_column() [2/2]

    + +
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    + + + + + + + + + + + + + + + + + + +
    closest_column_result closest_column (float8 [] m,
    float8 [] x 
    )
    +
    + +
    +
    + +

    ◆ closest_columns() [1/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    closest_columns_result closest_columns (float8 [] m,
    float8 [] x,
    integer num,
    regproc dist 
    )
    +
    + +
    +
    + +

    ◆ closest_columns() [2/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    closest_columns_result closest_columns (float8 [] m,
    float8 [] x,
    integer num 
    )
    +
    + +
    +
    + +

    ◆ cosine_similarity()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 cosine_similarity (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( \frac{\langle \vec x, \vec y \rangle} {\| \vec x \| \cdot \| \vec y \|} \)
    + +
    +
    + +

    ◆ deconstruct_2d_array()

    + +
    +
    + + + + + + + + +
    set<record> deconstruct_2d_array (float8 [] in_array)
    +
    +
    Parameters
    + + +
    in_array2-D array
    +
    +
    + +
    +
    + +

    ◆ dist_angle()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 dist_angle (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( \arccos\left(\frac{\langle \vec x, \vec y \rangle} {\| \vec x \| \cdot \| \vec y \|}\right) \)
    + +
    +
    + +

    ◆ dist_inf_norm()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 dist_inf_norm (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( \| x - y \|_\infty = \max_{i=1}^n \|x_i - y_i\| \)
    + +
    +
    + +

    ◆ dist_jaccard()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 dist_jaccard (text [] x,
    text [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_m) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( 1 - \frac{|x \cap y|}{|x \cup y|} \)
    + +
    +
    + +

    ◆ dist_norm1()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 dist_norm1 (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( \| x - y \|_1 = \sum_{i=1}^n |x_i - y_i| \)
    + +
    +
    + +

    ◆ dist_norm2()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 dist_norm2 (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( \| x - y \|_2 = \sqrt{\sum_{i=1}^n (x_i - y_i)^2} \)
    + +
    +
    + +

    ◆ dist_pnorm()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 dist_pnorm (float8 [] x,
    float8 [] y,
    float8 p 
    )
    +
    +
    Parameters
    + + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    pScalar \( p > 0 \)
    +
    +
    +
    Returns
    \( \| x - y \|_p = (\sum_{i=1}^n \|x_i - y_i\|^p)^{\frac{1}{p}} \)
    + +
    +
    + +

    ◆ dist_tanimoto()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 dist_tanimoto (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( 1 - \frac{\langle \vec x, \vec y \rangle} {\| \vec x \|^2 \cdot \| \vec y \|^2 - \langle \vec x, \vec y \rangle} \)
    + +
    +
    + +

    ◆ get_col()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] get_col (float8 [] in_2d_array,
    integer index 
    )
    +
    +
    Parameters
    + + + +
    in_2d_arrayInput 2-D array
    index
    +
    +
    + +
    +
    + +

    ◆ get_row()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] get_row (float8 [] in_2d_array,
    integer index 
    )
    +
    +
    Parameters
    + + + +
    in_2d_arrayInput 2-D array
    index
    +
    +
    + +
    +
    + +

    ◆ index_2d_array()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] index_2d_array (float8 [] in_2d_array,
    integer index 
    )
    +
    +
    Parameters
    + + + +
    in_2d_arrayInput 2-D array
    index
    +
    +
    + +
    +
    + +

    ◆ matrix_agg()

    + +
    +
    + + + + + + + + +
    aggregate float8 [] matrix_agg (float8 [] x)
    +
    +

    Given vectors \( \vec x_1, \dots, \vec x_n \in \mathbb R^m \), return matrix \( ( \vec x_1 \dots \vec x_n ) \in \mathbb R^{m \times n}\).

    +
    Parameters
    + + +
    xVector \( x_i \)
    +
    +
    +
    Returns
    Matrix with columns \( x_1, \dots, x_n \)
    + +
    +
    + +

    ◆ matrix_agg_final()

    + +
    +
    + + + + + + + + +
    float8 [] matrix_agg_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ matrix_agg_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] matrix_agg_transition (float8 [] state,
    float8 [] x 
    )
    +
    + +
    +
    + +

    ◆ matrix_column()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] matrix_column (float8 [] matrix,
    integer col 
    )
    +
    +
    Parameters
    + + + +
    matrixTwo-dimensional matrix
    colColumn of the matrix to return (0-based index)
    +
    +
    + +
    +
    + +

    ◆ norm1()

    + +
    +
    + + + + + + + + +
    float8 norm1 (float8 [] x)
    +
    +
    Parameters
    + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    +
    +
    +
    Returns
    \( \| x \|_1 = \sum_{i=1}^n |x_i| \)
    + +
    +
    + +

    ◆ norm2()

    + +
    +
    + + + + + + + + +
    float8 norm2 (float8 [] x)
    +
    +
    Parameters
    + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    +
    +
    +
    Returns
    \( \| x \|_2 = \sqrt{\sum_{i=1}^n x_i^2} \)
    + +
    +
    + +

    ◆ normalized_avg()

    + +
    +
    + + + + + + + + +
    aggregate float8 [] normalized_avg (float8 [] x)
    +
    +

    Given vectors \( x_1, \dots, x_n \), define \( \widetilde{x} := \frac 1n \sum_{i=1}^n \frac{x_i}{\| x_i \|} \), and compute the normalized average \( \frac{\widetilde{x}}{\| \widetilde{x} \|} \).

    +
    Parameters
    + + +
    xPoint \( x_i \)
    +
    +
    +
    Returns
    Normalized average \( \frac{\widetilde{x}}{\| \widetilde{x} \|} \)
    + +
    +
    + +

    ◆ normalized_avg_vector_final()

    + +
    +
    + + + + + + + + +
    float8 [] normalized_avg_vector_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ normalized_avg_vector_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] normalized_avg_vector_transition (float8 [] state,
    float8 [] x 
    )
    +
    + +
    +
    + +

    ◆ squared_dist_norm2()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 squared_dist_norm2 (float8 [] x,
    float8 [] y 
    )
    +
    +
    Parameters
    + + + +
    xVector \( \vec x = (x_1, \dots, x_n) \)
    yVector \( \vec y = (y_1, \dots, y_n) \)
    +
    +
    +
    Returns
    \( \| x - y \|_2^2 = \sum_{i=1}^n (x_i - y_i)^2 \)
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/linear_8sql__in.html b/docs/docs/v2.1.0/linear_8sql__in.html new file mode 100644 index 00000000..30f7940e --- /dev/null +++ b/docs/docs/v2.1.0/linear_8sql__in.html @@ -0,0 +1,696 @@ + + + + + + + + +MADlib: linear.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    linear.sql_in File Reference
    +
    +
    + +

    SQL functions for linear regression. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    void linregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, boolean heteroskedasticity_option)
     Linear regression training function with grouping support. More...
     
    void linregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols)
     
    void linregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname)
     
    varchar linregr_train ()
     
    varchar linregr_train (varchar message)
     
    bytea8 linregr_transition (bytea8 state, float8 y, float8[] x)
     
    bytea8 linregr_merge_states (bytea8 state1, bytea8 state2)
     
    linregr_result linregr_final (bytea8 state)
     
    bytea8 hetero_linregr_transition (bytea8 state, float8 y, float8[] x, float8[] coef)
     
    bytea8 hetero_linregr_merge_states (bytea8 state1, bytea8 state2)
     
    heteroskedasticity_test_result hetero_linregr_final (bytea8 state)
     
    aggregate bytea8 linregr (float8 dependentVariable, float8[] independentVariables)
     Compute linear regression coefficients and diagnostic statistics. More...
     
    aggregate bytea8 heteroskedasticity_test_linregr (float8 dependentVariable, float8[] independentVariables, float8[] olsCoefficients)
     Compute studentized Breuch-Pagan heteroskedasticity test for linear regression. More...
     
    float8 linregr_predict (float8[] coef, float8[] col_ind_var)
     Predict the boolean value of a dependent variable for a specific independent variable value in a linear regression model. More...
     
    text linregr_predict (text message)
     
    text linregr_predict ()
     
    +

    Detailed Description

    +
    Date
    January 2011
    +
    See also
    For a brief introduction to linear regression, see the module description Linear Regression.
    +

    Function Documentation

    + +

    ◆ hetero_linregr_final()

    + +
    +
    + + + + + + + + +
    heteroskedasticity_test_result hetero_linregr_final (bytea8 state)
    +
    + +
    +
    + +

    ◆ hetero_linregr_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    bytea8 hetero_linregr_merge_states (bytea8 state1,
    bytea8 state2 
    )
    +
    + +
    +
    + +

    ◆ hetero_linregr_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    bytea8 hetero_linregr_transition (bytea8 state,
    float8 y,
    float8 [] x,
    float8 [] coef 
    )
    +
    + +
    +
    + +

    ◆ heteroskedasticity_test_linregr()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate bytea8 heteroskedasticity_test_linregr (float8 dependentVariable,
    float8 [] independentVariables,
    float8 [] olsCoefficients 
    )
    +
    +
    Parameters
    + + + + +
    dependentVariableColumn containing the dependent variable
    independentVariablesColumn containing the array of independent variables
    olsCoefficientsColumn containing the array of the OLS coefficients (as obtained by linregr)
    +
    +
    +
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    +
    Returns
    A composite value:
      +
    • test_statistic FLOAT8[] - Prob > test_statistc
      • +
    • p_value FLOAT8[] - Prob > test_statistc
      • +
    +
    +
    Usage
     SELECT (heteoskedasticity_test_linregr(dependentVariable,
+ independentVariables, coef)).*
+ FROM (
+   SELECT linregr(dependentVariable, independentVariables).coef
+ ) AS ols_coef, sourceName as src;
+
    + +
    +
    + +

    ◆ linregr()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    aggregate bytea8 linregr (float8 dependentVariable,
    float8 [] independentVariables 
    )
    +
    +
    Parameters
    + + + +
    dependentVariableColumn containing the dependent variable
    independentVariablesColumn containing the array of independent variables
    +
    +
    +
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    +
    Returns
    A composite value:
      +
    • coef FLOAT8[] - Array of coefficients, \( \boldsymbol c \)
      • +
    • r2 FLOAT8 - Coefficient of determination, \( R^2 \)
      • +
    • std_err FLOAT8[] - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
      • +
    • t_stats FLOAT8[] - Array of t-statistics, \( \boldsymbol t \)
      • +
    • p_values FLOAT8[] - Array of p-values, \( \boldsymbol p \)
      • +
    • condition_no FLOAT8 - The condition number of matrix \( X^T X \).
      • +
    +
    +
    Usage
      +
    • Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:
      + 
      SELECT (linregr(dependentVariable,
+        independentVariables)).*
+FROM sourceName;
      • +
    • Get vector of coefficients \( \boldsymbol c \):
      + 
      SELECT (linregr(dependentVariable,
+        independentVariables)).coef
+FROM sourceName;
      • +
    • Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the coefficient of determination \( R^2 \), and the array of p-values \( \boldsymbol p \): 
      SELECT (lr).coef, (lr).r2, (lr).p_values
+FROM (
+    SELECT linregr( dependentVariable,
+                    independentVariables) AS lr
+    FROM sourceName
+) AS subq;
      • +
    +
    + +
    +
    + +

    ◆ linregr_final()

    + +
    +
    + + + + + + + + +
    linregr_result linregr_final (bytea8 state)
    +
    + +
    +
    + +

    ◆ linregr_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    bytea8 linregr_merge_states (bytea8 state1,
    bytea8 state2 
    )
    +
    + +
    +
    + +

    ◆ linregr_predict() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 linregr_predict (float8 [] coef,
    float8 [] col_ind_var 
    )
    +
    +
    Parameters
    + + + +
    coefCoefficients obtained by running linear regression.
    col_indIndependent variable array
    +
    +
    +
    Returns
    DOUBLE PRECISION Predicted value
    +

    This function computes the dot product of the independent variables and the coefficients. This requires the length of the two vectors to be the same.

    + +
    +
    + +

    ◆ linregr_predict() [2/3]

    + +
    +
    + + + + + + + + +
    text linregr_predict (text message)
    +
    + +
    +
    + +

    ◆ linregr_predict() [3/3]

    + +
    +
    + + + + + + + +
    text linregr_predict ()
    +
    + +
    +
    + +

    ◆ linregr_train() [1/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void linregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols,
    boolean heteroskedasticity_option 
    )
    +
    + +
    +
    + +

    ◆ linregr_train() [2/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void linregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols 
    )
    +
    + +
    +
    + +

    ◆ linregr_train() [3/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void linregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname 
    )
    +
    + +
    +
    + +

    ◆ linregr_train() [4/5]

    + +
    +
    + + + + + + + +
    varchar linregr_train ()
    +
    + +
    +
    + +

    ◆ linregr_train() [5/5]

    + +
    +
    + + + + + + + + +
    varchar linregr_train (varchar message)
    +
    + +
    +
    + +

    ◆ linregr_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    bytea8 linregr_transition (bytea8 state,
    float8 y,
    float8 [] x 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/lmf_8sql__in.html b/docs/docs/v2.1.0/lmf_8sql__in.html new file mode 100644 index 00000000..ba1a5eb7 --- /dev/null +++ b/docs/docs/v2.1.0/lmf_8sql__in.html @@ -0,0 +1,876 @@ + + + + + + + + +MADlib: lmf.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    lmf.sql_in File Reference
    +
    +
    + +

    SQL functions for low-rank matrix factorization. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    float8 [] lmf_igd_transition (float8[] state, integer row_num, integer column_num, float8 val, float8[] previous_state, integer row_dim, integer column_dim, integer max_rank, float8 stepsize, float8 scale_factor)
     
    float8 [] lmf_igd_merge (float8[] state1, float8[] state2)
     
    float8 [] lmf_igd_final (float8[] state)
     
    aggregate float8 [] lmf_igd_step (integer row_num, integer column_num, float8 val, float8[] previous_state, integer row_dim, integer column_dim, integer max_rank, float8 stepsize, float8 scale_factor)
     
    float8 internal_lmf_igd_distance (float8[] state1, float8[] state2)
     
    lmf_result internal_lmf_igd_result (float8[] state)
     
    void internal_execute_using_lmf_igd_args (varchar sql, integer, integer, integer, float8, float8, integer, float8)
     
    integer internal_compute_lmf_igd (varchar rel_args, varchar rel_state, varchar rel_source, varchar col_row, varchar col_column, varchar col_value)
     
    integer lmf_igd_run (varchar rel_output, regclass rel_source, varchar col_row, varchar col_column, varchar col_value, integer row_dim="SELECT max(col_row) FROM rel_source", integer column_dim="SELECT max(col_col) FROM rel_source", integer max_rank=20, float8 stepsize=0.01, float8 scale_factor=0.1, integer num_iterations=10, float8 tolerance=0.0001)
     Low-rank matrix factorization of a incomplete matrix into two factors. More...
     
    integer lmf_igd_run (varchar rel_output, regclass rel_source, varchar col_row, varchar col_column, varchar col_value, integer row_dim, integer column_dim, integer max_rank, float8 stepsize, float8 scale_factor)
     
    integer lmf_igd_run (varchar rel_output, regclass rel_source, varchar col_row, varchar col_column, varchar col_value, integer row_dim, integer column_dim, integer max_rank, float8 stepsize)
     
    integer lmf_igd_run (varchar rel_output, regclass rel_source, varchar col_row, varchar col_column, varchar col_value, integer row_dim, integer column_dim, integer max_rank)
     
    integer lmf_igd_run (varchar rel_output, regclass rel_source, varchar col_row, varchar col_column, text col_value)
     
    +

    Detailed Description

    +
    Date
    June 2012
    +
    See also
    For a brief introduction to Low-rank Matrix Factorization, see the module description Low-Rank Matrix Factorization.
    +

    Function Documentation

    + +

    ◆ internal_compute_lmf_igd()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer internal_compute_lmf_igd (varchar rel_args,
    varchar rel_state,
    varchar rel_source,
    varchar col_row,
    varchar col_column,
    varchar col_value 
    )
    +
    + +
    +
    + +

    ◆ internal_execute_using_lmf_igd_args()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void internal_execute_using_lmf_igd_args (varchar sql,
    integer ,
    integer ,
    integer ,
    float8 ,
    float8 ,
    integer ,
    float8  
    )
    +
    + +
    +
    + +

    ◆ internal_lmf_igd_distance()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 internal_lmf_igd_distance (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ internal_lmf_igd_result()

    + +
    +
    + + + + + + + + +
    lmf_result internal_lmf_igd_result (float8 [] state)
    +
    + +
    +
    + +

    ◆ lmf_igd_final()

    + +
    +
    + + + + + + + + +
    float8 [] lmf_igd_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ lmf_igd_merge()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] lmf_igd_merge (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ lmf_igd_run() [1/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer lmf_igd_run (varchar rel_output,
    regclass rel_source,
    varchar col_row,
    varchar col_column,
    varchar col_value,
    integer row_dim = "SELECT max(col_row) FROM rel_source",
    integer column_dim = "SELECT max(col_col) FROM rel_source",
    integer max_rank = 20,
    float8 stepsize = 0.01,
    float8 scale_factor = 0.1,
    integer num_iterations = 10,
    float8 tolerance = 0.0001 
    )
    +
    +

    This function takes as input the table representation of a incomplete matrix in the sparse (i, j, value) format and decomposes it into the specified set of most significant features of matrices of U and V matrix. The input matrix is expected to have dimension [1:row_dim][1:column_dim], but in sparse format.

    +
    Parameters
    + + + + + + + + + + + + + +
    rel_outputName of the table that the factors will be appended to
    rel_sourceName of the table/view with the source data
    col_rowName of the column containing cell row number
    col_columnName of the column containing cell column number
    col_valueName of the column containing cell value
    row_dimMaximum number of rows of input
    column_dimMaximum number of columns of input
    max_rankRank of desired approximation
    stepsizeHyper-parameter that decides how aggressive that the gradient steps are
    scale_factorHyper-parameter that decides scale of initial factors
    num_iterationsMaximum number if iterations to perform regardless of convergence
    toleranceAcceptable level of error in convergence.
    +
    +
    + +
    +
    + +

    ◆ lmf_igd_run() [2/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer lmf_igd_run (varchar rel_output,
    regclass rel_source,
    varchar col_row,
    varchar col_column,
    varchar col_value,
    integer row_dim,
    integer column_dim,
    integer max_rank,
    float8 stepsize,
    float8 scale_factor 
    )
    +
    + +
    +
    + +

    ◆ lmf_igd_run() [3/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer lmf_igd_run (varchar rel_output,
    regclass rel_source,
    varchar col_row,
    varchar col_column,
    varchar col_value,
    integer row_dim,
    integer column_dim,
    integer max_rank,
    float8 stepsize 
    )
    +
    + +
    +
    + +

    ◆ lmf_igd_run() [4/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer lmf_igd_run (varchar rel_output,
    regclass rel_source,
    varchar col_row,
    varchar col_column,
    varchar col_value,
    integer row_dim,
    integer column_dim,
    integer max_rank 
    )
    +
    + +
    +
    + +

    ◆ lmf_igd_run() [5/5]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    integer lmf_igd_run (varchar rel_output,
    regclass rel_source,
    varchar col_row,
    varchar col_column,
    text col_value 
    )
    +
    + +
    +
    + +

    ◆ lmf_igd_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] lmf_igd_step (integer row_num,
    integer column_num,
    float8 val,
    float8 [] previous_state,
    integer row_dim,
    integer column_dim,
    integer max_rank,
    float8 stepsize,
    float8 scale_factor 
    )
    +
    + +
    +
    + +

    ◆ lmf_igd_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] lmf_igd_transition (float8 [] state,
    integer row_num,
    integer column_num,
    float8 val,
    float8 [] previous_state,
    integer row_dim,
    integer column_dim,
    integer max_rank,
    float8 stepsize,
    float8 scale_factor 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/logistic_8sql__in.html b/docs/docs/v2.1.0/logistic_8sql__in.html new file mode 100644 index 00000000..ad28ac0a --- /dev/null +++ b/docs/docs/v2.1.0/logistic_8sql__in.html @@ -0,0 +1,1274 @@ + + + + + + + + +MADlib: logistic.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    logistic.sql_in File Reference
    +
    +
    + +

    SQL functions for logistic regression. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    float8 [] __logregr_cg_step_transition (float8[], boolean, float8[], float8[])
     
    float8 [] __logregr_irls_step_transition (float8[], boolean, float8[], float8[])
     
    float8 [] __logregr_igd_step_transition (float8[], boolean, float8[], float8[])
     
    float8 [] __logregr_cg_step_merge_states (float8[] state1, float8[] state2)
     
    float8 [] __logregr_irls_step_merge_states (float8[] state1, float8[] state2)
     
    float8 [] __logregr_igd_step_merge_states (float8[] state1, float8[] state2)
     
    float8 [] __logregr_cg_step_final (float8[] state)
     
    float8 [] __logregr_irls_step_final (float8[] state)
     
    float8 [] __logregr_igd_step_final (float8[] state)
     
    aggregate float8 [] __logregr_cg_step (boolean y, float8[] x, float8[] previous_state)
     
    aggregate float8 [] __logregr_irls_step (boolean y, float8[] x, float8[] previous_state)
     
    aggregate float8 [] __logregr_igd_step (boolean y, float8[] x, float8[] previous_state)
     
    float8 __logregr_cg_step_distance (float8[] state1, float8[] state2)
     
    __logregr_result __logregr_cg_result (float8[] state)
     
    float8 __logregr_irls_step_distance (float8[] state1, float8[] state2)
     
    __logregr_result __logregr_irls_result (float8[] state)
     
    float8 __logregr_igd_step_distance (float8[] state1, float8[] state2)
     
    __logregr_result __logregr_igd_result (float8[] state)
     
    void logregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose)
     Compute logistic-regression coefficients and diagnostic statistics. More...
     
    void logregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname)
     
    void logregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols)
     
    void logregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer max_iter)
     
    void logregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer max_iter, varchar optimizer)
     
    void logregr_train (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer max_iter, varchar optimizer, float8 tolerance)
     
    text logregr_train (text message)
     
    text logregr_train ()
     
    float8 logistic (float8 x)
     Evaluate the usual logistic function in an under-/overflow-safe way. More...
     
    boolean logregr_predict (float8[] coef, float8[] col_ind_var)
     Predict the boolean value of a dependent variable for a specific independent variable value in a logistic regression model. More...
     
    text logregr_predict (text message)
     
    text logregr_predict ()
     
    float8 logregr_predict_prob (float8[] coef, float8[] col_ind_var)
     Compute the probability of the boolean dependent variable being True for a specific independent variable iin a logistic regression model. More...
     
    text logregr_predict_prob (text message)
     
    text logregr_predict_prob ()
     
    +

    Detailed Description

    +
    Date
    January 2011
    +
    See also
    For a brief introduction to logistic regression, see the module description Logistic Regression.
    +

    Function Documentation

    + +

    ◆ __logregr_cg_result()

    + +
    +
    + + + + + + + + +
    __logregr_result __logregr_cg_result (float8 [] state)
    +
    + +
    +
    + +

    ◆ __logregr_cg_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __logregr_cg_step (boolean y,
    float8 [] x,
    float8 [] previous_state 
    )
    +
    + +
    +
    + +

    ◆ __logregr_cg_step_distance()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 __logregr_cg_step_distance (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __logregr_cg_step_final()

    + +
    +
    + + + + + + + + +
    float8 [] __logregr_cg_step_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __logregr_cg_step_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __logregr_cg_step_merge_states (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __logregr_cg_step_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __logregr_cg_step_transition (float8 [],
    boolean ,
    float8 [],
    float8 [] 
    )
    +
    + +
    +
    + +

    ◆ __logregr_igd_result()

    + +
    +
    + + + + + + + + +
    __logregr_result __logregr_igd_result (float8 [] state)
    +
    + +
    +
    + +

    ◆ __logregr_igd_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __logregr_igd_step (boolean y,
    float8 [] x,
    float8 [] previous_state 
    )
    +
    + +
    +
    + +

    ◆ __logregr_igd_step_distance()

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    + + + + + + + + + + + + + + + + + + +
    float8 __logregr_igd_step_distance (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __logregr_igd_step_final()

    + +
    +
    + + + + + + + + +
    float8 [] __logregr_igd_step_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __logregr_igd_step_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __logregr_igd_step_merge_states (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __logregr_igd_step_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __logregr_igd_step_transition (float8 [],
    boolean ,
    float8 [],
    float8 [] 
    )
    +
    + +
    +
    + +

    ◆ __logregr_irls_result()

    + +
    +
    + + + + + + + + +
    __logregr_result __logregr_irls_result (float8 [] state)
    +
    + +
    +
    + +

    ◆ __logregr_irls_step()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    aggregate float8 [] __logregr_irls_step (boolean y,
    float8 [] x,
    float8 [] previous_state 
    )
    +
    + +
    +
    + +

    ◆ __logregr_irls_step_distance()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 __logregr_irls_step_distance (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __logregr_irls_step_final()

    + +
    +
    + + + + + + + + +
    float8 [] __logregr_irls_step_final (float8 [] state)
    +
    + +
    +
    + +

    ◆ __logregr_irls_step_merge_states()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 [] __logregr_irls_step_merge_states (float8 [] state1,
    float8 [] state2 
    )
    +
    + +
    +
    + +

    ◆ __logregr_irls_step_transition()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    float8 [] __logregr_irls_step_transition (float8 [],
    boolean ,
    float8 [],
    float8 [] 
    )
    +
    + +
    +
    + +

    ◆ logistic()

    + +
    +
    + + + + + + + + +
    float8 logistic (float8 x)
    +
    +
    Parameters
    + + +
    x
    +
    +
    +
    Returns
    \( \frac{1}{1 + \exp(-x)} \)
    +

    Evaluating this expression directly can lead to under- or overflows. This function performs the evaluation in a safe manner, making use of the following observations:

    +

    In order for the outcome of \( \exp(x) \) to be within the range of the minimum positive double-precision number (i.e., \( 2^{-1074} \)) and the maximum positive double-precision number (i.e., \( (1 + (1 - 2^{52})) * 2^{1023}) \), \( x \) has to be within the natural logarithm of these numbers, so roughly in between -744 and 709. However, \( 1 + \exp(x) \) will just evaluate to 1 if \( \exp(x) \) is less than the machine epsilon (i.e., \( 2^{-52} \)) or, equivalently, if \( x \) is less than the natural logarithm of that; i.e., in any case if \( x \) is less than -37. Note that taking the reciprocal of the largest double-precision number will not cause an underflow. Hence, no further checks are necessary.

    + +
    +
    + +

    ◆ logregr_predict() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    boolean logregr_predict (float8 [] coef,
    float8 [] col_ind_var 
    )
    +
    +
    Parameters
    + + + +
    coefCoefficients obtained by running logistic regression.
    col_indIndependent variable array
    +
    +
    +
    Returns
    Boolean value of the dependent variable
    +

    This function computes the dot product of the independent variables and the coefficients. This requires the length of the two vectors to be the same.

    + +
    +
    + +

    ◆ logregr_predict() [2/3]

    + +
    +
    + + + + + + + + +
    text logregr_predict (text message)
    +
    + +
    +
    + +

    ◆ logregr_predict() [3/3]

    + +
    +
    + + + + + + + +
    text logregr_predict ()
    +
    + +
    +
    + +

    ◆ logregr_predict_prob() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    float8 logregr_predict_prob (float8 [] coef,
    float8 [] col_ind_var 
    )
    +
    +
    Parameters
    + + + +
    coefCoefficients obtained by running logistic regression.
    col_indIndependent variable array
    +
    +
    +
    Returns
    Probability value of the dependent variable being True
    +

    This function computes the dot product of the independent variables and the coefficients, hence requires the length of the two vectors to be the same.

    + +
    +
    + +

    ◆ logregr_predict_prob() [2/3]

    + +
    +
    + + + + + + + + +
    text logregr_predict_prob (text message)
    +
    + +
    +
    + +

    ◆ logregr_predict_prob() [3/3]

    + +
    +
    + + + + + + + +
    text logregr_predict_prob ()
    +
    + +
    +
    + +

    ◆ logregr_train() [1/8]

    + +
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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void logregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols,
    integer max_iter,
    varchar optimizer,
    float8 tolerance,
    boolean verbose 
    )
    +
    +

    To include an intercept in the model, set one coordinate in the independentVariables array to 1.

    +
    Parameters
    + + + + + + + + + + +
    source_tableName of the source relation containing the training data
    out_tableName of the output relation to store the model results 
                  Columns of the output relation are as follows:
+               - <tt>coef FLOAT8[]</tt> - Array of coefficients, \form#79
+               - <tt>log_likelihood FLOAT8</tt> - Log-likelihood \form#80
+               - <tt>std_err FLOAT8[]</tt> - Array of standard errors,
+
    \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
      +
    • z_stats FLOAT8[] - Array of Wald z-statistics, \( \boldsymbol z \)
      • +
    • p_values FLOAT8[] - Array of Wald p-values, \( \boldsymbol p \)
      • +
    • odds_ratios FLOAT8[]: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)
      • +
    • condition_no FLOAT8 - The condition number of matrix \( X^T A X \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration)
      • +
    +
    dependent_varnameName of the dependent column (of type BOOLEAN)
    independent_varnameName of the independent column (of type DOUBLE PRECISION[])
    grouping_colComma delimited list of column names to group-by
    max_iterThe maximum number of iterations
    optimizerThe optimizer to use (either 'irls'/'newton' for iteratively reweighted least squares or 'cg' for conjugent gradient)
    toleranceThe difference between log-likelihood values in successive iterations that should indicate convergence. This value should be non-negative and a zero value here disables the convergence criterion, and execution will only stop after maxNumIterations iterations.
    verboseIf true, any error or warning message will be printed to the console (irrespective of the 'client_min_messages' set by server). If false, no error/warning message is printed to console.
    +
    +
    +
    Usage
      +
    • Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:
      + 
      SELECT logregr_train('sourceName', 'outName'
+          'dependentVariable', 'independentVariables');
+         SELECT * from outName;
+
      • +
    • Get vector of coefficients \( \boldsymbol c \):
      + 
      SELECT coef from outName;
      • +
    • Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \): 
      SELECT coef, log_likelihood, p_values FROM outName;
      • +
    +
    +
    Note
    This function starts an iterative algorithm. It is not an aggregate function. Source, output, and column names have to be passed as strings (due to limitations of the SQL syntax).
    + +
    +
    + +

    ◆ logregr_train() [2/8]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void logregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname 
    )
    +
    + +
    +
    + +

    ◆ logregr_train() [3/8]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void logregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols 
    )
    +
    + +
    +
    + +

    ◆ logregr_train() [4/8]

    + +
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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void logregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols,
    integer max_iter 
    )
    +
    + +
    +
    + +

    ◆ logregr_train() [5/8]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void logregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols,
    integer max_iter,
    varchar optimizer 
    )
    +
    + +
    +
    + +

    ◆ logregr_train() [6/8]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void logregr_train (varchar source_table,
    varchar out_table,
    varchar dependent_varname,
    varchar independent_varname,
    varchar grouping_cols,
    integer max_iter,
    varchar optimizer,
    float8 tolerance 
    )
    +
    + +
    +
    + +

    ◆ logregr_train() [7/8]

    + +
    +
    + + + + + + + + +
    text logregr_train (text message)
    +
    + +
    +
    + +

    ◆ logregr_train() [8/8]

    + +
    +
    + + + + + + + +
    text logregr_train ()
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib.png b/docs/docs/v2.1.0/madlib.png new file mode 100644 index 0000000000000000000000000000000000000000..be014c60fe6bc45123bc5648fc233bf08ce02f04 GIT binary patch literal 2209 zcmYjTdpwiv8-EOih{$1^!?qGX=h&N&LUU$j2S(94td>Z{`&Oca;*~=xjEdP<4mGMt zh~7^0ww!vMIw&PtY7TSW$nW0k_s8$~T+jVn_xJvOulu^L=l*=2=T8FOQ%wb-0zr_P zw-=5Go@8*_D#?R!Mo*OwK`;rykL(VnQ2BeT7Xf0{iHT@QDFT?SCjl5hmc1b0tRN;~ zM_0fxXJdeXRcQ@;#aW1lZ}uceZ^30jg3*8`rlP0zpr#58=ZlemBQ29LSLD)CIBgPys2?eoqTNg;=@@gmjFrXC+Bwbie&DvBp zP>C2Dq<3Xan51CDL1>Tw5UwEqZiF%2Nd$F)G6BcNg8L)_N6%a;HQGnKm}F-?Kf|r!bmINze@A~G8KRx+ioll#4OxE3{y;|=%}xuCZHRO zWwMrHaegZ*@TPzky4fnL-DmYeA##?2g5};{C`P*Y;lGC(o8pL|qU8!*@KQwAQO0h> zNgC$EWmCPYT&sXk={>lFXb5tc4nlniGaU^7&#LU(pRaCOxQQf@e7yqvLGp@Ms;&L0 zQ-@LW8Tz0V%RC*hqXmgZCi!;IZ9e9j0Ih3!`T`RPQc}*WXg_GvlVLuaU}#RJ&1dU_ z;J^m1noJ!+0fLx;QcGn6hkwjzjJm;oJ5Ex8n9tEqqwfSX5E+as9UG@^1l^thJ>ept z!iE_N8kE1p)ic={xIi*mzP%nC4@>tzaKa}7Hb~3in>`4k5MwD1e!U+v1P=eVSR$ST zB`VOIisrlPZ*d8ZU`_NdUN|3j@4gC^ulf3ve{w- zQhN;`&y0_Wehvb|`iA=fy!E)NVeo!oyk%Pw5#aQ4$;$H(~g`=a`}dfnV3_Ub~F zXDXD4&Zh<*+JapcG0N0pll_IRdvoMe;FJoo^X^f5!$_!=H2W&1xxR3Mt(00S z7_fSYAoJAk=`kbj1l?)RUjGW`?~iCmA`E@(wQ-NxsMdBgoonw-`sHakMjC1;Nft47 zjE`>LPD#-DfeSDyZhDCs?=quAti9IRTq`D)BumqGRi1j1^y2XALR-2{rstwbLWO5i zbTEwLksMKNKV*IWM1JQwjZu9qUZl@IJk?f*PQPcz=^|)#mU*#~!SeaQC{-&`?X1Im z@6u&L#WhF%wpKdZo1Iz^W0BeZV>+2t9B`CAH@Qn+s{PyOprV^oq_;t|me4eYKa~3=T<%bvv0IEDXYI85q-o}j z@lP=yT8A9TpPjY(i;gKw%xQLQwP*Q8Q_NW}5CYRB(b_D>YrEn~#?Fih4jL5pRH08R z*Cp1lHQ(tlsw8m;=B{U<*l%lCFg3ZEjYl?3CEh$zjB60}Eo z#>(K5u;;GQ0g5}{@NjOonJB)H5t+iprZ&J{nv@Jnmlan|{Z73smaHk|v4@jId2-8k0tHM`g`WZr+cI)G6FOHB1} z8-OfM3CDi*hq(-!NAysbJ6HG1@m2}z8lk09khE}Av$gM?hUGeK3hZE42h!S5itkHI zDUzdEvqyi0C1#m{FQA$B^w+xbXWz1o92!CcB?^hI85Hj4=hUdrn+B9z*2vv~(Nqh@ z*Ip{!Ka#%xbS!+14z;N~UBarjW)`;W;rbRmtzz7N=@s4LBeh4i>BU53Iq=`e2XFF6 zn6aD(LY1YlzDJw6CO_159#jr&ecYgR7(X#}eNf47da5zY>5N&o<6UuF;t*T0J%+1|y$V#YB2u5<2_WzZ;U@=UQ85FoXFg zCV8p$bV!MHu1Lz)Z_0TszsHts$g*Hr{f=>DAJ+_IdY);-GJlS#Mr5=x&=h^=iQY(T zLUa5LX0v$XUFme*$?El{@Y>U5VG5lV4cn&U$%p#Gw@l&@MBjMNx~5~8+#g4Vv%Y71 jt)jk=*zeQd8}%5vbZ@Sz_mCY$_OIdXj>qxbXi5JC7BdY4 literal 0 HcmV?d00001 diff --git a/docs/docs/v2.1.0/madlib__keras_8sql__in.html b/docs/docs/v2.1.0/madlib__keras_8sql__in.html new file mode 100644 index 00000000..2ae497ca --- /dev/null +++ b/docs/docs/v2.1.0/madlib__keras_8sql__in.html @@ -0,0 +1,1915 @@ + + + + + + + + +MADlib: madlib_keras.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    madlib_keras.sql_in File Reference
    +
    +
    + +

    Fit, evaluate and predict for one model. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    void madlib_keras_fit (varchar source_table, varchar model, varchar model_arch_table, integer model_id, varchar compile_params, varchar fit_params, integer num_iterations, boolean use_gpus=false, varchar validation_table=NULL, integer metrics_compute_frequency=NULL, boolean warm_start=NULL, varchar name=NULL, varchar description=NULL, varchar object_table=NULL)
     
    bytea fit_transition (bytea state, bytea[] dependent_var, bytea[] independent_var, integer[] dependent_var_shape, integer[] independent_var_shape, text model_architecture, text compile_params, text fit_params, integer dist_key, integer[] dist_key_mapping, integer current_seg_id, integer[] segments_per_host, integer[] images_per_seg, integer[] accessible_gpus_for_seg, bytea prev_serialized_weights, bytea custom_function_map)
     
    bytea fit_transition_wide (bytea state, bytea dependent_var1, bytea dependent_var2, bytea dependent_var3, bytea dependent_var4, bytea dependent_var5, bytea independent_var1, bytea independent_var2, bytea independent_var3, bytea independent_var4, bytea independent_var5, integer[] dependent_var_shape, integer[] independent_var_shape, text model_architecture, text compile_params, text fit_params, integer dist_key, integer[] dist_key_mapping, integer current_seg_id, integer[] segments_per_host, integer[] images_per_seg, integer[] accessible_gpus_for_seg, bytea prev_serialized_weights, bytea custom_function_map)
     
    bytea fit_merge (bytea state1, bytea state2)
     
    bytea fit_final (bytea state)
     
    aggregate bytea fit_step (bytea, bytea, bytea, bytea, bytea, bytea, bytea, bytea, bytea, bytea, integer[], integer[], text, text, text, integer, integer[], integer, integer[], integer[], integer[], bytea, bytea)
     
    aggregate bytea fit_step (bytea[], bytea[], integer[], integer[], text, text, text, integer, integer[], integer, integer[], integer[], integer[], bytea, bytea)
     
    void madlib_keras_predict (varchar model_table, varchar test_table, varchar id_col, varchar independent_varname, varchar output_table, varchar pred_type="prob", boolean use_gpus=false, integer mst_key=NULL)
     
    void madlib_keras_predict (varchar model_table, varchar test_table, varchar id_col, varchar independent_varname, varchar output_table, integer pred_type, boolean use_gpus=false, integer mst_key=NULL)
     
    void madlib_keras_predict (varchar model_table, varchar test_table, varchar id_col, varchar independent_varname, varchar output_table, float8 pred_type, boolean use_gpus=false, integer mst_key=NULL)
     
    float8 [] internal_keras_predict (real[] independent_var, real[] independent_var2, real[] independent_var3, real[] independent_var4, real[] independent_var5, text model_architecture, bytea model_weights, float8 normalizing_const, integer current_seg_id, integer[] seg_ids, integer[] images_per_seg, integer gpus_per_host, integer[] segments_per_host)
     
    void madlib_keras_predict_byom (varchar model_arch_table, integer model_id, varchar test_table, varchar id_col, varchar independent_varname, varchar output_table, varchar pred_type="prob", boolean use_gpus=NULL, text[] class_values=NULL, float8 normalizing_const=NULL, integer dependent_count=1)
     
    void madlib_keras_predict_byom (varchar model_arch_table, integer model_id, varchar test_table, varchar id_col, varchar independent_varname, varchar output_table, integer pred_type, boolean use_gpus=NULL, text[] class_values=NULL, float8 normalizing_const=NULL)
     
    void madlib_keras_predict_byom (varchar model_arch_table, integer model_id, varchar test_table, varchar id_col, varchar independent_varname, varchar output_table, float8 pred_type, boolean use_gpus=NULL, text[] class_values=NULL, float8 normalizing_const=NULL)
     
    void madlib_keras_evaluate (varchar model_table, varchar test_table, varchar output_table, boolean use_gpus, integer mst_key)
     
    void madlib_keras_evaluate (varchar model_table, varchar test_table, varchar output_table, boolean use_gpus)
     
    void madlib_keras_evaluate (varchar model_table, varchar test_table, varchar output_table)
     
    real [] internal_keras_eval_transition (real[] state, bytea[] dependent_var, bytea[] independent_var, integer[] dependent_var_shape, integer[] independent_var_shape, text model_architecture, bytea serialized_weights, text compile_params, integer dist_key, integer[] dist_key_mapping, integer current_seg_id, integer[] segments_per_host, integer[] images_per_seg, integer[] accessible_gpus_for_seg, boolean should_clear_session, bytea custom_function_map)
     
    real [] internal_keras_eval_merge (real[] state1, real[] state2)
     
    real [2] internal_keras_eval_final (real[] state)
     
    aggregate real [2] internal_keras_evaluate (bytea[], bytea[], integer[], integer[], text, bytea, text, integer, integer[], integer, integer[], integer[], integer[], boolean, bytea)
     
    varchar madlib_keras_fit (varchar message)
     
    varchar madlib_keras_fit ()
     
    varchar madlib_keras_evaluate (varchar message)
     
    varchar madlib_keras_evaluate ()
     
    varchar madlib_keras_predict (varchar message)
     
    varchar madlib_keras_predict ()
     
    varchar madlib_keras_predict_byom (varchar message)
     
    varchar madlib_keras_predict_byom ()
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    June 2019
    +

    Function Documentation

    + +

    ◆ fit_final()

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    bytea fit_final (bytea state)
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    ◆ fit_merge()

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    bytea fit_merge (bytea state1,
    bytea state2 
    )
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    ◆ fit_step() [1/2]

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    aggregate bytea fit_step (bytea ,
    bytea ,
    bytea ,
    bytea ,
    bytea ,
    bytea ,
    bytea ,
    bytea ,
    bytea ,
    bytea ,
    integer [],
    integer [],
    text ,
    text ,
    text ,
    integer ,
    integer [],
    integer ,
    integer [],
    integer [],
    integer [],
    bytea ,
    bytea  
    )
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    ◆ fit_step() [2/2]

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    aggregate bytea fit_step (bytea [],
    bytea [],
    integer [],
    integer [],
    text ,
    text ,
    text ,
    integer ,
    integer [],
    integer ,
    integer [],
    integer [],
    integer [],
    bytea ,
    bytea  
    )
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    ◆ fit_transition()

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    bytea fit_transition (bytea state,
    bytea [] dependent_var,
    bytea [] independent_var,
    integer [] dependent_var_shape,
    integer [] independent_var_shape,
    text model_architecture,
    text compile_params,
    text fit_params,
    integer dist_key,
    integer [] dist_key_mapping,
    integer current_seg_id,
    integer [] segments_per_host,
    integer [] images_per_seg,
    integer [] accessible_gpus_for_seg,
    bytea prev_serialized_weights,
    bytea custom_function_map 
    )
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    ◆ fit_transition_wide()

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    bytea fit_transition_wide (bytea state,
    bytea dependent_var1,
    bytea dependent_var2,
    bytea dependent_var3,
    bytea dependent_var4,
    bytea dependent_var5,
    bytea independent_var1,
    bytea independent_var2,
    bytea independent_var3,
    bytea independent_var4,
    bytea independent_var5,
    integer [] dependent_var_shape,
    integer [] independent_var_shape,
    text model_architecture,
    text compile_params,
    text fit_params,
    integer dist_key,
    integer [] dist_key_mapping,
    integer current_seg_id,
    integer [] segments_per_host,
    integer [] images_per_seg,
    integer [] accessible_gpus_for_seg,
    bytea prev_serialized_weights,
    bytea custom_function_map 
    )
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    ◆ internal_keras_eval_final()

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    real [2] internal_keras_eval_final (real [] state)
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    ◆ internal_keras_eval_merge()

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    real [] internal_keras_eval_merge (real [] state1,
    real [] state2 
    )
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    ◆ internal_keras_eval_transition()

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    real [] internal_keras_eval_transition (real [] state,
    bytea [] dependent_var,
    bytea [] independent_var,
    integer [] dependent_var_shape,
    integer [] independent_var_shape,
    text model_architecture,
    bytea serialized_weights,
    text compile_params,
    integer dist_key,
    integer [] dist_key_mapping,
    integer current_seg_id,
    integer [] segments_per_host,
    integer [] images_per_seg,
    integer [] accessible_gpus_for_seg,
    boolean should_clear_session,
    bytea custom_function_map 
    )
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    ◆ internal_keras_evaluate()

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    aggregate real [2] internal_keras_evaluate (bytea [],
    bytea [],
    integer [],
    integer [],
    text ,
    bytea ,
    text ,
    integer ,
    integer [],
    integer ,
    integer [],
    integer [],
    integer [],
    boolean ,
    bytea  
    )
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    ◆ internal_keras_predict()

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    float8 [] internal_keras_predict (real [] independent_var,
    real [] independent_var2,
    real [] independent_var3,
    real [] independent_var4,
    real [] independent_var5,
    text model_architecture,
    bytea model_weights,
    float8 normalizing_const,
    integer current_seg_id,
    integer [] seg_ids,
    integer [] images_per_seg,
    integer gpus_per_host,
    integer [] segments_per_host 
    )
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    ◆ madlib_keras_evaluate() [1/5]

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    void madlib_keras_evaluate (varchar model_table,
    varchar test_table,
    varchar output_table,
    boolean use_gpus,
    integer mst_key 
    )
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    ◆ madlib_keras_evaluate() [2/5]

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    void madlib_keras_evaluate (varchar model_table,
    varchar test_table,
    varchar output_table,
    boolean use_gpus 
    )
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    ◆ madlib_keras_evaluate() [3/5]

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    void madlib_keras_evaluate (varchar model_table,
    varchar test_table,
    varchar output_table 
    )
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    ◆ madlib_keras_evaluate() [4/5]

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    varchar madlib_keras_evaluate (varchar message)
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    ◆ madlib_keras_evaluate() [5/5]

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    varchar madlib_keras_evaluate ()
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    ◆ madlib_keras_fit() [1/3]

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    void madlib_keras_fit (varchar source_table,
    varchar model,
    varchar model_arch_table,
    integer model_id,
    varchar compile_params,
    varchar fit_params,
    integer num_iterations,
    boolean use_gpus = false,
    varchar validation_table = NULL,
    integer metrics_compute_frequency = NULL,
    boolean warm_start = NULL,
    varchar name = NULL,
    varchar description = NULL,
    varchar object_table = NULL 
    )
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    ◆ madlib_keras_fit() [2/3]

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    varchar madlib_keras_fit (varchar message)
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    ◆ madlib_keras_fit() [3/3]

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    varchar madlib_keras_fit ()
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    ◆ madlib_keras_predict() [1/5]

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    void madlib_keras_predict (varchar model_table,
    varchar test_table,
    varchar id_col,
    varchar independent_varname,
    varchar output_table,
    varchar pred_type = "prob",
    boolean use_gpus = false,
    integer mst_key = NULL 
    )
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    ◆ madlib_keras_predict() [2/5]

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    void madlib_keras_predict (varchar model_table,
    varchar test_table,
    varchar id_col,
    varchar independent_varname,
    varchar output_table,
    integer pred_type,
    boolean use_gpus = false,
    integer mst_key = NULL 
    )
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    ◆ madlib_keras_predict() [3/5]

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    void madlib_keras_predict (varchar model_table,
    varchar test_table,
    varchar id_col,
    varchar independent_varname,
    varchar output_table,
    float8 pred_type,
    boolean use_gpus = false,
    integer mst_key = NULL 
    )
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    ◆ madlib_keras_predict() [4/5]

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    varchar madlib_keras_predict (varchar message)
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    ◆ madlib_keras_predict() [5/5]

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    varchar madlib_keras_predict ()
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    ◆ madlib_keras_predict_byom() [1/5]

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    void madlib_keras_predict_byom (varchar model_arch_table,
    integer model_id,
    varchar test_table,
    varchar id_col,
    varchar independent_varname,
    varchar output_table,
    varchar pred_type = "prob",
    boolean use_gpus = NULL,
    text [] class_values = NULL,
    float8 normalizing_const = NULL,
    integer dependent_count = 1 
    )
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    ◆ madlib_keras_predict_byom() [2/5]

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    void madlib_keras_predict_byom (varchar model_arch_table,
    integer model_id,
    varchar test_table,
    varchar id_col,
    varchar independent_varname,
    varchar output_table,
    integer pred_type,
    boolean use_gpus = NULL,
    text [] class_values = NULL,
    float8 normalizing_const = NULL 
    )
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    ◆ madlib_keras_predict_byom() [3/5]

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    void madlib_keras_predict_byom (varchar model_arch_table,
    integer model_id,
    varchar test_table,
    varchar id_col,
    varchar independent_varname,
    varchar output_table,
    float8 pred_type,
    boolean use_gpus = NULL,
    text [] class_values = NULL,
    float8 normalizing_const = NULL 
    )
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    ◆ madlib_keras_predict_byom() [4/5]

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    varchar madlib_keras_predict_byom (varchar message)
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    ◆ madlib_keras_predict_byom() [5/5]

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    varchar madlib_keras_predict_byom ()
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    + + + + diff --git a/docs/docs/v2.1.0/madlib__keras__automl_8sql__in.html b/docs/docs/v2.1.0/madlib__keras__automl_8sql__in.html new file mode 100644 index 00000000..fca26b50 --- /dev/null +++ b/docs/docs/v2.1.0/madlib__keras__automl_8sql__in.html @@ -0,0 +1,297 @@ + + + + + + + + +MADlib: madlib_keras_automl.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
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    + + + + + + + + +
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    + 2.1.0 +
    +
    User Documentation for Apache MADlib
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    +Functions
    +
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    madlib_keras_automl.sql_in File Reference
    +
    +
    + +

    Functions to run automated machine learning (autoML) methods for model architecture search and hyperparameter tuning. +More...

    + + + + + + +

    +Functions

    void hyperband_schedule (varchar schedule_table, integer r, integer eta=3, integer skip_last=0)
     
    void madlib_keras_automl (varchar source_table, varchar model_output_table, varchar model_arch_table, varchar model_selection_table, integer[] model_id_list, varchar compile_params_grid, varchar fit_params_grid, varchar automl_method="hyperband", varchar automl_params=NULL, integer random_state=NULL, varchar object_table=NULL, boolean use_gpus=false, varchar validation_table=NULL, integer metrics_compute_frequency=NULL, varchar name=NULL, varchar description=NULL, boolean use_caching=false)
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    August 2020
    +

    Function Documentation

    + +

    ◆ hyperband_schedule()

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    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void hyperband_schedule (varchar schedule_table,
    integer r,
    integer eta = 3,
    integer skip_last = 0 
    )
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    ◆ madlib_keras_automl()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_automl (varchar source_table,
    varchar model_output_table,
    varchar model_arch_table,
    varchar model_selection_table,
    integer [] model_id_list,
    varchar compile_params_grid,
    varchar fit_params_grid,
    varchar automl_method = "hyperband",
    varchar automl_params = NULL,
    integer random_state = NULL,
    varchar object_table = NULL,
    boolean use_gpus = false,
    varchar validation_table = NULL,
    integer metrics_compute_frequency = NULL,
    varchar name = NULL,
    varchar description = NULL,
    boolean use_caching = false 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib__keras__custom__function_8sql__in.html b/docs/docs/v2.1.0/madlib__keras__custom__function_8sql__in.html new file mode 100644 index 00000000..d48d20d4 --- /dev/null +++ b/docs/docs/v2.1.0/madlib__keras__custom__function_8sql__in.html @@ -0,0 +1,450 @@ + + + + + + + + +MADlib: madlib_keras_custom_function.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    madlib_keras_custom_function.sql_in File Reference
    +
    +
    + +

    Function to load serialized Python objects into a table. +More...

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    +Functions

    void load_custom_function (varchar object_table, bytea object, text name, text description)
     
    void load_custom_function (varchar object_table, bytea object, text name)
     
    varchar load_custom_function (varchar message)
     
    varchar load_custom_function ()
     
    void delete_custom_function (varchar object_table, integer id)
     
    void delete_custom_function (varchar object_table, text name)
     
    varchar delete_custom_function (varchar message)
     
    varchar delete_custom_function ()
     
    void load_top_k_accuracy_function (varchar object_table, integer k)
     
    varchar load_top_k_accuracy_function (varchar message)
     
    varchar load_top_k_accuracy_function ()
     
    bytea top_k_categorical_acc_pickled (integer n, varchar fn_name)
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    May 2020
    +

    Function Documentation

    + +

    ◆ delete_custom_function() [1/4]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    void delete_custom_function (varchar object_table,
    integer id 
    )
    +
    + +
    +
    + +

    ◆ delete_custom_function() [2/4]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    void delete_custom_function (varchar object_table,
    text name 
    )
    +
    + +
    +
    + +

    ◆ delete_custom_function() [3/4]

    + +
    +
    + + + + + + + + +
    varchar delete_custom_function (varchar message)
    +
    + +
    +
    + +

    ◆ delete_custom_function() [4/4]

    + +
    +
    + + + + + + + +
    varchar delete_custom_function ()
    +
    + +
    +
    + +

    ◆ load_custom_function() [1/4]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_custom_function (varchar object_table,
    bytea object,
    text name,
    text description 
    )
    +
    + +
    +
    + +

    ◆ load_custom_function() [2/4]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_custom_function (varchar object_table,
    bytea object,
    text name 
    )
    +
    + +
    +
    + +

    ◆ load_custom_function() [3/4]

    + +
    +
    + + + + + + + + +
    varchar load_custom_function (varchar message)
    +
    + +
    +
    + +

    ◆ load_custom_function() [4/4]

    + +
    +
    + + + + + + + +
    varchar load_custom_function ()
    +
    + +
    +
    + +

    ◆ load_top_k_accuracy_function() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    void load_top_k_accuracy_function (varchar object_table,
    integer k 
    )
    +
    + +
    +
    + +

    ◆ load_top_k_accuracy_function() [2/3]

    + +
    +
    + + + + + + + + +
    varchar load_top_k_accuracy_function (varchar message)
    +
    + +
    +
    + +

    ◆ load_top_k_accuracy_function() [3/3]

    + +
    +
    + + + + + + + +
    varchar load_top_k_accuracy_function ()
    +
    + +
    +
    + +

    ◆ top_k_categorical_acc_pickled()

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    bytea top_k_categorical_acc_pickled (integer n,
    varchar fn_name 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib__keras__fit__multiple__model_8sql__in.html b/docs/docs/v2.1.0/madlib__keras__fit__multiple__model_8sql__in.html new file mode 100644 index 00000000..d73a4db0 --- /dev/null +++ b/docs/docs/v2.1.0/madlib__keras__fit__multiple__model_8sql__in.html @@ -0,0 +1,631 @@ + + + + + + + + +MADlib: madlib_keras_fit_multiple_model.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    madlib_keras_fit_multiple_model.sql_in File Reference
    +
    +
    + + + + + + + + + + + + + + + + +

    +Functions

    void madlib_keras_fit_multiple_model (varchar source_table, varchar model_output_table, varchar model_selection_table, integer num_iterations, boolean use_gpus, varchar validation_table, integer metrics_compute_frequency, boolean warm_start, varchar name, varchar description, boolean use_caching=false)
     
    void madlib_keras_fit_multiple_model (varchar source_table, varchar model_output_table, varchar model_selection_table, integer num_iterations, boolean use_gpus, varchar validation_table, integer metrics_compute_frequency, boolean warm_start, varchar name)
     
    void madlib_keras_fit_multiple_model (varchar source_table, varchar model_output_table, varchar model_selection_table, integer num_iterations, boolean use_gpus, varchar validation_table, integer metrics_compute_frequency, boolean warm_start)
     
    void madlib_keras_fit_multiple_model (varchar source_table, varchar model_output_table, varchar model_selection_table, integer num_iterations, boolean use_gpus, varchar validation_table, integer metrics_compute_frequency)
     
    void madlib_keras_fit_multiple_model (varchar source_table, varchar model_output_table, varchar model_selection_table, integer num_iterations, boolean use_gpus, varchar validation_table)
     
    void madlib_keras_fit_multiple_model (varchar source_table, varchar model_output_table, varchar model_selection_table, integer num_iterations, boolean use_gpus)
     
    bytea fit_transition_multiple_model (bytea[] dependent_var, bytea[] independent_var, integer[] dependent_var_shape, integer[] independent_var_shape, text model_architecture, text compile_params, text fit_params, integer dist_key, integer[] dist_key_mapping, integer current_seg_id, integer[] segments_per_host, integer[] images_per_seg, integer[] accessible_gpus_for_seg, bytea serialized_weights, boolean is_final_training_call, boolean use_caching, bytea custom_function_map)
     
    +

    Function Documentation

    + +

    ◆ fit_transition_multiple_model()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    bytea fit_transition_multiple_model (bytea [] dependent_var,
    bytea [] independent_var,
    integer [] dependent_var_shape,
    integer [] independent_var_shape,
    text model_architecture,
    text compile_params,
    text fit_params,
    integer dist_key,
    integer [] dist_key_mapping,
    integer current_seg_id,
    integer [] segments_per_host,
    integer [] images_per_seg,
    integer [] accessible_gpus_for_seg,
    bytea serialized_weights,
    boolean is_final_training_call,
    boolean use_caching,
    bytea custom_function_map 
    )
    +
    + +
    +
    + +

    ◆ madlib_keras_fit_multiple_model() [1/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_fit_multiple_model (varchar source_table,
    varchar model_output_table,
    varchar model_selection_table,
    integer num_iterations,
    boolean use_gpus,
    varchar validation_table,
    integer metrics_compute_frequency,
    boolean warm_start,
    varchar name,
    varchar description,
    boolean use_caching = false 
    )
    +
    + +
    +
    + +

    ◆ madlib_keras_fit_multiple_model() [2/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_fit_multiple_model (varchar source_table,
    varchar model_output_table,
    varchar model_selection_table,
    integer num_iterations,
    boolean use_gpus,
    varchar validation_table,
    integer metrics_compute_frequency,
    boolean warm_start,
    varchar name 
    )
    +
    + +
    +
    + +

    ◆ madlib_keras_fit_multiple_model() [3/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_fit_multiple_model (varchar source_table,
    varchar model_output_table,
    varchar model_selection_table,
    integer num_iterations,
    boolean use_gpus,
    varchar validation_table,
    integer metrics_compute_frequency,
    boolean warm_start 
    )
    +
    + +
    +
    + +

    ◆ madlib_keras_fit_multiple_model() [4/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_fit_multiple_model (varchar source_table,
    varchar model_output_table,
    varchar model_selection_table,
    integer num_iterations,
    boolean use_gpus,
    varchar validation_table,
    integer metrics_compute_frequency 
    )
    +
    + +
    +
    + +

    ◆ madlib_keras_fit_multiple_model() [5/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_fit_multiple_model (varchar source_table,
    varchar model_output_table,
    varchar model_selection_table,
    integer num_iterations,
    boolean use_gpus,
    varchar validation_table 
    )
    +
    + +
    +
    + +

    ◆ madlib_keras_fit_multiple_model() [6/6]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void madlib_keras_fit_multiple_model (varchar source_table,
    varchar model_output_table,
    varchar model_selection_table,
    integer num_iterations,
    boolean use_gpus 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib__keras__gpu__info_8sql__in.html b/docs/docs/v2.1.0/madlib__keras__gpu__info_8sql__in.html new file mode 100644 index 00000000..209f44dc --- /dev/null +++ b/docs/docs/v2.1.0/madlib__keras__gpu__info_8sql__in.html @@ -0,0 +1,242 @@ + + + + + + + + +MADlib: madlib_keras_gpu_info.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    madlib_keras_gpu_info.sql_in File Reference
    +
    +
    + +

    Utility function to report number and type of GPUs in the database cluster. +More...

    + + + + + + + + + + + + +

    +Functions

    text [] gpu_info_tensorflow ()
     
    text [] gpu_info_nvidia ()
     
    void gpu_configuration (text output_table, text source)
     
    void gpu_configuration (text output_table)
     
    varchar gpu_configuration ()
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    Nov 2019
    +

    Function Documentation

    + +

    ◆ gpu_configuration() [1/3]

    + +
    +
    + + + + + + + + + + + + + + + + + + +
    void gpu_configuration (text output_table,
    text source 
    )
    +
    + +
    +
    + +

    ◆ gpu_configuration() [2/3]

    + +
    +
    + + + + + + + + +
    void gpu_configuration (text output_table)
    +
    + +
    +
    + +

    ◆ gpu_configuration() [3/3]

    + +
    +
    + + + + + + + +
    varchar gpu_configuration ()
    +
    + +
    +
    + +

    ◆ gpu_info_nvidia()

    + +
    +
    + + + + + + + +
    text [] gpu_info_nvidia ()
    +
    + +
    +
    + +

    ◆ gpu_info_tensorflow()

    + +
    +
    + + + + + + + +
    text [] gpu_info_tensorflow ()
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib__keras__model__selection_8sql__in.html b/docs/docs/v2.1.0/madlib__keras__model__selection_8sql__in.html new file mode 100644 index 00000000..8487d765 --- /dev/null +++ b/docs/docs/v2.1.0/madlib__keras__model__selection_8sql__in.html @@ -0,0 +1,314 @@ + + + + + + + + +MADlib: madlib_keras_model_selection.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    madlib_keras_model_selection.sql_in File Reference
    +
    +
    + +

    Explore network architectures and hyperparameters by training many models a time. +More...

    + + + + + + + + +

    +Functions

    void load_model_selection_table (varchar model_arch_table, varchar model_selection_table, integer[] model_id_list, varchar[] compile_params_list, varchar[] fit_params_list, varchar object_table)
     
    void load_model_selection_table (varchar model_arch_table, varchar model_selection_table, integer[] model_id_list, varchar[] compile_params_list, varchar[] fit_params_list)
     
    void generate_model_configs (varchar model_arch_table, varchar model_selection_table, integer[] model_id_list, varchar compile_params_grid, varchar fit_params_grid, varchar search_type="grid", integer num_configs=NULL, integer random_state=NULL, varchar object_table=NULL)
     
    +

    Detailed Description

    +

    Generate configurations for model architecture search and hyperparameter tuning.

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    August 2019
    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    August 2020
    +

    Function Documentation

    + +

    ◆ generate_model_configs()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void generate_model_configs (varchar model_arch_table,
    varchar model_selection_table,
    integer [] model_id_list,
    varchar compile_params_grid,
    varchar fit_params_grid,
    varchar search_type = "grid",
    integer num_configs = NULL,
    integer random_state = NULL,
    varchar object_table = NULL 
    )
    +
    + +
    +
    + +

    ◆ load_model_selection_table() [1/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_model_selection_table (varchar model_arch_table,
    varchar model_selection_table,
    integer [] model_id_list,
    varchar [] compile_params_list,
    varchar [] fit_params_list,
    varchar object_table 
    )
    +
    + +
    +
    + +

    ◆ load_model_selection_table() [2/2]

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void load_model_selection_table (varchar model_arch_table,
    varchar model_selection_table,
    integer [] model_id_list,
    varchar [] compile_params_list,
    varchar [] fit_params_list 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib__xgboost_8sql__in.html b/docs/docs/v2.1.0/madlib__xgboost_8sql__in.html new file mode 100644 index 00000000..86f21a91 --- /dev/null +++ b/docs/docs/v2.1.0/madlib__xgboost_8sql__in.html @@ -0,0 +1,375 @@ + + + + + + + + +MADlib: madlib_xgboost.sql_in File Reference + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    +
    + 2.1.0 +
    +
    User Documentation for Apache MADlib
    +
    + + + + + + +
    +
    +
    + + + +
    +
    + +
    +
    +
    + +
    + +
    +
    + + +
    + +
    + +
    +
    +Functions
    +
    +
    madlib_xgboost.sql_in File Reference
    +
    +
    + +

    SQL functions for xgboost. +More...

    + + + + + + + + + + +

    +Functions

    bytea __serialize_pandas_dframe_as_bytea__ (text source_table, text id_column, text class_label, text features)
     
    xgb_gridsearch_train_results_type __xgboost_train_parallel__ (bytea dframe, text[] features_all, text class_label, text params, text class_weights, numeric train_set_size, text id_column, text train_set_split_var)
     
    void xgboost (text source_table, text grid_search_results_tbl, text id_column, text class_label, text list_of_features, text[] list_of_features_to_exclude=NULL, text params_str=NULL, text class_weights=NULL, numeric train_set_size=0.8, text train_set_split_var=NULL)
     
    void xgboost_predict (text scoring_tbl, text mdl_table, text predict_output_table, text id_column, text class_label=NULL, integer params_index=1)
     
    +

    Detailed Description

    +

    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

    +

    http://www.apache.org/licenses/LICENSE-2.0

    +

    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

    +
    Date
    05/12/2022
    +

    Function Documentation

    + +

    ◆ __serialize_pandas_dframe_as_bytea__()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    bytea __serialize_pandas_dframe_as_bytea__ (text source_table,
    text id_column,
    text class_label,
    text features 
    )
    +
    + +
    +
    + +

    ◆ __xgboost_train_parallel__()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    xgb_gridsearch_train_results_type __xgboost_train_parallel__ (bytea dframe,
    text [] features_all,
    text class_label,
    text params,
    text class_weights,
    numeric train_set_size,
    text id_column,
    text train_set_split_var 
    )
    +
    + +
    +
    + +

    ◆ xgboost()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void xgboost (text source_table,
    text grid_search_results_tbl,
    text id_column,
    text class_label,
    text list_of_features,
    text [] list_of_features_to_exclude = NULL,
    text params_str = NULL,
    text class_weights = NULL,
    numeric train_set_size = 0.8,
    text train_set_split_var = NULL 
    )
    +
    + +
    +
    + +

    ◆ xgboost_predict()

    + +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    void xgboost_predict (text scoring_tbl,
    text mdl_table,
    text predict_output_table,
    text id_column,
    text class_label = NULL,
    integer params_index = 1 
    )
    +
    + +
    +
    +
    +
    + + + + diff --git a/docs/docs/v2.1.0/madlib_extra.css b/docs/docs/v2.1.0/madlib_extra.css new file mode 100644 index 00000000..bbc884da --- /dev/null +++ b/docs/docs/v2.1.0/madlib_extra.css @@ -0,0 +1,156 @@ +/* MADlib CSS customizations */ + +/* Indent paragraphs in the main text, but not in framed boxes */ +div.contents > p, div.contents > pre, div.contents > ul, div.contents > div.fragment, dd { + margin-left: 20px; +} + +/* Increase spacing between titled paragraphs in the main text, but not in + framed boxes */ +div.contents > dl { + margin-top: 2em; +} + +/* Increase spacing between list items in the main text */ +div.contents li { + margin-top: 1em; +} + +/* No automtic line wrapping at white spaces in 
     or \verbatim
+   environments. */
+pre.fragment {
+    word-wrap: normal;
+}
+
+/* Distinguish backgrounds for syntax, example commands, and results */
+pre.syntax {
+        border: 1px solid #999999;
+        color: #00004D;
+        background-color: #CBD4E7;
+        padding: 4px 6px;
+        margin: 4px 8px 4px 2px;
+        overflow: auto;
+        word-wrap: normal;
+        font-size:  9pt;
+        line-height: 125%;
+        font-family: monospace, fixed;
+        font-size: 105%;
+}
+
+pre.example {
+        border: 1px solid #999999;
+        background-color: #E8E8E8;
+        padding: 4px 6px;
+        margin: 4px 8px 4px 2px;
+        overflow: auto;
+        word-wrap: normal;
+        font-size:  9pt;
+        line-height: 125%;
+        font-family: monospace, fixed;
+        font-size: 105%;
+}
+
+pre.result {
+        border: 1px solid #999999;
+        background-color: #FFFFCC;
+        padding: 4px 6px;
+        margin: 4px 8px 4px 2px;
+        overflow: auto;
+        word-wrap: normal;
+        font-size:  9pt;
+        line-height: 125%;
+        font-family: monospace, fixed;
+        font-size: 105%;
+}
+
+
+/* No padding for paragraph headers (in its infinite wisdom, doxygen uses 
    
+   environments for that) */
+dl {
+    padding-left: 0;
+    margin-top: 1em;
+}
+
+/* Increase the font size for paragraph headers */
+dt {
+    font-size: 120%;
+    margin-bottom: 1em;
+}
+
+/* The first column should align with normal text. So we cannot use
+   border-spacing. */
+table.params {
+    border-spacing: 0;
+}
+
+/* Add some padding instead of border-spacing */
+td.paramname {
+    padding: 1px 1em 1px 0;
+}
+
+/* We move the bar a out of the text frame, so that the text aligns well with
+   the rest. Note: margin-left + border-width-left + padding-left = 0 */
+/* dl.note, dl.warning, dl.attention, dl.pre, dl.post, dl.invariant, dl.deprecated, dl.todo, dl.test, dl.bug
+{
+    margin-left: -6px;
+    padding-left: 2px;
+}
+*/
+
+/* Style parameter lists formatted with definition lists. */
+dl.arglist {
+  margin-left: 40px;
+  margin-top: 0px;
+}
+
+dl.arglist dt {
+  font-size: 100%;
+  font-weight: bold;
+  color: #00004D;
+  margin-bottom: 0px;
+}
+
+div.toc {
+    background-color: #FFF5B8;
+}
+
+/* Increase font size for toc.li from 10px to 14px */
+div.toc li {
+        font: 14px/1.4 Verdana,DejaVu Sans,Geneva,sans-serif;
+        margin-top: 5px;
+        padding-left: 10px;
+        padding-top: 2px;
+}
+
+
+div.versionlist li.head {
+  font: 12px/1.2 Verdana, DejaVu Sans, Geneva, sans-serif;
+  display: inline;
+  margin-right: 10px;
+}
+
+div.versionlist ul {
+  display: inline;
+  align: right;
+}
+
+div.versionlist li {
+  font: 10px/1.2 Verdana,DejaVu Sans,Geneva,sans-serif;
+  display: inline;
+  margin-right: 10px;
+}
+
+/* Table style for output table columns and descriptions */
+table.output {
+  border: 0;
+  margin-left: 20px;
+}
+
+.output th {
+  text-align: right;
+  vertical-align: top;
+  padding-right: 15px;
+  font-weight: normal;
+  color: #354C7B;
+ }
+
diff --git a/docs/docs/v2.1.0/mainpage_8dox.html b/docs/docs/v2.1.0/mainpage_8dox.html
new file mode 100644
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+
+
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+
+MADlib: mainpage.dox File Reference
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
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    mainpage.dox File Reference
      
    
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diff --git a/docs/docs/v2.1.0/marginal_8sql__in.html b/docs/docs/v2.1.0/marginal_8sql__in.html
new file mode 100644
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+
+
+
+
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+
+MADlib: marginal.sql_in File Reference
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+
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
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+
    
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+
    
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+
    
+  
    
+Functions  
    
+  
    
+
    marginal.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for linear regression.  
+More...
    
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+Functions
    float8 [] marginal_logregr_step_transition (float8[] state, boolean y, float8[] x, float8[] coef)
     
    float8 [] marginal_logregr_step_merge_states (float8[] state1, float8[] state2)
     
    marginal_logregr_result marginal_logregr_step_final (float8[] state)
     
    aggregate marginal_logregr_result marginal_logregr (boolean dependentVariable, float8[] independentVariables, float8[] coef)
     Compute marginal effects for logistic regression.  More...
     
    varchar margins_logregr (varchar message)
     
    varchar margins_logregr ()
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer[] marginal_vars, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose_mode)
     A wrapper function for the various marginal regression analyzes.  More...
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable)
     Marginal effects with default variables.  More...
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols)
     Marginal effects with default variable_names.  More...
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer[] marginal_vars)
     Marginal effects with default variable_names.  More...
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer[] marginal_vars, integer max_iter)
     Marginal effects with default variable_names.  More...
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer[] marginal_vars, integer max_iter, varchar optimizer)
     Marginal effects with default variable_names.  More...
     
    void margins_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer[] marginal_vars, integer max_iter, varchar optimizer, float8 tolerance)
     Marginal effects with default variable_names.  More...
     
    float8 [] mlogregr_marginal_step_transition (float8[] state, integer y, integer num_categories, integer ref_category, float8[] x, float8[] coef)
     
    float8 [] mlogregr_marginal_step_merge_states (float8[] state1, float8[] state2)
     
    marginal_mlogregr_result mlogregr_marginal_step_final (float8[] state)
     
    aggregate marginal_mlogregr_result marginal_mlogregr (integer dependentVariable, integer num_categories, integer ref_category, float8[] independentVariables, float8[] coef)
     Compute marginal effects for multinomial logistic regression.  More...
     
    varchar margins_mlogregr (varchar message)
     
    varchar margins_mlogregr ()
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer[] marginal_vars, varchar optimizer_params, boolean verbose_mode)
     A wrapper function for the various marginal multinomial regression.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer[] marginal_vars, varchar optimizer_params)
     Marginal effects with default variable_names.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer[] marginal_vars, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose_mode)
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, integer ref_category, varchar grouping_cols, integer[] marginal_vars, integer max_iter)
     Marginal effects with default variable_names.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, integer ref_category, varchar grouping_cols, integer[] marginal_vars, integer max_iter, varchar optimizer)
     Marginal effects with default variable_names.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, integer ref_category, varchar grouping_cols, integer[] marginal_vars, integer max_iter, varchar optimizer, float8 tolerance)
     Marginal effects with default variable_names.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable)
     Marginal effects with default variables.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, integer ref_category)
     Marginal effects with default variables.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, integer ref_category, varchar grouping_cols)
     Marginal effects with default variable_names.  More...
     
    void margins_mlogregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, integer ref_category, varchar grouping_cols, integer[] marginal_vars)
     Marginal effects with default variable_names.  More...
     
    float8 [] __sub_array (float8[] value_array, integer[] index_array)
     
    float8 [] __margins_linregr_int_transition (float8[] state, float8[] x, float8[] coef, float8[] vcov, float8[] derivative)
     
    float8 [] __margins_linregr_int_merge (float8[] state1, float8[] state2)
     
    margins_result __margins_linregr_int_final (float8[] state)
     
    aggregate margins_result __margins_int_linregr_agg (float8[] independentVariables, float8[] coef, float8[] vcov, float8[] derivative_matrix)
     Compute marginal effects for linear regression.  More...
     
    float8 [] __margins_logregr_int_transition (float8[] state, float8[] x, float8[] coef, float8[] vcov, float8[] basis_indices, float8[] derivative, float8[] categorical_indices, float8[] x_set, float8[] x_unset)
     
    float8 [] __margins_logregr_int_merge (float8[] state1, float8[] state2)
     
    margins_result __margins_logregr_int_final (float8[] state)
     
    aggregate margins_result __margins_int_logregr_agg (float8[] independentVariables, float8[] coef, float8[] vcov, float8[] basis_indices, float8[] derivative_matrix, float8[] categorical_indices, float8[] x_set, float8[] x_unset)
     Compute marginal effects for logistic regression.  More...
     
    float8 [] __margins_mlogregr_int_transition (float8[] state, float8[] x, float8[] coef, float8[] vcov, float8[] basis_indices, float8[] derivative_matrix, float8[] categorical_indices, float8[] x_set, float8[] x_unset)
     
    float8 [] __margins_mlogregr_int_merge (float8[] state1, float8[] state2)
     
    margins_result __margins_mlogregr_int_final (float8[] state)
     
    aggregate margins_result __margins_int_mlogregr_agg (float8[] independentVariables, float8[] coef, float8[] vcov, float8[] basis_indices, float8[] derivative_matrix, float8[] categorical_indices, float8[] x_set, float8[] x_unset)
     Compute marginal effects for multinomial logistic regression.  More...
     
    float8 [] __margins_coxph_int_transition (float8[] state, float8[] x, float8[] coef, float8[] vcov, float8[] basis_indices, float8[] derivative_matrix, float8[] categorical_indices, float8[] x_set, float8[] x_unset)
     
    float8 [] __margins_coxph_int_merge (float8[] state1, float8[] state2)
     
    margins_result __margins_coxph_int_final (float8[] state)
     
    margins_result __margins_compute_stats (float8[] marginal_effects, float8[] std_err)
     
    aggregate margins_result __margins_int_coxph_agg (float8[] independentVariables, float8[] coef, float8[] vcov, float8[] basis_indices, float8[] derivative_matrix, float8[] categorical_indices, float8[] x_set, float8[] x_unset)
     Compute marginal effects for multinomial logistic regression.  More...
     
    void margins (varchar model_table, varchar out_table, varchar x_design, varchar source_table, varchar marginal_vars)
     Marginal effects with default variable_names.  More...
     
    void margins (varchar model_table, varchar out_table, varchar x_design, varchar source_table)
     
    void margins (varchar model_table, varchar out_table, varchar x_design)
     
    void margins (varchar model_table, varchar out_table)
     
    varchar margins (varchar message)
     
    varchar margins ()
     
    
+
    Detailed Description
    
+
    Date
    January 2011
    
+
    See also
    Calculates marginal effects for various regression models. 
    
+
    Function Documentation
    
+
+
    ◆ __margins_compute_stats()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    margins_result __margins_compute_stats (float8 [] marginal_effects, 
    float8 [] std_err 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_coxph_int_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    margins_result __margins_coxph_int_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_coxph_int_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_coxph_int_merge (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_coxph_int_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
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+          
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+        
+        
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+        
+        
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+        
+      
    float8 [] __margins_coxph_int_transition (float8 [] state, 
    float8 [] x, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] basis_indices, 
    float8 [] derivative_matrix, 
    float8 [] categorical_indices, 
    float8 [] x_set, 
    float8 [] x_unset 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_int_coxph_agg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
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+          
+          
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+        
+      
    aggregate margins_result __margins_int_coxph_agg (float8 [] independentVariables, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] basis_indices, 
    float8 [] derivative_matrix, 
    float8 [] categorical_indices, 
    float8 [] x_set, 
    float8 [] x_unset 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    dependentVariableColumn containing the dependent variable 
    independentVariablesColumn containing the array of independent variables 
    coefColumn containing the array of the coefficients (as obtained by logregr)
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • margins FLOAT8[]  - Array of marginal effects
      • 
+
    • std_err FLOAT8[] - Array of standard-errors (calculated by the delta method),
      • 
+
    • z_stats FLOAT8[] - Array of z-statistics
      • 
+
    • p_values FLOAT8[] - Array of p-values
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_int_linregr_agg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
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+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate margins_result __margins_int_linregr_agg (float8 [] independentVariables, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] derivative_matrix 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    independentVariablesColumn containing the array of independent variables 
    coefColumn containing the array of the coefficients (as obtained by logregr)
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • margins FLOAT8[]  - Array of marginal effects
      • 
+
    • std_err FLOAT8[] - Array of standard-errors (calculated by the delta method),
      • 
+
    • z_stats FLOAT8[] - Array of z-statistics
      • 
+
    • p_values FLOAT8[] - Array of p-values * 
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_int_logregr_agg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate margins_result __margins_int_logregr_agg (float8 [] independentVariables, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] basis_indices, 
    float8 [] derivative_matrix, 
    float8 [] categorical_indices, 
    float8 [] x_set, 
    float8 [] x_unset 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    dependentVariableColumn containing the dependent variable 
    independentVariablesColumn containing the array of independent variables 
    coefColumn containing the array of the coefficients (as obtained by logregr)
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • margins FLOAT8[]  - Array of marginal effects
      • 
+
    • std_err FLOAT8[] - Array of standard-errors (calculated by the delta method),
      • 
+
    • z_stats FLOAT8[] - Array of z-statistics
      • 
+
    • p_values FLOAT8[] - Array of p-values
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_int_mlogregr_agg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate margins_result __margins_int_mlogregr_agg (float8 [] independentVariables, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] basis_indices, 
    float8 [] derivative_matrix, 
    float8 [] categorical_indices, 
    float8 [] x_set, 
    float8 [] x_unset 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    dependentVariableColumn containing the dependent variable 
    independentVariablesColumn containing the array of independent variables 
    coefColumn containing the array of the coefficients (as obtained by logregr)
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • margins FLOAT8[]  - Array of marginal effects
      • 
+
    • std_err FLOAT8[] - Array of standard-errors (calculated by the delta method),
      • 
+
    • z_stats FLOAT8[] - Array of z-statistics
      • 
+
    • p_values FLOAT8[] - Array of p-values
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_linregr_int_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    margins_result __margins_linregr_int_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_linregr_int_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_linregr_int_merge (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_linregr_int_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_linregr_int_transition (float8 [] state, 
    float8 [] x, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] derivative 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_logregr_int_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    margins_result __margins_logregr_int_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_logregr_int_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_logregr_int_merge (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_logregr_int_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_logregr_int_transition (float8 [] state, 
    float8 [] x, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] basis_indices, 
    float8 [] derivative, 
    float8 [] categorical_indices, 
    float8 [] x_set, 
    float8 [] x_unset 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_mlogregr_int_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    margins_result __margins_mlogregr_int_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_mlogregr_int_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_mlogregr_int_merge (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __margins_mlogregr_int_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __margins_mlogregr_int_transition (float8 [] state, 
    float8 [] x, 
    float8 [] coef, 
    float8 [] vcov, 
    float8 [] basis_indices, 
    float8 [] derivative_matrix, 
    float8 [] categorical_indices, 
    float8 [] x_set, 
    float8 [] x_unset 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __sub_array()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __sub_array (float8 [] value_array, 
    integer [] index_array 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ marginal_logregr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate marginal_logregr_result marginal_logregr (boolean dependentVariable, 
    float8 [] independentVariables, 
    float8 [] coef 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    dependentVariableColumn containing the dependent variable 
    independentVariablesColumn containing the array of independent variables 
    coefColumn containing the array of the coefficients (as obtained by logregr)
    
+  
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Returns
    A composite value:
      
+
    • margins FLOAT8[]  - Array of marginal effects
      • 
+
    • coefFLOAT8[]  - The coefficients for the regression
      • 
+
    • std_err FLOAT8[] - Array of standard-errors (calculated by the delta method),
      • 
+
    • z_stats FLOAT8[] - Array of z-statistics
      • 
+
    • p_values FLOAT8[] - Array of p-values
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+ 
       SELECT marginal_logregr(dependentVariable,
+ independentVariables, coef)
+ FROM dataTable;
+
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ marginal_logregr_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    marginal_logregr_result marginal_logregr_step_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ marginal_logregr_step_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] marginal_logregr_step_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ marginal_logregr_step_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] marginal_logregr_step_transition (float8 [] state, 
    boolean y, 
    float8 [] x, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ marginal_mlogregr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate marginal_mlogregr_result marginal_mlogregr (integer dependentVariable, 
    integer num_categories, 
    integer ref_category, 
    float8 [] independentVariables, 
    float8 [] coef 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    dependentVariableColumn containing the dependent variable 
    independentVariablesColumn containing the array of independent variables 
    num_categoriesNumber of categories 
    ref_categoryReference category 
    coefColumn containing the array of the coefficients (as obtained by mlogregr)
    
+  
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Returns
    A composite value:
      
+
    • margins FLOAT8[]  - Array of marginal effects
      • 
+
    • coef FLOAT8[]  - The coefficients for the regression
      • 
+
    • std_err FLOAT8[] - Array of standard-errors (using the delta method),
      • 
+
    • z_stats FLOAT8[] - Array of z-statistics
      • 
+
    • p_values FLOAT8[] - Array of p-values
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+ 
       SELECT marginal_mlogregr(dependentVariable,
+ independentVariables, coef)
+ FROM dataTable;
+
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ margins() [1/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins (varchar model_table, 
    varchar out_table, 
    varchar x_design, 
    varchar source_table, 
    varchar marginal_vars 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins() [2/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins (varchar model_table, 
    varchar out_table, 
    varchar x_design, 
    varchar source_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins() [3/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins (varchar model_table, 
    varchar out_table, 
    varchar x_design 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins() [4/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins (varchar model_table, 
    varchar out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins() [5/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar margins (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ margins() [6/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar margins ()
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [1/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar margins_logregr (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [2/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar margins_logregr ()
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [3/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance, 
    boolean verbose_mode 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    source_tableString identifying the input table 
    out_tableString identifying the output table to be created 
    dependent_varnameColumn containing the dependent variable 
    independent_varnameColumn containing the array of independent variables 
    grouping_colsSet of columns to group by. 
    marginal_varsSubset of independent variables to calculate marginal effects for. 
    max_iterMaximum number of iterations 
    optimizerOptimizer to be used (newton/irls, cg or idg) 
    toleranceResiual tolerance 
    verbose_modeVerbose mode (on/off)
    
+  
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Returns
    void
    
+
    Usage
    For function summary information. Run sql> select margins_logregr('help'); OR sql> select margins_logregr(); OR sql> select margins_logregr('?'); For function usage information. Run sql> select margins_logregr('usage');
      
+
    • Compute the coefficients, and the get the marginal diagnostic statistics: 
      +  select margins_logregr(source_table, out_table, dependentVariable, independentVariables);
+ 
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [4/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [5/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [6/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer [] marginal_vars 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [7/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [8/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter, 
    varchar optimizer 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_logregr() [9/9]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [1/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar margins_mlogregr (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [2/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar margins_mlogregr ()
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [3/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    varchar optimizer_params, 
    boolean verbose_mode 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    source_tableString identifying the input table 
    out_tableString identifying the output table to be created 
    dependent_varnameColumn containing the dependent variable 
    independent_varnameColumn containing the array of independent variables 
    ref_categoryReference category for the multinomial logistic regression 
    grouping_colsSet of columns to group by. 
    marginal_varsSubset of independent variables to calculate marginal effects for. 
    max_iterMaximum number of iterations 
    optimizerOptimizer to be used (newton/irls, cg or idg) 
    toleranceResiual tolerance 
    verbose_modeVerbose mode (on/off)
    
+  
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Returns
    void
    
+
    Usage
    For function summary information. Run sql> select margins_mlogregr('help'); OR sql> select margins_mlogregr(); OR sql> select margins_mlogregr('?'); For function usage information. Run sql> select margins_mlogregr('usage'); 
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [4/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    varchar optimizer_params 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [5/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance, 
    boolean verbose_mode 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [6/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [7/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter, 
    varchar optimizer 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [8/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [9/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [10/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    integer ref_category 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [11/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    integer ref_category, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ margins_mlogregr() [12/12]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void margins_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    integer ref_category, 
    varchar grouping_cols, 
    integer [] marginal_vars 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_marginal_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    marginal_mlogregr_result mlogregr_marginal_step_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_marginal_step_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] mlogregr_marginal_step_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_marginal_step_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
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+        
+        
+          
+          
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+        
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+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] mlogregr_marginal_step_transition (float8 [] state, 
    integer y, 
    integer num_categories, 
    integer ref_category, 
    float8 [] x, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/matrix__ops_8sql__in.html b/docs/docs/v2.1.0/matrix__ops_8sql__in.html
new file mode 100644
index 00000000..52df0ed0
--- /dev/null
+++ b/docs/docs/v2.1.0/matrix__ops_8sql__in.html
@@ -0,0 +1,6322 @@
+
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+
+MADlib: matrix_ops.sql_in File Reference
+
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+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
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+
    
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+
    
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+
    
+  
    
+Functions  
    
+  
    
+
    matrix_ops.sql_in File Reference
      
    
+
    
+
    
+
+
    Implementation of matrix operations in SQL.  
+More...
    
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+Functions
    text matrix_info (text message)
     
    text matrix_info ()
     
    matrix_result matrix_mult (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out, text out_args)
     Multiplies two matrices. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column index.  More...
     
    matrix_result matrix_mult (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out)
     
    text matrix_mult (text message)
     
    text matrix_mult ()
     
    integer [] matrix_ndims (text matrix_in, text in_args, boolean is_block)
     get the ndims of a matrix in an array format  More...
     
    integer [] matrix_ndims (text matrix_in, text in_args)
     
    text matrix_ndims (text message)
     
    text matrix_ndims ()
     
    matrix_result matrix_add (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out, text out_args)
     Adds two matrices. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column index.  More...
     
    matrix_result matrix_add (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out)
     
    text matrix_add (text message)
     
    text matrix_add ()
     
    matrix_result matrix_sub (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out, text out_args)
     Subs two matrices. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column id.  More...
     
    matrix_result matrix_sub (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out)
     
    text matrix_sub (text message)
     
    text matrix_sub ()
     
    float8 [] matrix_extract_row (text matrix_in, text in_args, integer index)
     Extract row from matrix given row index. It requires that all the values are NON-NULL. This is the dense or sparse representation of the matrix where the matrix elements are indexed by row id for dense and by the row and column id for sparse.  More...
     
    text matrix_extract_row (text message)
     
    text matrix_extract_row ()
     
    float8 [] matrix_extract_col (text matrix_in, text in_args, integer index)
     Extract column from matrix given column index. It requires that all the values are NON-NULL. This is the dense or sparse representation of the matrix where the matrix elements are indexed by row id for dense and by the row and column id for sparse.  More...
     
    text matrix_extract_col (text message)
     
    text matrix_extract_col ()
     
    matrix_result matrix_zeros (integer row_dim, integer col_dim, text matrix_out, text out_args)
     Initializes matrix with zeros. It requires that all the values are NON-NULL.  More...
     
    matrix_result matrix_zeros (integer row_dim, integer col_dim, text matrix_out)
     
    text matrix_zeros (text message)
     
    text matrix_zeros ()
     
    matrix_result matrix_max (text matrix_in, text in_args, integer dim, text matrix_out, boolean fetch_index)
     Get max value along dimension from matrix. Also returns corresponding index if set fetch_index. It requires that all the values are NON-NULL. This is the dense or sparse representation of the matrix where the matrix elements are indexed by row id for dense and by the row and column id for sparse.  More...
     
    matrix_result matrix_max (text matrix_in, text in_args, integer dim, text matrix_out)
     
    text matrix_max (text message)
     
    text matrix_max ()
     
    matrix_result matrix_min (text matrix_in, text in_args, integer dim, text matrix_out, boolean fetch_index)
     Get min value along dimension from matrix. Also returns corresponding index if set fetch_index. It requires that all the values are NON-NULL. This is the dense or sparse representation of the matrix where the matrix elements are indexed by row id for dense and by the row and column id for sparse.  More...
     
    matrix_result matrix_min (text matrix_in, text in_args, integer dim, text matrix_out)
     
    text matrix_min (text message)
     
    text matrix_min ()
     
    float8 [] matrix_sum (text matrix_in, text in_args, integer dim)
     Calculate sum along dimension for matrix. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column id.  More...
     
    float8 [] matrix_sum (text matrix_in, text in_args)
     
    text matrix_sum (text message)
     
    text matrix_sum ()
     
    float8 [] matrix_mean (text matrix_in, text in_args, integer dim)
     Calculate mean along dimension for matrix. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column id.  More...
     
    float8 [] matrix_mean (text matrix_in, text in_args)
     
    text matrix_mean (text message)
     
    text matrix_mean ()
     
    matrix_result matrix_scalar_mult (text matrix_in, text in_args, float8 scalar, text matrix_out, text out_args)
     Multiplies one matrix with scalar. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column id.  More...
     
    matrix_result matrix_scalar_mult (text matrix_in, text in_args, float8 scalar, text matrix_out)
     
    text matrix_scalar_mult (text message)
     
    text matrix_scalar_mult ()
     
    float8 [] matrix_vec_mult (text matrix_in, text in_args, float8[] vector)
     Multiplies one matrix with vector. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column id.  More...
     
    text matrix_vec_mult (text message)
     
    text matrix_vec_mult ()
     
    matrix_result matrix_elem_mult (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out, text out_args)
     Multiplies two matrices by element. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column id.  More...
     
    matrix_result matrix_elem_mult (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out)
     
    text matrix_elem_mult (text message)
     
    text matrix_elem_mult ()
     
    matrix_result matrix_trans (text matrix_in, text in_args, text matrix_out, text out_args)
     Transpose matrix. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column index.  More...
     
    matrix_result matrix_trans (text matrix_in, text in_args, text matrix_out)
     
    text matrix_trans (text message)
     
    text matrix_trans ()
     
    matrix_result matrix_sparsify (text matrix_in, text in_args, text matrix_out, text out_args)
     Converts matrix to sparse representation. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row and column index.  More...
     
    matrix_result matrix_sparsify (text matrix_in, text in_args, text matrix_out)
     
    text matrix_sparsify (text message)
     
    text matrix_sparsify ()
     
    matrix_result matrix_densify (text matrix_in, text in_args, text matrix_out, text out_args)
     Converts matrix to dense representation. It requires that all the values are NON-NULL. This is the sparse representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_densify (text matrix_in, text in_args, text matrix_out)
     
    text matrix_densify (text message)
     
    text matrix_densify ()
     
    void matrix_scale_and_add (text matrix_a, text a_args, text matrix_b, text b_args, float8 scale, text matrix_out, text out_args)
     Scale and add matrix operation ( R <- A + sB)  More...
     
    void matrix_scale_and_add (text matrix_a, text a_args, text matrix_b, text b_args, float8 scale, text matrix_out)
     
    float8 matrix_norm (text matrix_in, text in_args, text norm_type)
     Compute matrix norm (of various types)  More...
     
    float8 matrix_norm (text matrix_in, text in_args)
     
    text matrix_norm (text message)
     
    text matrix_norm ()
     
    matrix_result matrix_block_mult (text matrix_a, text a_args, text matrix_b, text b_args, text matrix_out, text out_args)
     
    matrix_result matrix_block_square (text matrix_in, text in_args, text matrix_out, text out_args)
     
    matrix_result matrix_block_trans (text matrix_in, text in_args, text matrix_out, text out_args)
     
    matrix_result matrix_square (text matrix_in, text in_args, text matrix_out, text out_args)
     Calculate square of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_square (text matrix_in, text in_args, text matrix_out)
     
    matrix_result matrix_diag (float8[] diag_elements, text matrix_out, text out_args)
     Create a diagonal matrix with a specified vector on the main diagonal. It always creates the sparse representation of the diagonal matrix where the matrix elements are indexed by the row and column index.  More...
     
    matrix_result matrix_diag (float8[] diag_elements, text matrix_out)
     
    text matrix_diag (text message)
     
    text matrix_diag ()
     
    float [] matrix_extract_diag (text matrix_in, text in_args)
     main diagonal matrix. It requires that all the matrix must be the square matrix. This is the sparse representation of the matrix where the matrix elements are indexed by the row and column index.  More...
     
    text matrix_extract_diag (text message)
     
    text matrix_extract_diag ()
     
    matrix_result matrix_identity (integer row_dim, text matrix_out, text out_args)
     Create an identity matrix with the dimensionality specified by an integer. It can specify the sparse or dense representation of the result matrix.  More...
     
    matrix_result matrix_identity (integer row_dim, text matrix_out)
     
    text matrix_identity (text message)
     
    text matrix_identity ()
     
    matrix_result matrix_random (integer row_dim, integer col_dim, text in_args, text distribution, text matrix_out, text out_args)
     Initializes matrix with random distribution. It requires that all the values are NON-NULL.  More...
     
    matrix_result matrix_random (integer row_id, integer col_id, text distribution, text matrix_out)
     
    matrix_result matrix_random (integer row_id, integer col_id, text matrix_out)
     
    matrix_result matrix_ones (integer row_dim, integer col_dim, text matrix_out, text out_args)
     Initializes matrix with ones. It requires that all the values are NON-NULL.  More...
     
    matrix_result matrix_ones (integer row_id, integer col_id, text matrix_out)
     
    text matrix_ones (text message)
     
    text matrix_ones ()
     
    matrix_result matrix_inverse (text matrix_in, text in_args, text matrix_out, text out_args)
     Calculate inverse of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_inverse (text matrix_in, text in_args, text matrix_out)
     
    text matrix_inverse (text message)
     
    text matrix_inverse ()
     
    matrix_result matrix_pinv (text matrix_in, text in_args, text matrix_out, text out_args)
     Calculate generalized inverse of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_pinv (text matrix_in, text in_args, text matrix_out)
     
    text matrix_pinv (text message)
     
    text matrix_pinv ()
     
    matrix_result matrix_lu (text matrix_in, text in_args, text matrix_out_prefix, text out_args)
     Calculate full pivoting LU decomposition of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_lu (text matrix_in, text in_args, text matrix_out_prefix)
     
    text matrix_lu (text message)
     
    text matrix_lu ()
     
    matrix_result matrix_eigen (text matrix_in, text in_args, text matrix_out, text out_args)
     Calculate eigenvalues of matrix. It requires that all the values are NON-NULL.  More...
     
    matrix_result matrix_eigen (text matrix_in, text in_args, text matrix_out)
     
    text matrix_eigen (text message)
     
    text matrix_eigen ()
     
    matrix_result matrix_cholesky (text matrix_in, text in_args, text matrix_out_prefix, text out_args)
     Cholesky decompose of matrix. Because it is required that input matrix should be symmetric, it is only the lower triangular part that will be used for the decompositon. The upper triangular part won't be read. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_cholesky (text matrix_in, text in_args, text matrix_out_prefix)
     
    text matrix_cholesky (text message)
     
    text matrix_cholesky ()
     
    matrix_result matrix_qr (text matrix_in, text in_args, text matrix_out_prefix, text out_args)
     QR decompose of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    matrix_result matrix_qr (text matrix_in, text in_args, text matrix_out_prefix)
     
    text matrix_qr (text message)
     
    text matrix_qr ()
     
    int8 matrix_rank (text matrix_in, text in_args)
     rank of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    text matrix_rank (text message)
     
    text matrix_rank ()
     
    float8 matrix_nuclear_norm (text matrix_in, text in_args)
     nuclear norm of matrix. It requires that all the values are NON-NULL. This is the dense representation of the matrix where the matrix elements are indexed by the row index.  More...
     
    text matrix_nuclear_norm (text message)
     
    text matrix_nuclear_norm ()
     
    float8 [] __matrix_vec_mult_in_mem (float8[] vector, float8[][] matrix)
     
    float8 [] __matrix_vec_mult_in_mem (float8[] vector, float8[] matrix)
     
    float8 [] __row_fold (float8[] row_in, integer[] pattern)
     The function folds (through multiplication) array x according to the pattern in array y, producing an array of the same length as array y.  More...
     
    float8 [] __bernoulli_vector (integer dim, float8 pos_val, float8 neg_val, float8 prob, integer seed)
     
    float8 [] __bernoulli_vector (integer dim)
     
    float8 [] __uniform_vector (integer dim, float8 a, float8 b, integer seed)
     
    float8 [] __uniform_vector (integer dim, float8 a, float8 b)
     
    float8 [] __normal_vector (integer dim, float8 mu, float8 sigma, integer seed)
     
    float8 [] __normal_vector (integer dim, float8 mu, float8 sigma)
     
    integer [] __rand_vector (integer dim)
     
    integer [] __rand_block (integer row_dim, integer col_dim)
     
    integer [] __rand_block (integer dim)
     
    set< float8[]> __matrix_row_split (float8[] row_in, integer size)
     
    float8 [] __matrix_densify_sfunc (float8[] state, integer col_dim, integer col_id, float8 val)
     
    aggregate float8 [] __matrix_densify_agg (integer, integer, float8)
     
    anyarray __array_abs_add_sfunc (anyarray x, anyarray y)
     
    aggregate anyarray __matrix_column_abs_sum_agg (anyarray)
     
    float8 [] __matrix_blockize_sfunc (float8[] state, integer row_id, float8[] row_vec, integer rsize)
     
    aggregate float8 [] __matrix_blockize_agg (integer, float8[], integer)
     
    float8 [] __matrix_unblockize_sfunc (float8[] state, integer total_col_dim, integer col_id, float8[] row_vec)
     
    aggregate float8 [] __matrix_unblockize_agg (integer, integer, float8[])
     
    float8 [] matrix_mem_mult (float[] matrix_a, float[] matrix_b, boolean trans_b)
     
    float8 [] matrix_mem_mult (float[] matrix_a, float[] matrix_b)
     
    float8 [] matrix_mem_trans (float[] matrix)
     
    float8 [] __matrix_mem_sum_sfunc (float[] state, float[] matrix)
     
    aggregate float8 [] __matrix_mem_sum (float8[])
     
    matrix_result __matrix_column_to_array_format (text matrix_in, text row_id, text matrix_out, boolean istemp)
     
    matrix_result matrix_blockize (text matrix_in, text in_args, integer rsize, integer csize, text matrix_out, text out_args)
     
    matrix_result matrix_blockize (text matrix_in, text in_args, integer rsize, integer csize, text matrix_out)
     
    matrix_result matrix_unblockize (text matrix_in, text in_args, text matrix_out, text out_args)
     
    set< float8[]> __matrix_unnest_block (float8[] block)
     
    float8 [] __matrix_compose_dense_transition (float8[] state, integer numrows, integer row_id, float8[] x)
     
    float8 [] __matrix_compose_sparse_transition (float8[] state, integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     
    float8 [] __matrix_compose_merge (float8[] stateleft, float8[] stateright)
     
    float8 [] __matrix_inv_final (float8[] state)
     
    float8 [] __matrix_pinv_final (float8[] state)
     
    float8 [] __matrix_eigen_final (float8[] state)
     
    float8 [] __matrix_cholesky_final (float8[] state)
     
    float8 [] __matrix_qr_final (float8[] state)
     
    int8 __matrix_rank_final (float8[] state)
     
    float8 [] __matrix_lu_final (float8[] state)
     
    float8 __matrix_nuclear_norm_final (float8[] state)
     
    aggregate float8 [] __matrix_dense_inverse (integer numrows, integer row_id, float8[] x)
     Compute inverse of a dense matrix.  More...
     
    aggregate float8 [] __matrix_sparse_inverse (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Compute inverse of a sparse matrix.  More...
     
    aggregate float8 [] __matrix_dense_pinv (integer numrows, integer row_id, float8[] x)
     Compute generalized inverse of a dense matrix.  More...
     
    aggregate float8 [] __matrix_sparse_pinv (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Compute generalized inverse of a sparse matrix.  More...
     
    aggregate float8 [] __matrix_dense_eigen (integer numrows, integer row_id, float8[] x)
     Compute eigen values of a dense matrix.  More...
     
    aggregate float8 [] __matrix_sparse_eigen (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Compute inverse of a sparse matrix.  More...
     
    aggregate float8 [] __matrix_dense_cholesky (integer numrows, integer row_id, float8[] x)
     Cholesky decompose of a dense matrix.  More...
     
    aggregate float8 [] __matrix_sparse_cholesky (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Cholesky decompose of a sparse matrix.  More...
     
    aggregate float8 [] __matrix_dense_qr (integer numrows, integer row_id, float8[] x)
     QR decompose of a dense matrix.  More...
     
    aggregate float8 [] __matrix_sparse_qr (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     QR decompose of a sparse matrix.  More...
     
    aggregate int8 __matrix_dense_rank (integer numrows, integer row_id, float8[] x)
     Compute rank of a dense matrix.  More...
     
    aggregate int8 __matrix_sparse_rank (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Compute rank of a sparse matrix.  More...
     
    aggregate float8 [] __matrix_dense_lu (integer numrows, integer row_id, float8[] x)
     Compute full pivoting LU decomposition of a dense matrix.  More...
     
    aggregate float8 [] __matrix_sparse_lu (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Compute full pivoting LU decomposition of a sparse matrix.  More...
     
    aggregate float8 __matrix_dense_nuclear_norm (integer numrows, integer row_id, float8[] x)
     Compute nuclear norm of a dense matrix.  More...
     
    aggregate float8 __matrix_sparse_nuclear_norm (integer numrows, integer numcols, integer row_id, integer col_id, float8 x)
     Compute nuclear norm of a sparse matrix.  More...
     
    
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    Detailed Description
    
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    Date
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    Function Documentation
    
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    matrix_result __matrix_column_to_array_format (text matrix_in, 
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    ◆ __matrix_compose_sparse_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __matrix_compose_sparse_transition (float8 [] state, 
    integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_cholesky()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_dense_cholesky (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_eigen()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_dense_eigen (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_inverse()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_dense_inverse (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_lu()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_dense_lu (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_nuclear_norm()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 __matrix_dense_nuclear_norm (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_pinv()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_dense_pinv (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_qr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_dense_qr (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_dense_rank()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate int8 __matrix_dense_rank (integer numrows, 
    integer row_id, 
    float8 [] x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_densify_agg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_densify_agg (integer , 
    integer , 
    float8  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_densify_sfunc()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
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+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __matrix_densify_sfunc (float8 [] state, 
    integer col_dim, 
    integer col_id, 
    float8 val 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_eigen_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __matrix_eigen_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_inv_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __matrix_inv_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_lu_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __matrix_lu_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_mem_sum()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_mem_sum (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_mem_sum_sfunc()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __matrix_mem_sum_sfunc (float [] state, 
    float [] matrix 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_nuclear_norm_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 __matrix_nuclear_norm_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_pinv_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __matrix_pinv_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_qr_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __matrix_qr_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_rank_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    int8 __matrix_rank_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_row_split()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    set<float8[]> __matrix_row_split (float8 [] row_in, 
    integer size 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_cholesky()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_sparse_cholesky (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_eigen()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_sparse_eigen (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_inverse()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_sparse_inverse (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_lu()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_sparse_lu (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_nuclear_norm()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 __matrix_sparse_nuclear_norm (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_pinv()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_sparse_pinv (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_qr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_sparse_qr (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_sparse_rank()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate int8 __matrix_sparse_rank (integer numrows, 
    integer numcols, 
    integer row_id, 
    integer col_id, 
    float8 x 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_unblockize_agg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] __matrix_unblockize_agg (integer , 
    integer , 
    float8 [] 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_unblockize_sfunc()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __matrix_unblockize_sfunc (float8 [] state, 
    integer total_col_dim, 
    integer col_id, 
    float8 [] row_vec 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_unnest_block()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    set<float8[]> __matrix_unnest_block (float8 [] block)
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_vec_mult_in_mem() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __matrix_vec_mult_in_mem (float8 [] vector, 
    float8 matrix[][] 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __matrix_vec_mult_in_mem() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __matrix_vec_mult_in_mem (float8 [] vector, 
    float8 [] matrix 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __normal_vector() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __normal_vector (integer dim, 
    float8 mu, 
    float8 sigma, 
    integer seed 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __normal_vector() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __normal_vector (integer dim, 
    float8 mu, 
    float8 sigma 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __rand_block() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    integer [] __rand_block (integer row_dim, 
    integer col_dim 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __rand_block() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    integer [] __rand_block (integer dim)
    
+
    
+
+
    
+
    
+
+
    ◆ __rand_vector()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    integer [] __rand_vector (integer dim)
    
+
    
+
+
    
+
    
+
+
    ◆ __row_fold()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __row_fold (float8 [] row_in, 
    integer [] pattern 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    rowArray x 
    patternArray y 
    foldedarray 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ __uniform_vector() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __uniform_vector (integer dim, 
    float8 a, 
    float8 b, 
    integer seed 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __uniform_vector() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __uniform_vector (integer dim, 
    float8 a, 
    float8 b 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_add() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_add (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    matrix_aName of the table containing the first matrix 
    a_rowName of the column containing the row index for the first matrix 
    a_colName of the column containing the column index for the first matrix 
    a_valName of the column containing the matrix values for the first matrix 
    matrix_bName of the table containing the second matrix 
    b_rowName of the column containing the row index for the second matrix 
    b_colName of the column containing the column index for the second matrix 
    b_valName of the column containing the matrix values for the second matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_add() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_add (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_add() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_add (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_add() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_add ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_block_mult()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_block_mult (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_block_square()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_block_square (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_block_trans()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_block_trans (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_blockize() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_blockize (text matrix_in, 
    text in_args, 
    integer rsize, 
    integer csize, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_blockize() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_blockize (text matrix_in, 
    text in_args, 
    integer rsize, 
    integer csize, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_cholesky() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_cholesky (text matrix_in, 
    text in_args, 
    text matrix_out_prefix, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_cholesky() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_cholesky (text matrix_in, 
    text in_args, 
    text matrix_out_prefix 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_cholesky() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_cholesky (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_cholesky() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_cholesky ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_densify() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_densify (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    in_rowName of the column containing the row index for the input matrix 
    in_colName of the column containing the column index for the input matrix 
    in_valName of the column containing the matrix values for the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_densify() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_densify (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_densify() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_densify (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_densify() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_densify ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_diag() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_diag (float8 [] diag_elements, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    diag_elementsName of the array containing the diagonal elements. It requaires Not NULL, Not empty, Not containing NULL elements 
    matrix_outName of the table where to output the result diagonal matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result diagonal matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_diag() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_diag (float8 [] diag_elements, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_diag() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_diag (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_diag() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_diag ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_eigen() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_eigen (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_eigen() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_eigen (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_eigen() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_eigen (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_eigen() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_eigen ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_elem_mult() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_elem_mult (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    matrix_aName of the table containing the first matrix 
    a_rowName of the column containing the row id for the first matrix 
    a_colName of the column containing the column id for the first matrix 
    a_valName of the column containing the matrix values for the first matrix 
    matrix_bName of the table containing the second matrix 
    b_rowName of the column containing the row id for the second matrix 
    b_colName of the column containing the column id for the second matrix 
    b_valName of the column containing the matrix values for the second matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_elem_mult() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_elem_mult (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_elem_mult() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_elem_mult (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_elem_mult() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_elem_mult ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_extract_col() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_extract_col (text matrix_in, 
    text in_args, 
    integer index 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsA string containing multiple named arguments of the form "name=value". This argument is used as a container for multiple parameters related to a single matrix. 
    indexColumn index for wanted. 
    
+  
    
+
    
+
    Returns
    Vector containing given column elements. 
    
+
+
    
+
    
+
+
    ◆ matrix_extract_col() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_extract_col (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_extract_col() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_extract_col ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_extract_diag() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float [] matrix_extract_diag (text matrix_in, 
    text in_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    in_rowName of the column containing the row index for the input matrix 
    in_colName of the column containing the column index for the input matrix 
    in_valName of the column containing the matrix values for the input matrix 
    use_temp_tableSpecify if use temp table for result 
    
+  
    
+
    
+
    Returns
    Array of main diagonal 
    
+
+
    
+
    
+
+
    ◆ matrix_extract_diag() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_extract_diag (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_extract_diag() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_extract_diag ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_extract_row() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_extract_row (text matrix_in, 
    text in_args, 
    integer index 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsA string containing multiple named arguments of the form "name=value". This argument is used as a container for multiple parameters related to a single matrix. 
    indexRow index for wanted. 
    
+  
    
+
    
+
    Returns
    Vector containing given row elements. 
    
+
+
    
+
    
+
+
    ◆ matrix_extract_row() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_extract_row (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_extract_row() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_extract_row ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_identity() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_identity (integer row_dim, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    dimName of a integer specifing the dimensinality. It requaires Not NULL, dim > 0. 
    matrix_outName of the table where to output the result identity matrix 
    out_argsName-value pair string containing options for matrix_out 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result identity matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_identity() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_identity (integer row_dim, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_identity() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_identity (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_identity() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_identity ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_info() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_info (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_info() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_info ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_inverse() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_inverse (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_inverse() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_inverse (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_inverse() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_inverse (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_inverse() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_inverse ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_lu() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_lu (text matrix_in, 
    text in_args, 
    text matrix_out_prefix, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_pName of the table where to output the result p matrix 
    matrix_lName of the table where to output the result l matrix 
    matrix_uName of the table where to output the result u matrix 
    matrix_qName of the table where to output the result q matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_lu() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_lu (text matrix_in, 
    text in_args, 
    text matrix_out_prefix 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_lu() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_lu (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_lu() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_lu ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_max() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_max (text matrix_in, 
    text in_args, 
    integer dim, 
    text matrix_out, 
    boolean fetch_index 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsA string containing multiple named arguments of the form "name=value". This argument is used as a container for multiple parameters related to a single matrix. 
    dimWhich dimension to collapse. 1 means row wise, and 2 means column wise 
    matrix_outResult matrix which contains one column: max, and another column: index if fetch_index is set. The type of column is array 
    fetch_indexTrue when want to get corresponding index of max value. Default is false 
    
+  
    
+
    
+
    Returns
    matrix_out. 
    
+
+
    
+
    
+
+
    ◆ matrix_max() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_max (text matrix_in, 
    text in_args, 
    integer dim, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_max() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_max (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_max() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_max ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mean() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_mean (text matrix_in, 
    text in_args, 
    integer dim 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsName-value pair string containing options for matrix_in 
    dimWhich dimension to collapse. 1 means row wise, and 2 means column wise 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mean() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_mean (text matrix_in, 
    text in_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mean() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_mean (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mean() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_mean ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mem_mult() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_mem_mult (float [] matrix_a, 
    float [] matrix_b, 
    boolean trans_b 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mem_mult() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_mem_mult (float [] matrix_a, 
    float [] matrix_b 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mem_trans()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] matrix_mem_trans (float [] matrix)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_min() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_min (text matrix_in, 
    text in_args, 
    integer dim, 
    text matrix_out, 
    boolean fetch_index 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsA string containing multiple named arguments of the form "name=value". This argument is used as a container for multiple parameters related to a single matrix. 
    dimWhich dimension to collapse. 1 means row wise, and 2 means column wise 
    matrix_outResult matrix which contains one column: min, and another column: index if fetch_index is set. The type of column is array 
    fetch_indexTrue when want to get corresponding index of min value. Default is false 
    
+  
    
+
    
+
    Returns
    matrix_out. 
    
+
+
    
+
    
+
+
    ◆ matrix_min() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_min (text matrix_in, 
    text in_args, 
    integer dim, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_min() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_min (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_min() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_min ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mult() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_mult (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    matrix_aName of the table containing the first matrix 
    a_rowName of the column containing the row index for the first matrix 
    a_colName of the column containing the column index for the first matrix 
    a_valName of the column containing the matrix values for the first matrix 
    a_transBoolean to indicate if first matrix should be transposed before multiplication 
    matrix_bName of the table containing the second matrix 
    b_rowName of the column containing the row index for the second matrix 
    b_colName of the column containing the column index for the second matrix 
    b_valName of the column containing the matrix values for the second matrix 
    b_transBoolean to indicate if second matrix should be transposed before multiplication 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_mult() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_mult (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mult() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_mult (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_mult() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_mult ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_ndims() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    integer [] matrix_ndims (text matrix_in, 
    text in_args, 
    boolean is_block 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    matrixName of the table containing the input matrix 
    in_rowName of the column containing the row index for the input matrix 
    in_colName of the column containing the column index for the input matrix 
    in_valName of the column containing the matrix values for the input matrix 
    
+  
    
+
    
+
    Returns
    an array including row_dims and col_dims 
    
+
+
    
+
    
+
+
    ◆ matrix_ndims() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    integer [] matrix_ndims (text matrix_in, 
    text in_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_ndims() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_ndims (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_ndims() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_ndims ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_norm() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 matrix_norm (text matrix_in, 
    text in_args, 
    text norm_type 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_aSource matrix table (dense matrix format) 
    norm_typeType of norm used (default: fro)
    
+  
    
+
    
+
    Returns
    DOUBLE PRECISION
    
+
    Usage Currenty, we support the following norms
    (a) 'fro': Computes the frobenius norm (b) 'one': Computes the one norm (c) 'inf': Computes the infinity norm (d) 'max': Computes the max norm (e) 'spec': Computes the spectral norm (f) '<positive float>="">': Computes the element-wise norm
    
+
    +SELECT matrix_norm('matrix_table_name', 'fro');
+
     
+
    
+
    
+
+
    ◆ matrix_norm() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 matrix_norm (text matrix_in, 
    text in_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_norm() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_norm (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_norm() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_norm ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_nuclear_norm() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 matrix_nuclear_norm (text matrix_in, 
    text in_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+  
    matrix_inName of the table containing the input matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_nuclear_norm() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_nuclear_norm (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_nuclear_norm() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_nuclear_norm ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_ones() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_ones (integer row_dim, 
    integer col_dim, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    row_dimName of the column containing the row index for the one matrix 
    col_dimName of the column containing the column index for the one matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_ones() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_ones (integer row_id, 
    integer col_id, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_ones() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_ones (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_ones() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_ones ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_pinv() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_pinv (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_pinv() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_pinv (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_pinv() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_pinv (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_pinv() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_pinv ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_qr() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_qr (text matrix_in, 
    text in_args, 
    text matrix_out_prefix, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_qName of the table where to output the q matrix of QR decomposition 
    matrix_rName of the table where to output the r matrix of QR decomposition 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_qr() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_qr (text matrix_in, 
    text in_args, 
    text matrix_out_prefix 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_qr() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_qr (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_qr() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_qr ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_random() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_random (integer row_dim, 
    integer col_dim, 
    text in_args, 
    text distribution, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    distributionName of the distribution to use (normal or uniform) 
    row_dimName of the column containing the row index for the one matrix 
    col_dimName of the column containing the column index for the one matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_random() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_random (integer row_id, 
    integer col_id, 
    text distribution, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_random() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_random (integer row_id, 
    integer col_id, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_rank() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    int8 matrix_rank (text matrix_in, 
    text in_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+  
    matrix_inName of the table containing the input matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_rank() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_rank (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_rank() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_rank ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_scalar_mult() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_scalar_mult (text matrix_in, 
    text in_args, 
    float8 scalar, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsName-value pair string containing options for matrix_in 
    scalarScalar value used to be multiplied with matrix_in 
    matrix_outName of the table where to output the result matrix 
    out_argsName-value pair string containing options for matrix_in 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_scalar_mult() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_scalar_mult (text matrix_in, 
    text in_args, 
    float8 scalar, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_scalar_mult() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_scalar_mult (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_scalar_mult() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_scalar_mult ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_scale_and_add() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void matrix_scale_and_add (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    float8 scale, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    matrix_aSource matrix table A (dense matrix format) 
    matrix_bSource matrix table B (dense matrix format) 
    scaleScale for matrix B 
    matrix_outOutput table for matrix R <- A + sB
    
+  
    
+
    
+
    Returns
    VOID
    
+
    Usage
    For matrix addition and subtration, you can use the same function with different values of scalar 
    +SELECT matrix_scale_and_add('matrix_a', 'matrix_b', 1, 'matrix_out');
+SELECT matrix_scale_and_add('matrix_a', 'matrix_b', -1, 'matrix_out');
+
     
    
+
+
    
+
    
+
+
    ◆ matrix_scale_and_add() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void matrix_scale_and_add (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    float8 scale, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sparsify() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_sparsify (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_sparsify() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_sparsify (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sparsify() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_sparsify (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sparsify() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_sparsify ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_square() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_square (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_square() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_square (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sub() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_sub (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    matrix_aName of the table containing the first matrix 
    a_rowName of the column containing the row id for the first matrix 
    a_colName of the column containing the column id for the first matrix 
    a_valName of the column containing the matrix values for the first matrix 
    matrix_bName of the table containing the second matrix 
    b_rowName of the column containing the row id for the second matrix 
    b_colName of the column containing the column id for the second matrix 
    b_valName of the column containing the matrix values for the second matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_sub() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_sub (text matrix_a, 
    text a_args, 
    text matrix_b, 
    text b_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sub() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_sub (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sub() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_sub ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sum() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_sum (text matrix_in, 
    text in_args, 
    integer dim 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsName-value pair string containing options for matrix_in 
    dimWhich dimension to collapse. 1 means row wise, and 2 means column wise 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sum() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_sum (text matrix_in, 
    text in_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sum() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_sum (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_sum() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_sum ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_trans() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_trans (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    matrix_inName of the table containing the input matrix 
    in_rowName of the column containing the row index for the input matrix 
    in_colName of the column containing the column index for the input matrix 
    in_valName of the column containing the matrix values for the input matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_trans() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_trans (text matrix_in, 
    text in_args, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_trans() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_trans (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_trans() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_trans ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_unblockize()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_unblockize (text matrix_in, 
    text in_args, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_vec_mult() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] matrix_vec_mult (text matrix_in, 
    text in_args, 
    float8 [] vector 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    matrix_inName of the table containing the matrix 
    in_argsName-value pair string containing options for matrix_in 
    vectorVector value used to be multiplied with matrix_in 
    
+  
    
+
    
+
    Returns
    Column vector which is the result of matrix_in * vector 
    
+
+
    
+
    
+
+
    ◆ matrix_vec_mult() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_vec_mult (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_vec_mult() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_vec_mult ()
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_zeros() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_zeros (integer row_dim, 
    integer col_dim, 
    text matrix_out, 
    text out_args 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    row_idName of the column containing the row index for the zero matrix 
    col_idName of the column containing the column index for the zero matrix 
    matrix_outName of the table where to output the result matrix 
    
+  
    
+
    
+
    Returns
    Name of the table containing the result matrix 
    
+
+
    
+
    
+
+
    ◆ matrix_zeros() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    matrix_result matrix_zeros (integer row_dim, 
    integer col_dim, 
    text matrix_out 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_zeros() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text matrix_zeros (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ matrix_zeros() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text matrix_zeros ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/measures_8sql__in.html b/docs/docs/v2.1.0/measures_8sql__in.html
new file mode 100644
index 00000000..e0100c0e
--- /dev/null
+++ b/docs/docs/v2.1.0/measures_8sql__in.html
@@ -0,0 +1,511 @@
+
+
+
+
+
+
+
+
+MADlib: measures.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    measures.sql_in File Reference
      
    
+
    
+
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    void graph_closeness (text apsp_table, text out_table, text vertex_filter_expr)
     
    void graph_closeness (text apsp_table, text out_table)
     
    varchar graph_closeness (varchar message)
     
    varchar graph_closeness ()
     
    void graph_diameter (text apsp_table, text out_table)
     
    varchar graph_diameter (varchar message)
     
    varchar graph_diameter ()
     
    void graph_avg_path_length (text apsp_table, text out_table)
     
    varchar graph_avg_path_length (varchar message)
     
    varchar graph_avg_path_length ()
     
    void graph_vertex_degrees (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, text grouping_cols)
     
    void graph_vertex_degrees (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table)
     
    varchar graph_vertex_degrees (varchar message)
     
    varchar graph_vertex_degrees ()
     
    
+
    Function Documentation
    
+
+
    ◆ graph_avg_path_length() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_avg_path_length (text apsp_table, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_avg_path_length() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar graph_avg_path_length (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ graph_avg_path_length() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar graph_avg_path_length ()
    
+
    
+
+
    
+
    
+
+
    ◆ graph_closeness() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_closeness (text apsp_table, 
    text out_table, 
    text vertex_filter_expr 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_closeness() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_closeness (text apsp_table, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_closeness() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar graph_closeness (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ graph_closeness() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar graph_closeness ()
    
+
    
+
+
    
+
    
+
+
    ◆ graph_diameter() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_diameter (text apsp_table, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_diameter() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar graph_diameter (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ graph_diameter() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar graph_diameter ()
    
+
    
+
+
    
+
    
+
+
    ◆ graph_vertex_degrees() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_vertex_degrees (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    text grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_vertex_degrees() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_vertex_degrees (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_vertex_degrees() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar graph_vertex_degrees (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ graph_vertex_degrees() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar graph_vertex_degrees ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/minibatch__preprocessing_8sql__in.html b/docs/docs/v2.1.0/minibatch__preprocessing_8sql__in.html
new file mode 100644
index 00000000..bf67d29c
--- /dev/null
+++ b/docs/docs/v2.1.0/minibatch__preprocessing_8sql__in.html
@@ -0,0 +1,378 @@
+
+
+
+
+
+
+
+
+MADlib: minibatch_preprocessing.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    minibatch_preprocessing.sql_in File Reference
      
    
+
    
+
    
+
+
    Utility that prepares input data for use by models that support mini-batch as an optimization option.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    void minibatch_preprocessor (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer buffer_size, boolean one_hot_encode_int_dep_var)
     
    void minibatch_preprocessor (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer buffer_size)
     
    void minibatch_preprocessor (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols)
     
    void minibatch_preprocessor (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname)
     
    varchar minibatch_preprocessor (varchar message)
     
    varchar minibatch_preprocessor ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    Mar 2018 
    
+
    Function Documentation
    
+
+
    ◆ minibatch_preprocessor() [1/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void minibatch_preprocessor (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols, 
    integer buffer_size, 
    boolean one_hot_encode_int_dep_var 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ minibatch_preprocessor() [2/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void minibatch_preprocessor (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols, 
    integer buffer_size 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ minibatch_preprocessor() [3/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void minibatch_preprocessor (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ minibatch_preprocessor() [4/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void minibatch_preprocessor (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ minibatch_preprocessor() [5/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar minibatch_preprocessor (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ minibatch_preprocessor() [6/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar minibatch_preprocessor ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/mlp_8sql__in.html b/docs/docs/v2.1.0/mlp_8sql__in.html
new file mode 100644
index 00000000..c30a70b6
--- /dev/null
+++ b/docs/docs/v2.1.0/mlp_8sql__in.html
@@ -0,0 +1,2178 @@
+
+
+
+
+
+
+
+
+MADlib: mlp.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    mlp.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for multilayer perceptron.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    float8 [] mlp_igd_transition (float8[] state, float8[] ind_var, float8[] dep_var, float8[] previous_state, float8[] layer_sizes, float8 learning_rate_init, integer activation, integer is_classification, float8 weight, float8[] warm_start_coeff, float8 lambda, float8 momentum, boolean is_nesterov)
     
    float8 [] mlp_minibatch_transition (float8[] state, float8[] ind_var, float8[] dep_var, float8[] previous_state, float8[] layer_sizes, float8 learning_rate_init, integer activation, integer is_classification, float8 weight, float8[] warm_start_coeff, float8 lambda, integer batch_size, integer n_epochs, float8 momentum, boolean is_nesterov)
     
    float8 [] mlp_alr_transition (float8[] state, float8[] ind_var, float8[] dep_var, float8[] previous_state, float8[] layer_sizes, float8 learning_rate_init, integer activation, integer is_classification, float8 weight, float8[] warm_start_coeff, float8 lambda, integer batch_size, integer n_epochs, integer opt_code, float8 rho, float8 beta1, float8 beta2, float8 eps)
     
    float8 [] mlp_igd_merge (float8[] state1, float8[] state2)
     
    float8 [] mlp_igd_final (float8[] state)
     
    float8 [] mlp_minibatch_merge (float8[] state1, float8[] state2)
     
    float8 [] mlp_minibatch_final (float8[] state)
     
    float8 [] mlp_alr_merge (float8[] state1, float8[] state2)
     
    float8 [] mlp_alr_final (float8[] state)
     
    aggregate float8 [] mlp_igd_step (float8[], float8[], float8[], float8[], float8, integer, integer, float8, float8[], float8, float8, boolean)
     
    aggregate float8 [] mlp_minibatch_step (float8[], float8[], float8[], float8[], float8, integer, integer, float8, float8[], float8, integer, integer, float8, boolean)
     
    aggregate float8 [] mlp_alr_step (float8[], float8[], float8[], float8[], float8, integer, integer, float8, float8[], float8, integer, integer, integer, float8, float8, float8, float8)
     
    float8 internal_mlp_igd_distance (float8[] state1, float8[] state2)
     
    mlp_result internal_mlp_igd_result (float8[] state)
     
    mlp_result internal_mlp_minibatch_result (float8[] state)
     
    mlp_result internal_mlp_alr_result (float8[] state)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights, boolean warm_start, boolean verbose, varchar grouping_col)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights, boolean warm_start, boolean verbose, varchar grouping_col)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights, boolean warm_start, boolean verbose)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights, boolean warm_start)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params)
     
    void mlp_classification (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights, boolean warm_start, boolean verbose)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights, boolean warm_start)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation, varchar weights)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params, varchar activation)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes, varchar optimizer_params)
     
    void mlp_regression (varchar source_table, varchar output_table, varchar independent_varname, varchar dependent_varname, integer[] hidden_layer_sizes)
     
    void mlp_predict (varchar model_table, varchar data_table, varchar id_col_name, varchar output_table, varchar pred_type)
     
    float8 [] internal_predict_mlp (float8[] coeff, float8[] independent_varname, float8 is_classification, float8 activation, float8[] layer_sizes, integer is_response, float8[] x_means, float8[] x_stds, integer array_dep_var_for_classification)
     
    text mlp_classification (text message)
     
    text mlp_classification ()
     
    text mlp_regression (text message)
     
    text mlp_regression ()
     
    text mlp_predict (text message)
     
    text mlp_predict ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    June 2012 
    
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    Function Documentation
    
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    ◆ internal_mlp_alr_result()
    
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    mlp_result internal_mlp_alr_result (float8 [] state)
    
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    ◆ internal_mlp_igd_distance()
    
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    float8 internal_mlp_igd_distance (float8 [] state1, 
    float8 [] state2 
    )
    
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    ◆ internal_mlp_igd_result()
    
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    mlp_result internal_mlp_igd_result (float8 [] state)
    
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    ◆ internal_mlp_minibatch_result()
    
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    mlp_result internal_mlp_minibatch_result (float8 [] state)
    
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    ◆ internal_predict_mlp()
    
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    float8 [] internal_predict_mlp (float8 [] coeff, 
    float8 [] independent_varname, 
    float8 is_classification, 
    float8 activation, 
    float8 [] layer_sizes, 
    integer is_response, 
    float8 [] x_means, 
    float8 [] x_stds, 
    integer array_dep_var_for_classification 
    )
    
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    ◆ mlp_alr_final()
    
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    float8 [] mlp_alr_final (float8 [] state)
    
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    ◆ mlp_alr_merge()
    
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    float8 [] mlp_alr_merge (float8 [] state1, 
    float8 [] state2 
    )
    
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    ◆ mlp_alr_step()
    
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    aggregate float8 [] mlp_alr_step (float8 [], 
    float8 [], 
    float8 [], 
    float8 [], 
    float8 , 
    integer , 
    integer , 
    float8 , 
    float8 [], 
    float8 , 
    integer , 
    integer , 
    integer , 
    float8 , 
    float8 , 
    float8 , 
    float8  
    )
    
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    ◆ mlp_alr_transition()
    
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    float8 [] mlp_alr_transition (float8 [] state, 
    float8 [] ind_var, 
    float8 [] dep_var, 
    float8 [] previous_state, 
    float8 [] layer_sizes, 
    float8 learning_rate_init, 
    integer activation, 
    integer is_classification, 
    float8 weight, 
    float8 [] warm_start_coeff, 
    float8 lambda, 
    integer batch_size, 
    integer n_epochs, 
    integer opt_code, 
    float8 rho, 
    float8 beta1, 
    float8 beta2, 
    float8 eps 
    )
    
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    ◆ mlp_classification() [1/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights, 
    boolean warm_start, 
    boolean verbose, 
    varchar grouping_col 
    )
    
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    ◆ mlp_classification() [2/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights, 
    boolean warm_start, 
    boolean verbose 
    )
    
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    ◆ mlp_classification() [3/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights, 
    boolean warm_start 
    )
    
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    ◆ mlp_classification() [4/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights 
    )
    
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    ◆ mlp_classification() [5/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation 
    )
    
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    ◆ mlp_classification() [6/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params 
    )
    
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    ◆ mlp_classification() [7/9]
    
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    void mlp_classification (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes 
    )
    
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    ◆ mlp_classification() [8/9]
    
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    text mlp_classification (text message)
    
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    ◆ mlp_classification() [9/9]
    
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    text mlp_classification ()
    
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    ◆ mlp_igd_final()
    
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    float8 [] mlp_igd_final (float8 [] state)
    
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    ◆ mlp_igd_merge()
    
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    float8 [] mlp_igd_merge (float8 [] state1, 
    float8 [] state2 
    )
    
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    ◆ mlp_igd_step()
    
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    aggregate float8 [] mlp_igd_step (float8 [], 
    float8 [], 
    float8 [], 
    float8 [], 
    float8 , 
    integer , 
    integer , 
    float8 , 
    float8 [], 
    float8 , 
    float8 , 
    boolean  
    )
    
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    ◆ mlp_igd_transition()
    
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    float8 [] mlp_igd_transition (float8 [] state, 
    float8 [] ind_var, 
    float8 [] dep_var, 
    float8 [] previous_state, 
    float8 [] layer_sizes, 
    float8 learning_rate_init, 
    integer activation, 
    integer is_classification, 
    float8 weight, 
    float8 [] warm_start_coeff, 
    float8 lambda, 
    float8 momentum, 
    boolean is_nesterov 
    )
    
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    ◆ mlp_minibatch_final()
    
+
+
    
+
    
+      
+        
+          
+          
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+          
+        
+      
    float8 [] mlp_minibatch_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_minibatch_merge()
    
+
+
    
+
    
+      
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+        
+      
    float8 [] mlp_minibatch_merge (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_minibatch_step()
    
+
+
    
+
    
+      
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+      
    aggregate float8 [] mlp_minibatch_step (float8 [], 
    float8 [], 
    float8 [], 
    float8 [], 
    float8 , 
    integer , 
    integer , 
    float8 , 
    float8 [], 
    float8 , 
    integer , 
    integer , 
    float8 , 
    boolean  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_minibatch_transition()
    
+
+
    
+
    
+      
+        
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+          
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+      
    float8 [] mlp_minibatch_transition (float8 [] state, 
    float8 [] ind_var, 
    float8 [] dep_var, 
    float8 [] previous_state, 
    float8 [] layer_sizes, 
    float8 learning_rate_init, 
    integer activation, 
    integer is_classification, 
    float8 weight, 
    float8 [] warm_start_coeff, 
    float8 lambda, 
    integer batch_size, 
    integer n_epochs, 
    float8 momentum, 
    boolean is_nesterov 
    )
    
+
    
+
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    ◆ mlp_predict() [1/3]
    
+
+
    
+
    
+      
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+        
+      
    void mlp_predict (varchar model_table, 
    varchar data_table, 
    varchar id_col_name, 
    varchar output_table, 
    varchar pred_type 
    )
    
+
    
+
+
    
+
    
+
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    ◆ mlp_predict() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text mlp_predict (text message)
    
+
    
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+
    
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    ◆ mlp_predict() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text mlp_predict ()
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_regression() [1/9]
    
+
+
    
+
    
+      
+        
+          
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+        
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+        
+        
+          
+          
+          
+        
+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights, 
    boolean warm_start, 
    boolean verbose, 
    varchar grouping_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_regression() [2/9]
    
+
+
    
+
    
+      
+        
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights, 
    boolean warm_start, 
    boolean verbose 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_regression() [3/9]
    
+
+
    
+
    
+      
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+          
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+          
+          
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+        
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+          
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+          
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+          
+        
+        
+          
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+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights, 
    boolean warm_start 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_regression() [4/9]
    
+
+
    
+
    
+      
+        
+          
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+          
+          
+        
+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation, 
    varchar weights 
    )
    
+
    
+
+
    
+
    
+
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    ◆ mlp_regression() [5/9]
    
+
+
    
+
    
+      
+        
+          
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+        
+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params, 
    varchar activation 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlp_regression() [6/9]
    
+
+
    
+
    
+      
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+          
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+        
+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes, 
    varchar optimizer_params 
    )
    
+
    
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    ◆ mlp_regression() [7/9]
    
+
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+      
    void mlp_regression (varchar source_table, 
    varchar output_table, 
    varchar independent_varname, 
    varchar dependent_varname, 
    integer [] hidden_layer_sizes 
    )
    
+
    
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    ◆ mlp_regression() [8/9]
    
+
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+
    
+      
+        
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    text mlp_regression (text message)
    
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    ◆ mlp_regression() [9/9]
    
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    text mlp_regression ()
    
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diff --git a/docs/docs/v2.1.0/modules.html b/docs/docs/v2.1.0/modules.html
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index 00000000..0a074e15
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+
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+MADlib: Modules
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+
    
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+  
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+   
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+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
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+  
    
+
    Modules
      
    
+
    
+
    
+
    Here is a list of all modules:
    
+
    [detail level 1234]
    
+
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     ▼Data Types and Transformations
     ►Arrays and MatricesMathematical operations for arrays and matrices 
     Encoding Categorical VariablesFunctions to encode categorical variables to prepare data for input into predictive algorithms 
     PathA function to perform complex pattern matching across rows and extract useful information about the matches 
     PivotPivoting and data summarization tools for preparing data for modeling operations 
     SessionizeSession reconstruction of data consisting of a time stampled sequence of events 
     StemmingProvides porter stemmer operations supporting other MADlib modules 
     ▼Deep LearningA collection of modules for deep learning 
     ►Model PreparationPrepare models and data for deep learning 
     Train Single ModelFit, evaluate and predict for one model 
     ►Train Multiple ModelsTrain multiple deep learning models at the same time for model architecture search and hyperparameter selection 
     ►Utilities for Deep LearningUtilities specific to deep learning workflows 
     ▼GraphGraph algorithms and measures associated with graphs 
     All Pairs Shortest PathFinds the shortest paths between every vertex pair in a given graph 
     Breadth-First SearchFinds the nodes reachable from a given source vertex using a breadth-first approach 
     HITSFind the HITS scores (authority and hub) of all vertices in a directed graph 
     ►MeasuresA collection of metrics computed on a graph 
     PageRankFind the PageRank of all vertices in a directed graph 
     Single Source Shortest PathFinds the shortest path from a single source vertex to every other vertex in a given graph 
     Weakly Connected ComponentsFind all weakly connected components of a graph 
     ▼Model SelectionFunctions for model selection and model evaluation 
     Cross ValidationEstimates the fit of a predictive model given a data set and specifications for the training, prediction, and error estimation functions 
     Prediction MetricsProvides various prediction accuracy metrics 
     Train-Test SplitA method for splitting a data set into separate training and testing sets 
     ▼SamplingA collection of methods for sampling from a population 
     Balanced SamplingA method to independently sample classes to produce a balanced data set. This is commonly used when classes are imbalanced, to ensure that subclasses are adequately represented in the sample 
     Stratified SamplingA method for independently sampling subpopulations (strata) 
     ▼StatisticsA collection of probability and statistics modules 
     ►Descriptive StatisticsMethods to compute descriptive statistics of a dataset 
     ►Inferential StatisticsMethods to compute inferential statistics of a dataset 
     Probability FunctionsProvides cumulative distribution, density/mass, and quantile functions for a wide range of probability distributions 
     ▼Supervised LearningMethods to perform a variety of supervised learning tasks 
     Conditional Random FieldConstructs a Conditional Random Fields (CRF) model for labeling sequential data 
     k-Nearest NeighborsFinds \(k\) nearest data points to the given data point and outputs majority vote value of output classes for classification, or average value of target values for regression 
     Neural NetworkSolves classification and regression problems with several fully connected layers and non-linear activation functions 
     ►Regression ModelsA collection of methods for modeling conditional expectation of a response variable 
     Support Vector MachinesSolves classification and regression problems by separating data with a hyperplane or other nonlinear decision boundary 
     ►Tree MethodsA collection of recursive partitioning (tree) methods 
     ▼Time Series AnalysisA collection of methods to analyze time series data 
     ARIMAGenerates a model with autoregressive, moving average, and integrated components for a time series dataset 
     ▼Unsupervised LearningA collection of methods for unsupervised learning tasks 
     ►Association RulesMethods used to discover patterns in transactional datasets 
     ►ClusteringMethods for clustering data 
     ►Dimensionality ReductionMethods for reducing the number of variables in a dataset to obtain a set of principle variables 
     ►Topic ModellingA collection of methods to uncover abstract topics in a document corpus 
     ▼Utilities
     Columns to VectorCreate a new table with all feature columns inserted into a single column as an array 
     Database FunctionsProvides a collection of user-defined functions for performing common tasks in the database 
     ►Linear SolversMethods that implement solutions for systems of consistent linear equations 
     Mini-Batch PreprocessorUtility that prepares input data for use by models that support mini-batch as an optimization option 
     PMML ExportImplements the PMML XML standard to describe and exchange models produced by data mining and machine learning algorithms 
     Term FrequencyProvides a collection of functions for performing common tasks related to text analytics 
     Vector to ColumnsConverts a feature array in a single column of an output table into multiple columns 
     ▼Early Stage Development
     Conjugate GradientFinds the solution to the function \( \boldsymbol Ax = \boldsymbol b \), where \(A\) is a symmetric, positive-definite matrix and \(x\) and \( \boldsymbol b \) are vectors 
     DBSCANPartitions a set of observations into clusters of arbitrary shape based on the density of nearby neighbors 
     Naive Bayes ClassificationConstructs a classification model from a dataset where each attribute independently contributes to the probability that a data point belongs to a category 
     Random SamplingProvides utility functions for sampling operations 
     XGBoostThis module allows you to use SQL to build gradient boosted tree models designed in XGBoost [1] 
     ▼Deprecated Modules
     Create Indicator VariablesProvides utility functions helpful for data preparation before modeling 
     Multinomial Logistic RegressionAlso called as softmax regression, models the relationship between one or more independent variables and a categorical dependent variable 
    
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diff --git a/docs/docs/v2.1.0/modules.js b/docs/docs/v2.1.0/modules.js
new file mode 100644
index 00000000..5c2bd67a
--- /dev/null
+++ b/docs/docs/v2.1.0/modules.js
@@ -0,0 +1,15 @@
+var modules =
+[
+    [ "Data Types and Transformations", "group__grp__datatrans.html", "group__grp__datatrans" ],
+    [ "Deep Learning", "group__grp__dl.html", "group__grp__dl" ],
+    [ "Graph", "group__grp__graph.html", "group__grp__graph" ],
+    [ "Model Selection", "group__grp__mdl.html", "group__grp__mdl" ],
+    [ "Sampling", "group__grp__sampling.html", "group__grp__sampling" ],
+    [ "Statistics", "group__grp__stats.html", "group__grp__stats" ],
+    [ "Supervised Learning", "group__grp__super.html", "group__grp__super" ],
+    [ "Time Series Analysis", "group__grp__tsa.html", "group__grp__tsa" ],
+    [ "Unsupervised Learning", "group__grp__unsupervised.html", "group__grp__unsupervised" ],
+    [ "Utilities", "group__grp__other__functions.html", "group__grp__other__functions" ],
+    [ "Early Stage Development", "group__grp__early__stage.html", "group__grp__early__stage" ],
+    [ "Deprecated Modules", "group__grp__deprecated.html", "group__grp__deprecated" ]
+];
\ No newline at end of file
diff --git a/docs/docs/v2.1.0/multilogistic_8sql__in.html b/docs/docs/v2.1.0/multilogistic_8sql__in.html
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+
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+MADlib: multilogistic.sql_in File Reference
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
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+  
    
+Functions  
    
+  
    
+
    multilogistic.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for multinomial logistic regression.  
+More...
    
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+Functions
    float8 [] __mlogregr_irls_step_transition (float8[] state, integer y, integer num_categories, integer ref_category, float8[] x, float8[] prev_state)
     
    float8 [] __mlogregr_irls_step_merge_states (float8[] state1, float8[] state2)
     
    float8 [] __mlogregr_irls_step_final (float8[] state)
     
    aggregate float8 [] __mlogregr_irls_step (integer y, integer numcategories, integer ref_category, float8[] x, float8[] previous_state)
     
    float8 __internal_mlogregr_irls_step_distance (float8[] state1, float8[] state2)
     
    mlogregr_result __internal_mlogregr_irls_result (float8[] state)
     
    mlogregr_summary_result __internal_mlogregr_summary_results (float8[] state)
     
    void mlogregr_train (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar optimizer_params)
     Compute multinomial logistic regression coefficients.  More...
     
    void mlogregr_train (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname, integer ref_category)
     
    void mlogregr_train (varchar source_table, varchar output_table, varchar dependent_varname, varchar independent_varname)
     
    varchar mlogregr_train (varchar message)
     
    varchar mlogregr_train ()
     
    integer __compute_mlogregr (varchar source_table, varchar dependent_varname, varchar independent_varname, integer num_categories, integer max_iter, varchar optimizer, float8 precision, integer ref_category)
     
    mlogregr_result mlogregr (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations=20, varchar optimizer="irls", float8 precision=0.0001, integer ref_category)
     Compute logistic-regression coefficients and diagnostic statistics.  More...
     
    mlogregr_result mlogregr (varchar source, varchar depvar, varchar indepvar)
     
    mlogregr_result mlogregr (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations)
     
    mlogregr_result mlogregr (varchar source, varchar depvar, varchar indepvar, integer max_num_iterations, varchar optimizer)
     
    set< __mlogregr_cat_coef > __mlogregr_format (float8[] coef, integer num_feature, integer num_category, integer ref_category)
     
    float8 [] __mlogregr_predict_prob (float8[] coef, integer ref_category, float8[] col_ind_var)
     
    integer __mlogregr_predict_response (float8[] coef, integer ref_category, float8[] col_ind_var)
     
    void mlogregr_predict (text model, text source, text id_col_name, text output, text pred_type)
     
    void mlogregr_predict (text model, text source, text id_col_name, text output)
     
    text mlogregr_predict (text message)
     
    
+
    Detailed Description
    
+
    Date
    July 2012
    
+
    See also
    For a brief introduction to multinomial logistic regression, see the module description Multinomial Logistic Regression. 
    
+
    Function Documentation
    
+
+
    ◆ __compute_mlogregr()
    
+
+
    
+
    
+      
+        
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+          
+          
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    integer __compute_mlogregr (varchar source_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer num_categories, 
    integer max_iter, 
    varchar optimizer, 
    float8 precision, 
    integer ref_category 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __internal_mlogregr_irls_result()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    mlogregr_result __internal_mlogregr_irls_result (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __internal_mlogregr_irls_step_distance()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 __internal_mlogregr_irls_step_distance (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __internal_mlogregr_summary_results()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    mlogregr_summary_result __internal_mlogregr_summary_results (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_format()
    
+
+
    
+
    
+      
+        
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+        
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+          
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+        
+      
    set<__mlogregr_cat_coef> __mlogregr_format (float8 [] coef, 
    integer num_feature, 
    integer num_category, 
    integer ref_category 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_irls_step()
    
+
+
    
+
    
+      
+        
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+        
+      
    aggregate float8 [] __mlogregr_irls_step (integer y, 
    integer numcategories, 
    integer ref_category, 
    float8 [] x, 
    float8 [] previous_state 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_irls_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __mlogregr_irls_step_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_irls_step_merge_states()
    
+
+
    
+
    
+      
+        
+          
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+        
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+        
+      
    float8 [] __mlogregr_irls_step_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_irls_step_transition()
    
+
+
    
+
    
+      
+        
+          
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+        
+      
    float8 [] __mlogregr_irls_step_transition (float8 [] state, 
    integer y, 
    integer num_categories, 
    integer ref_category, 
    float8 [] x, 
    float8 [] prev_state 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_predict_prob()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
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+          
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+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __mlogregr_predict_prob (float8 [] coef, 
    integer ref_category, 
    float8 [] col_ind_var 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __mlogregr_predict_response()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    integer __mlogregr_predict_response (float8 [] coef, 
    integer ref_category, 
    float8 [] col_ind_var 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
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+        
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+          
+          
+        
+      
    mlogregr_result mlogregr (varchar source, 
    varchar depvar, 
    varchar indepvar, 
    integer max_num_iterations = 20, 
    varchar optimizer = "irls", 
    float8 precision = 0.0001, 
    integer ref_category 
    )
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+  
    sourceName of the source relation containing the training data 
    depvarName of the dependent column (of type INTEGER < numcategories) 
    indepvarName of the independent column (of type DOUBLE PRECISION[]) 
    max_num_iterationsThe maximum number of iterations 
    optimizerThe optimizer to use ( 'irls'/'newton' for iteratively reweighted least squares) 
    precisionThe difference between log-likelihood values in successive iterations that should indicate convergence. Note that a non-positive value here disables the convergence criterion, and execution will only stop after \ max_num_iterations iterations. 
    ref_categoryThe reference category specified by the user
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • ref_category INTEGER - Reference category
      • 
+
    • coef FLOAT8[] - Array of coefficients, \( \boldsymbol c \)
      • 
+
    • log_likelihood FLOAT8 - Log-likelihood \( l(\boldsymbol c) \)
      • 
+
    • std_err FLOAT8[] - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
      • 
+
    • z_stats FLOAT8[] - Array of Wald z-statistics, \( \boldsymbol z \)
      • 
+
    • p_values FLOAT8[] - Array of Wald p-values, \( \boldsymbol p \)
      • 
+
    • odds_ratios FLOAT8[]: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)
      • 
+
    • condition_no FLOAT8 - The condition number of matrix \( X^T A X \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration)
      • 
+
    • num_iterations INTEGER - The number of iterations before the algorithm terminated
      • 
+
    
+
    
+
    Usage
      
+
    • Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:
      
+ 
      SELECT * FROM mlogregr('sourceName', 'dependentVariable',
+   'numCategories', 'independentVariables');
      • 
+
    • Get vector of coefficients \( \boldsymbol c \):
      
+ 
      SELECT (mlogregr('sourceName', 'dependentVariable',
+   'numCategories', 'independentVariables')).coef;
      • 
+
    • Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \): 
      SELECT coef, log_likelihood, p_values
+   FROM mlogregr('sourceName', 'dependentVariable',
+  'numCategories', 'independentVariables');
      • 
+
    
+
    
+
    Note
    This function starts an iterative algorithm. It is not an aggregate function. Source and column names have to be passed as strings (due to limitations of the SQL syntax). 
    
+
+
    
+
    
+
+
    ◆ mlogregr() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
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+        
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+        
+        
+          
+          
+          
+        
+      
    mlogregr_result mlogregr (varchar source, 
    varchar depvar, 
    varchar indepvar 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr() [3/4]
    
+
+
    
+
    
+      
+        
+          
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+        
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+          
+        
+        
+          
+          
+          
+        
+      
    mlogregr_result mlogregr (varchar source, 
    varchar depvar, 
    varchar indepvar, 
    integer max_num_iterations 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
+        
+          
+          
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+        
+        
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    mlogregr_result mlogregr (varchar source, 
    varchar depvar, 
    varchar indepvar, 
    integer max_num_iterations, 
    varchar optimizer 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_predict() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+          
+          
+        
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+        
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlogregr_predict (text model, 
    text source, 
    text id_col_name, 
    text output, 
    text pred_type 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_predict() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
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+          
+          
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+        
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlogregr_predict (text model, 
    text source, 
    text id_col_name, 
    text output 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_predict() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text mlogregr_predict (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_train() [1/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
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+        
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlogregr_train (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar optimizer_params 
    )
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+  
    source_tableName of the source relation containing the training data 
    output_tableName of the output relation to contain the resulting model 
    dependent_varnameName of the dependent column (of type INTEGER) 
    independent_varnameName of the independent column (or an array expression) 
    ref_categoryThe reference category specified by the user 
    optimizer_paramsComma-separated list of parameters for the optimizer function
    
+  
    
+
    
+
    Returns
    An output table (named 'output_table' above) containing following columns:
      
+
    • ref_category INTEGER - Reference category
      • 
+
    • coef FLOAT8[] - Array of coefficients, \( \boldsymbol c \)
      • 
+
    • log_likelihood FLOAT8 - Log-likelihood \( l(\boldsymbol c) \)
      • 
+
    • std_err FLOAT8[] - Array of standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
      • 
+
    • z_stats FLOAT8[] - Array of Wald z-statistics, \( \boldsymbol z \)
      • 
+
    • p_values FLOAT8[] - Array of Wald p-values, \( \boldsymbol p \)
      • 
+
    • odds_ratios FLOAT8[]: Array of odds ratios, \( \mathit{odds}(c_1), \dots, \mathit{odds}(c_k) \)
      • 
+
    • condition_no FLOAT8 - The condition number of matrix \( X^T A X \) during the iteration immediately preceding convergence (i.e., \( A \) is computed using the coefficients of the previous iteration) An output table (named 'output_table'_summary) containing following columns:
      • 
+
    • regression_type VARCHAR - The regression type run (in this case it will be 'mlogit')
      • 
+
    • source_table VARCHAR - Source table containing the training data
      • 
+
    • output_table VARCHAR - Output table containing the trained model
      • 
+
    • dependent_varname VARCHAR - Name of the dependent column used for training
      • 
+
    • independent_varname VARCHAR - Name of the independent column used for training (or the ARRAY expression used for training)
      • 
+
    • ref_category INTEGER - The reference category specified by the user
      • 
+
    • num_iterations INTEGER - The number of iterations before the algorithm terminated
      • 
+
    • num_rows_processed INTEGER - The number of rows from training data used for training
      • 
+
    • num_missing_rows_skipped INTEGER - The number of rows skipped during training
      • 
+
    
+
    
+
    Usage
      
+
    • Get vector of coefficients \( \boldsymbol c \) and all diagnostic statistics:
      
+ 
      SELECT mlogregr_train('sourceName', 'outputName',
+         'dependentVariable', 'independentVariables');
+         SELECT * from outputName;
+   
      • 
+
    • Get vector of coefficients \( \boldsymbol c \):
      
+ 
      SELECT coef from outputName;
      • 
+
    • Get a subset of the output columns, e.g., only the array of coefficients \( \boldsymbol c \), the log-likelihood of determination \( l(\boldsymbol c) \), and the array of p-values \( \boldsymbol p \): 
      SELECT coef, log_likelihood, p_values
+   FROM outputName;
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_train() [2/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlogregr_train (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_train() [3/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
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+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mlogregr_train (varchar source_table, 
    varchar output_table, 
    varchar dependent_varname, 
    varchar independent_varname 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_train() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar mlogregr_train (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_train() [5/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar mlogregr_train ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/multiresponseglm_8sql__in.html b/docs/docs/v2.1.0/multiresponseglm_8sql__in.html
new file mode 100644
index 00000000..cdd0fb9a
--- /dev/null
+++ b/docs/docs/v2.1.0/multiresponseglm_8sql__in.html
@@ -0,0 +1,231 @@
+
+
+
+
+
+
+
+
+MADlib: multiresponseglm.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    multiresponseglm.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for multinomial regression.  
+More...
    
+
+
+
+
+
+
+
+
+
    
+Functions
    bytea8 __multinom_merge_states (bytea8 state1, bytea8 state2)
     
    bytea8 __multinom_final (bytea8 state)
     
    bytea8 __multinom_logit_transition (bytea8, float8, float8[], bytea8, smallint)
     
    
+
    Detailed Description
    
+
    Date
    July 2014
    
+
    See also
    For a brief introduction to multinomial regression, see the module description Multinomial Regression. 
    
+
    Function Documentation
    
+
+
    ◆ __multinom_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bytea8 __multinom_final (bytea8 state)
    
+
    
+
+
    
+
    
+
+
    ◆ __multinom_logit_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 __multinom_logit_transition (bytea8 , 
    float8 , 
    float8 [], 
    bytea8 , 
    smallint  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __multinom_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 __multinom_merge_states (bytea8 state1, 
    bytea8 state2 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/nav_f.png b/docs/docs/v2.1.0/nav_f.png
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wZ=Q8~_Ju`#59=RjDrmm`tMD@M=!-l18IR?&vFVdQ&MBb@0HFXL=0 ? varName.substring(i+1) : varName;
+  return eval(n.replace(/\-/g,'_'));
+}
+
+function stripPath(uri)
+{
+  return uri.substring(uri.lastIndexOf('/')+1);
+}
+
+function stripPath2(uri)
+{
+  var i = uri.lastIndexOf('/');
+  var s = uri.substring(i+1);
+  var m = uri.substring(0,i+1).match(/\/d\w\/d\w\w\/$/);
+  return m ? uri.substring(i-6) : s;
+}
+
+function hashValue()
+{
+  return $(location).attr('hash').substring(1).replace(/[^\w\-]/g,'');
+}
+
+function hashUrl()
+{
+  return '#'+hashValue();
+}
+
+function pathName()
+{
+  return $(location).attr('pathname').replace(/[^-A-Za-z0-9+&@#/%?=~_|!:,.;\(\)]/g, '');
+}
+
+function localStorageSupported()
+{
+  try {
+    return 'localStorage' in window && window['localStorage'] !== null && window.localStorage.getItem;
+  }
+  catch(e) {
+    return false;
+  }
+}
+
+
+function storeLink(link)
+{
+  if (!$("#nav-sync").hasClass('sync') && localStorageSupported()) {
+      window.localStorage.setItem('navpath',link);
+  }
+}
+
+function deleteLink()
+{
+  if (localStorageSupported()) {
+    window.localStorage.setItem('navpath','');
+  }
+}
+
+function cachedLink()
+{
+  if (localStorageSupported()) {
+    return window.localStorage.getItem('navpath');
+  } else {
+    return '';
+  }
+}
+
+function getScript(scriptName,func,show)
+{
+  var head = document.getElementsByTagName("head")[0];
+  var script = document.createElement('script');
+  script.id = scriptName;
+  script.type = 'text/javascript';
+  script.onload = func;
+  script.src = scriptName+'.js';
+  if ($.browser.msie && $.browser.version<=8) {
+    // script.onload does not work with older versions of IE
+    script.onreadystatechange = function() {
+      if (script.readyState=='complete' || script.readyState=='loaded') {
+        func(); if (show) showRoot();
+      }
+    }
+  }
+  head.appendChild(script); 
+}
+
+function createIndent(o,domNode,node,level)
+{
+  var level=-1;
+  var n = node;
+  while (n.parentNode) { level++; n=n.parentNode; }
+  if (node.childrenData) {
+    var imgNode = document.createElement("span");
+    imgNode.className = 'arrow';
+    imgNode.style.paddingLeft=(16*level).toString()+'px';
+    imgNode.innerHTML=arrowRight;
+    node.plus_img = imgNode;
+    node.expandToggle = document.createElement("a");
+    node.expandToggle.href = "javascript:void(0)";
+    node.expandToggle.onclick = function() {
+      if (node.expanded) {
+        $(node.getChildrenUL()).slideUp("fast");
+        node.plus_img.innerHTML=arrowRight;
+        node.expanded = false;
+      } else {
+        expandNode(o, node, false, false);
+      }
+    }
+    node.expandToggle.appendChild(imgNode);
+    domNode.appendChild(node.expandToggle);
+  } else {
+    var span = document.createElement("span");
+    span.className = 'arrow';
+    span.style.width   = 16*(level+1)+'px';
+    span.innerHTML = ' ';
+    domNode.appendChild(span);
+  }
+}
+
+var animationInProgress = false;
+
+function gotoAnchor(anchor,aname,updateLocation)
+{
+  var pos, docContent = $('#doc-content');
+  var ancParent = $(anchor.parent());
+  if (ancParent.hasClass('memItemLeft') ||
+      ancParent.hasClass('fieldname') ||
+      ancParent.hasClass('fieldtype') ||
+      ancParent.is(':header'))
+  {
+    pos = ancParent.position().top;
+  } else if (anchor.position()) {
+    pos = anchor.position().top;
+  }
+  if (pos) {
+    var dist = Math.abs(Math.min(
+               pos-docContent.offset().top,
+               docContent[0].scrollHeight-
+               docContent.height()-docContent.scrollTop()));
+    animationInProgress=true;
+    docContent.animate({
+      scrollTop: pos + docContent.scrollTop() - docContent.offset().top
+    },Math.max(50,Math.min(500,dist)),function(){
+      if (updateLocation) window.location.href=aname;
+      animationInProgress=false;
+    });
+  }
+}
+
+function newNode(o, po, text, link, childrenData, lastNode)
+{
+  var node = new Object();
+  node.children = Array();
+  node.childrenData = childrenData;
+  node.depth = po.depth + 1;
+  node.relpath = po.relpath;
+  node.isLast = lastNode;
+
+  node.li = document.createElement("li");
+  po.getChildrenUL().appendChild(node.li);
+  node.parentNode = po;
+
+  node.itemDiv = document.createElement("div");
+  node.itemDiv.className = "item";
+
+  node.labelSpan = document.createElement("span");
+  node.labelSpan.className = "label";
+
+  createIndent(o,node.itemDiv,node,0);
+  node.itemDiv.appendChild(node.labelSpan);
+  node.li.appendChild(node.itemDiv);
+
+  var a = document.createElement("a");
+  node.labelSpan.appendChild(a);
+  node.label = document.createTextNode(text);
+  node.expanded = false;
+  a.appendChild(node.label);
+  if (link) {
+    var url;
+    if (link.substring(0,1)=='^') {
+      url = link.substring(1);
+      link = url;
+    } else {
+      url = node.relpath+link;
+    }
+    a.className = stripPath(link.replace('#',':'));
+    if (link.indexOf('#')!=-1) {
+      var aname = '#'+link.split('#')[1];
+      var srcPage = stripPath(pathName());
+      var targetPage = stripPath(link.split('#')[0]);
+      a.href = srcPage!=targetPage ? url : "javascript:void(0)";
+      a.onclick = function(){
+        storeLink(link);
+        if (!$(a).parent().parent().hasClass('selected'))
+        {
+          $('.item').removeClass('selected');
+          $('.item').removeAttr('id');
+          $(a).parent().parent().addClass('selected');
+          $(a).parent().parent().attr('id','selected');
+        }
+        var anchor = $(aname);
+        gotoAnchor(anchor,aname,true);
+      };
+    } else {
+      a.href = url;
+      a.onclick = function() { storeLink(link); }
+    }
+  } else {
+    if (childrenData != null)
+    {
+      a.className = "nolink";
+      a.href = "javascript:void(0)";
+      a.onclick = node.expandToggle.onclick;
+    }
+  }
+
+  node.childrenUL = null;
+  node.getChildrenUL = function() {
+    if (!node.childrenUL) {
+      node.childrenUL = document.createElement("ul");
+      node.childrenUL.className = "children_ul";
+      node.childrenUL.style.display = "none";
+      node.li.appendChild(node.childrenUL);
+    }
+    return node.childrenUL;
+  };
+
+  return node;
+}
+
+function showRoot()
+{
+  var headerHeight = $("#top").height();
+  var footerHeight = $("#nav-path").height();
+  var windowHeight = $(window).height() - headerHeight - footerHeight;
+  (function (){ // retry until we can scroll to the selected item
+    try {
+      var navtree=$('#nav-tree');
+      navtree.scrollTo('#selected',0,{offset:-windowHeight/2});
+    } catch (err) {
+      setTimeout(arguments.callee, 0);
+    }
+  })();
+}
+
+function expandNode(o, node, imm, showRoot)
+{
+  if (node.childrenData && !node.expanded) {
+    if (typeof(node.childrenData)==='string') {
+      var varName    = node.childrenData;
+      getScript(node.relpath+varName,function(){
+        node.childrenData = getData(varName);
+        expandNode(o, node, imm, showRoot);
+      }, showRoot);
+    } else {
+      if (!node.childrenVisited) {
+        getNode(o, node);
+      } if (imm || ($.browser.msie && $.browser.version>8)) {
+        // somehow slideDown jumps to the start of tree for IE9 :-(
+        $(node.getChildrenUL()).show();
+      } else {
+        $(node.getChildrenUL()).slideDown("fast");
+      }
+      node.plus_img.innerHTML = arrowDown;
+      node.expanded = true;
+    }
+  }
+}
+
+function glowEffect(n,duration)
+{
+  n.addClass('glow').delay(duration).queue(function(next){
+    $(this).removeClass('glow');next();
+  });
+}
+
+function highlightAnchor()
+{
+  var aname = hashUrl();
+  var anchor = $(aname);
+  if (anchor.parent().attr('class')=='memItemLeft'){
+    var rows = $('.memberdecls tr[class$="'+hashValue()+'"]');
+    glowEffect(rows.children(),300); // member without details
+  } else if (anchor.parent().attr('class')=='fieldname'){
+    glowEffect(anchor.parent().parent(),1000); // enum value
+  } else if (anchor.parent().attr('class')=='fieldtype'){
+    glowEffect(anchor.parent().parent(),1000); // struct field
+  } else if (anchor.parent().is(":header")) {
+    glowEffect(anchor.parent(),1000); // section header
+  } else {
+    glowEffect(anchor.next(),1000); // normal member
+  }
+  gotoAnchor(anchor,aname,false);
+}
+
+function selectAndHighlight(hash,n)
+{
+  var a;
+  if (hash) {
+    var link=stripPath(pathName())+':'+hash.substring(1);
+    a=$('.item a[class$="'+link+'"]');
+  }
+  if (a && a.length) {
+    a.parent().parent().addClass('selected');
+    a.parent().parent().attr('id','selected');
+    highlightAnchor();
+  } else if (n) {
+    $(n.itemDiv).addClass('selected');
+    $(n.itemDiv).attr('id','selected');
+  }
+  if ($('#nav-tree-contents .item:first').hasClass('selected')) {
+    $('#nav-sync').css('top','30px');
+  } else {
+    $('#nav-sync').css('top','5px');
+  }
+  showRoot();
+}
+
+function showNode(o, node, index, hash)
+{
+  if (node && node.childrenData) {
+    if (typeof(node.childrenData)==='string') {
+      var varName    = node.childrenData;
+      getScript(node.relpath+varName,function(){
+        node.childrenData = getData(varName);
+        showNode(o,node,index,hash);
+      },true);
+    } else {
+      if (!node.childrenVisited) {
+        getNode(o, node);
+      }
+      $(node.getChildrenUL()).css({'display':'block'});
+      node.plus_img.innerHTML = arrowDown;
+      node.expanded = true;
+      var n = node.children[o.breadcrumbs[index]];
+      if (index+11) hash = '#'+parts[1].replace(/[^\w\-]/g,'');
+    else hash='';
+  }
+  if (hash.match(/^#l\d+$/)) {
+    var anchor=$('a[name='+hash.substring(1)+']');
+    glowEffect(anchor.parent(),1000); // line number
+    hash=''; // strip line number anchors
+  }
+  var url=root+hash;
+  var i=-1;
+  while (NAVTREEINDEX[i+1]<=url) i++;
+  if (i==-1) { i=0; root=NAVTREE[0][1]; } // fallback: show index
+  if (navTreeSubIndices[i]) {
+    gotoNode(o,i,root,hash,relpath)
+  } else {
+    getScript(relpath+'navtreeindex'+i,function(){
+      navTreeSubIndices[i] = eval('NAVTREEINDEX'+i);
+      if (navTreeSubIndices[i]) {
+        gotoNode(o,i,root,hash,relpath);
+      }
+    },true);
+  }
+}
+
+function showSyncOff(n,relpath)
+{
+    n.html('');
+}
+
+function showSyncOn(n,relpath)
+{
+    n.html('');
+}
+
+function toggleSyncButton(relpath)
+{
+  var navSync = $('#nav-sync');
+  if (navSync.hasClass('sync')) {
+    navSync.removeClass('sync');
+    showSyncOff(navSync,relpath);
+    storeLink(stripPath2(pathName())+hashUrl());
+  } else {
+    navSync.addClass('sync');
+    showSyncOn(navSync,relpath);
+    deleteLink();
+  }
+}
+
+function initNavTree(toroot,relpath)
+{
+  var o = new Object();
+  o.toroot = toroot;
+  o.node = new Object();
+  o.node.li = document.getElementById("nav-tree-contents");
+  o.node.childrenData = NAVTREE;
+  o.node.children = new Array();
+  o.node.childrenUL = document.createElement("ul");
+  o.node.getChildrenUL = function() { return o.node.childrenUL; };
+  o.node.li.appendChild(o.node.childrenUL);
+  o.node.depth = 0;
+  o.node.relpath = relpath;
+  o.node.expanded = false;
+  o.node.isLast = true;
+  o.node.plus_img = document.createElement("span");
+  o.node.plus_img.className = 'arrow';
+  o.node.plus_img.innerHTML = arrowRight;
+
+  if (localStorageSupported()) {
+    var navSync = $('#nav-sync');
+    if (cachedLink()) {
+      showSyncOff(navSync,relpath);
+      navSync.removeClass('sync');
+    } else {
+      showSyncOn(navSync,relpath);
+    }
+    navSync.click(function(){ toggleSyncButton(relpath); });
+  }
+
+  $(window).load(function(){
+    navTo(o,toroot,hashUrl(),relpath);
+    showRoot();
+  });
+
+  $(window).bind('hashchange', function(){
+     if (window.location.hash && window.location.hash.length>1){
+       var a;
+       if ($(location).attr('hash')){
+         var clslink=stripPath(pathName())+':'+hashValue();
+         a=$('.item a[class$="'+clslink.replace(/1|%O$WD@{VPM$7~Ar*{o?;hlAFyLXmaDC0y
znK1_#cQqJWPES%4Uujug^TE?jMft$}Eq^WaR~)%f)vSNs&gek&x%A9X9sM
+
+
+
+
+
+
+
+MADlib: ordinal.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    ordinal.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for ordinal regression.  
+More...
    
+
+
+
+
+
+
+
+
+
    
+Functions
    bytea8 __ordinal_merge_states (bytea8 state1, bytea8 state2)
     
    bytea8 __ordinal_final (bytea8 state)
     
    bytea8 __ordinal_logit_transition (bytea8, float8, float8[], bytea8, smallint)
     
    
+
    Detailed Description
    
+
    Date
    July 2014
    
+
    See also
    For a brief introduction to ordinal regression, see the module description Ordinal Regression. 
    
+
    Function Documentation
    
+
+
    ◆ __ordinal_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bytea8 __ordinal_final (bytea8 state)
    
+
    
+
+
    
+
    
+
+
    ◆ __ordinal_logit_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 __ordinal_logit_transition (bytea8 , 
    float8 , 
    float8 [], 
    bytea8 , 
    smallint  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __ordinal_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 __ordinal_merge_states (bytea8 state1, 
    bytea8 state2 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/pagerank_8sql__in.html b/docs/docs/v2.1.0/pagerank_8sql__in.html
new file mode 100644
index 00000000..597f7085
--- /dev/null
+++ b/docs/docs/v2.1.0/pagerank_8sql__in.html
@@ -0,0 +1,544 @@
+
+
+
+
+
+
+
+
+MADlib: pagerank.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    pagerank.sql_in File Reference
      
    
+
    
+
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    void pagerank (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, float8 damping_factor, integer max_iter, float8 threshold, varchar grouping_cols, bigint[] personalization_vertices)
     
    void pagerank (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, float8 damping_factor, integer max_iter, float8 threshold, varchar grouping_cols)
     
    void pagerank (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, float8 damping_factor, integer max_iter, float8 threshold)
     
    void pagerank (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, float8 damping_factor, integer max_iter)
     
    void pagerank (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, float8 damping_factor)
     
    void pagerank (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table)
     
    varchar pagerank (varchar message)
     
    varchar pagerank ()
     
    
+
    Function Documentation
    
+
+
    ◆ pagerank() [1/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
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+        
+          
+          
+          
+        
+      
    void pagerank (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    float8 damping_factor, 
    integer max_iter, 
    float8 threshold, 
    varchar grouping_cols, 
    bigint [] personalization_vertices 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pagerank() [2/8]
    
+
+
    
+
    
+      
+        
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+        
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+          
+          
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+        
+      
    void pagerank (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    float8 damping_factor, 
    integer max_iter, 
    float8 threshold, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pagerank() [3/8]
    
+
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+
    
+      
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+        
+      
    void pagerank (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    float8 damping_factor, 
    integer max_iter, 
    float8 threshold 
    )
    
+
    
+
+
    
+
    
+
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    ◆ pagerank() [4/8]
    
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+
    
+      
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+        
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+          
+          
+        
+      
    void pagerank (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    float8 damping_factor, 
    integer max_iter 
    )
    
+
    
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+
    
+
    
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+
    ◆ pagerank() [5/8]
    
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+      
    void pagerank (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    float8 damping_factor 
    )
    
+
    
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    ◆ pagerank() [6/8]
    
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+      
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+      
    void pagerank (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table 
    )
    
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    ◆ pagerank() [7/8]
    
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+      
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+      
    varchar pagerank (varchar message)
    
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    ◆ pagerank() [8/8]
    
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    varchar pagerank ()
    
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diff --git a/docs/docs/v2.1.0/path_8sql__in.html b/docs/docs/v2.1.0/path_8sql__in.html
new file mode 100644
index 00000000..5424ff4c
--- /dev/null
+++ b/docs/docs/v2.1.0/path_8sql__in.html
@@ -0,0 +1,468 @@
+
+
+
+
+
+
+
+
+MADlib: path.sql_in File Reference
+
+
+
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+
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+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
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+            
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+        
    
+
    
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+
    
+  
    
+Functions  
    
+  
    
+
    path.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for pathing functions.  
+More...
    
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+Functions
    path_match_result path_pattern_match (text symbols, text pattern, float8[] row_id, boolean overlapping_patterns)
     
    text path (varchar source_table, varchar output_table, varchar partition_expr, varchar order_expr, varchar symbol_expr, varchar pattern_expr, varchar agg_func, boolean persist_rows, boolean overlapping_patterns)
     
    text path (varchar source_table, varchar output_table, varchar partition_expr, varchar order_expr, varchar symbol_expr, varchar pattern_expr, varchar agg_func, boolean persist_rows)
     
    text path (varchar source_table, varchar output_table, varchar partition_expr, varchar order_expr, varchar symbol_expr, varchar pattern_expr, varchar agg_func)
     
    text path (varchar source_table, varchar output_table, varchar partition_expr, varchar order_expr, varchar symbol_expr, varchar pattern_expr)
     
    text path (text message)
     
    text path ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    Sep 2015 
    
+
    Function Documentation
    
+
+
    ◆ path() [1/6]
    
+
+
    
+
    
+      
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+      
    text path (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar order_expr, 
    varchar symbol_expr, 
    varchar pattern_expr, 
    varchar agg_func, 
    boolean persist_rows, 
    boolean overlapping_patterns 
    )
    
+
    
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+
    
+
    
+
+
    ◆ path() [2/6]
    
+
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+
    
+      
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    text path (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar order_expr, 
    varchar symbol_expr, 
    varchar pattern_expr, 
    varchar agg_func, 
    boolean persist_rows 
    )
    
+
    
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+
    
+
+
    ◆ path() [3/6]
    
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+
    
+      
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+      
    text path (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar order_expr, 
    varchar symbol_expr, 
    varchar pattern_expr, 
    varchar agg_func 
    )
    
+
    
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+
    
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+
    ◆ path() [4/6]
    
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+
    
+      
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    text path (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar order_expr, 
    varchar symbol_expr, 
    varchar pattern_expr 
    )
    
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    ◆ path() [5/6]
    
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+
    
+      
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+        
+      
    text path (text message)
    
+
    
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+
    
+
    
+
+
    ◆ path() [6/6]
    
+
+
    
+
    
+      
+        
+          
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+        
+      
    text path ()
    
+
    
+
+
    
+
    
+
+
    ◆ path_pattern_match()
    
+
+
    
+
    
+      
+        
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+        
+        
+          
+          
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+          
+        
+        
+          
+          
+          
+        
+      
    path_match_result path_pattern_match (text symbols, 
    text pattern, 
    float8 [] row_id, 
    boolean overlapping_patterns 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
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+
+
diff --git a/docs/docs/v2.1.0/pca_8sql__in.html b/docs/docs/v2.1.0/pca_8sql__in.html
new file mode 100644
index 00000000..fc03b85d
--- /dev/null
+++ b/docs/docs/v2.1.0/pca_8sql__in.html
@@ -0,0 +1,1842 @@
+
+
+
+
+
+
+
+
+MADlib: pca.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    pca.sql_in File Reference
      
    
+
    
+
    
+
+
    Principal Component Analysis.  
+More...
    
+
+
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+
+
    
+Functions
    void pca_train (text source_table, text pc_table, text row_id, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table, float8 variance)
     
    void pca_train (text source_table, text pc_table, text row_id, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table)
     
    void pca_train (text source_table, text pc_table, text row_id, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation)
     
    void pca_train (text source_table, text pc_table, text row_id, integer k, text grouping_cols, integer lanczos_iter)
     
    void pca_train (text source_table, text pc_table, text row_id, integer k, text grouping_cols)
     
    void pca_train (text source_table, text pc_table, text row_id, integer k)
     
    void pca_train (text source_table, text pc_table, text row_id, float8 variance, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table)
     
    void pca_train (text source_table, text pc_table, text row_id, float8 variance, text grouping_cols, integer lanczos_iter, boolean use_correlation)
     
    void pca_train (text source_table, text pc_table, text row_id, float8 variance, text grouping_cols, integer lanczos_iter)
     
    void pca_train (text source_table, text pc_table, text row_id, float8 variance, text grouping_cols)
     
    void pca_train (text source_table, text pc_table, text row_id, float8 variance)
     
    text pca_train (varchar usage_string)
     
    varchar pca_train ()
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table, float8 variance)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, text grouping_cols, integer lanczos_iter)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, text grouping_cols)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, float8 variance, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, float8 variance, text grouping_cols, integer lanczos_iter, boolean use_correlation)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, float8 variance, text grouping_cols, integer lanczos_iter)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, float8 variance, text grouping_cols)
     
    void pca_sparse_train (text source_table, text pc_table, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, float8 variance)
     
    text pca_sparse_train (varchar usage_string)
     
    text pca_sparse_train ()
     
    void _pca_union (text source_table, text pc_table, text pc_table_mean, text row_id, integer k, text grouping_cols, integer lanczos_iter, boolean use_correlation, text result_summary_table, text result_summary_table_temp, float8 variance, integer grp_id, text grouping_where_clause, text sparse_where_condition, text select_grouping_cols, text temp_table_columns, boolean is_sparse, text col_id, text val_id, integer row_dim, integer col_dim)
     
    
+
    Detailed Description
    
+
    See also
    For a brief introduction to Principal Component Analysis, see the module description Dimensionality Reduction. 
    
+
    Function Documentation
    
+
+
    ◆ _pca_union()
    
+
+
    
+
    
+      
+        
+          
+          
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+        
+      
    void _pca_union (text source_table, 
    text pc_table, 
    text pc_table_mean, 
    text row_id, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table, 
    text result_summary_table_temp, 
    float8 variance, 
    integer grp_id, 
    text grouping_where_clause, 
    text sparse_where_condition, 
    text select_grouping_cols, 
    text temp_table_columns, 
    boolean is_sparse, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_sparse_train() [1/13]
    
+
+
    
+
    
+      
+        
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+        
+        
+          
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+          
+          
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table, 
    float8 variance 
    )
    
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    ◆ pca_sparse_train() [2/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table 
    )
    
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    ◆ pca_sparse_train() [3/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation 
    )
    
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    ◆ pca_sparse_train() [4/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter 
    )
    
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    ◆ pca_sparse_train() [5/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    text grouping_cols 
    )
    
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    ◆ pca_sparse_train() [6/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k 
    )
    
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    ◆ pca_sparse_train() [7/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    float8 variance, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table 
    )
    
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    ◆ pca_sparse_train() [8/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    float8 variance, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation 
    )
    
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    ◆ pca_sparse_train() [9/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    float8 variance, 
    text grouping_cols, 
    integer lanczos_iter 
    )
    
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    ◆ pca_sparse_train() [10/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    float8 variance, 
    text grouping_cols 
    )
    
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    ◆ pca_sparse_train() [11/13]
    
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    void pca_sparse_train (text source_table, 
    text pc_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    float8 variance 
    )
    
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    ◆ pca_sparse_train() [12/13]
    
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    text pca_sparse_train (varchar usage_string)
    
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    ◆ pca_sparse_train() [13/13]
    
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    text pca_sparse_train ()
    
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    ◆ pca_train() [1/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table, 
    float8 variance 
    )
    
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    ◆ pca_train() [2/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table 
    )
    
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    ◆ pca_train() [3/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation 
    )
    
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    ◆ pca_train() [4/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    integer k, 
    text grouping_cols, 
    integer lanczos_iter 
    )
    
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    ◆ pca_train() [5/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    integer k, 
    text grouping_cols 
    )
    
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    ◆ pca_train() [6/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    integer k 
    )
    
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    ◆ pca_train() [7/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    float8 variance, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation, 
    text result_summary_table 
    )
    
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    ◆ pca_train() [8/13]
    
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+      
    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    float8 variance, 
    text grouping_cols, 
    integer lanczos_iter, 
    boolean use_correlation 
    )
    
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    ◆ pca_train() [9/13]
    
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+      
    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    float8 variance, 
    text grouping_cols, 
    integer lanczos_iter 
    )
    
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    ◆ pca_train() [10/13]
    
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+      
    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    float8 variance, 
    text grouping_cols 
    )
    
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    ◆ pca_train() [11/13]
    
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    void pca_train (text source_table, 
    text pc_table, 
    text row_id, 
    float8 variance 
    )
    
+
    
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    ◆ pca_train() [12/13]
    
+
+
    
+
    
+      
+        
+          
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+        
+      
    text pca_train (varchar usage_string)
    
+
    
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+
    
+
    
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    ◆ pca_train() [13/13]
    
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+
    
+
    
+      
+        
+          
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+      
    varchar pca_train ()
    
+
    
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+
    
+
    
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+
diff --git a/docs/docs/v2.1.0/pca__project_8sql__in.html b/docs/docs/v2.1.0/pca__project_8sql__in.html
new file mode 100644
index 00000000..61ae2e9a
--- /dev/null
+++ b/docs/docs/v2.1.0/pca__project_8sql__in.html
@@ -0,0 +1,714 @@
+
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+MADlib: pca_project.sql_in File Reference
+
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
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+  
    
+Functions  
    
+  
    
+
    pca_project.sql_in File Reference
      
    
+
    
+
    
+
+
    Principal Component Analysis Projection.  
+More...
    
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+Functions
    void pca_project (text source_table, text pc_table, text out_table, text row_id, text residual_table, text result_summary_table)
     
    void pca_project (text source_table, text pc_table, text out_table, text row_id)
     
    void pca_project (text source_table, text pc_table, text out_table, text row_id, text residual_table)
     
    varchar pca_project (text usage_string)
     
    varchar pca_project ()
     
    void pca_sparse_project (text source_table, text pc_table, text out_table, text row_id, text col_id, text val_id, int4 row_dim, int4 col_dim, text residual_table, text result_summary_table)
     
    void pca_sparse_project (text source_table, text pc_table, text out_table, text row_id, text col_id, text val_id, int4 row_dim, int4 col_dim)
     
    void pca_sparse_project (text source_table, text pc_table, text out_table, text row_id, text col_id, text val_id, int4 row_dim, int4 col_dim, text residual_table)
     
    void _pca_project_union (text source_table, text pc_table, text out_table, text row_id, text original_row_id, text grouping_cols, text grouping_cols_clause, text residual_table, text result_summary_table, integer grp_id, text grouping_where_clause, text sparse_where_condition, text select_grouping_cols, text grouping_cols_values, text temp_source_table_columns, text temp_pc_table_columns, boolean is_sparse, text col_id, text val_id, integer row_dim, integer col_dim)
     
    varchar pca_sparse_project (text usage_string)
     
    varchar pca_sparse_project ()
     
    
+
    Detailed Description
    
+
    See also
    For a brief introduction to Principal Component Analysis, see the module description Dimensionality Reduction. 
    
+
    Function Documentation
    
+
+
    ◆ _pca_project_union()
    
+
+
    
+
    
+      
+        
+          
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+        
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+        
+        
+          
+          
+          
+        
+      
    void _pca_project_union (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id, 
    text original_row_id, 
    text grouping_cols, 
    text grouping_cols_clause, 
    text residual_table, 
    text result_summary_table, 
    integer grp_id, 
    text grouping_where_clause, 
    text sparse_where_condition, 
    text select_grouping_cols, 
    text grouping_cols_values, 
    text temp_source_table_columns, 
    text temp_pc_table_columns, 
    boolean is_sparse, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_project() [1/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
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+        
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+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pca_project (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id, 
    text residual_table, 
    text result_summary_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_project() [2/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+          
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+        
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+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pca_project (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_project() [3/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pca_project (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id, 
    text residual_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_project() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar pca_project (text usage_string)
    
+
    
+
+
    
+
    
+
+
    ◆ pca_project() [5/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar pca_project ()
    
+
    
+
+
    
+
    
+
+
    ◆ pca_sparse_project() [1/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pca_sparse_project (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    int4 row_dim, 
    int4 col_dim, 
    text residual_table, 
    text result_summary_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_sparse_project() [2/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
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+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pca_sparse_project (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    int4 row_dim, 
    int4 col_dim 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_sparse_project() [3/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pca_sparse_project (text source_table, 
    text pc_table, 
    text out_table, 
    text row_id, 
    text col_id, 
    text val_id, 
    int4 row_dim, 
    int4 col_dim, 
    text residual_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pca_sparse_project() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar pca_sparse_project (text usage_string)
    
+
    
+
+
    
+
    
+
+
    ◆ pca_sparse_project() [5/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar pca_sparse_project ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/pivot_8sql__in.html b/docs/docs/v2.1.0/pivot_8sql__in.html
new file mode 100644
index 00000000..53b8e93f
--- /dev/null
+++ b/docs/docs/v2.1.0/pivot_8sql__in.html
@@ -0,0 +1,683 @@
+
+
+
+
+
+
+
+
+MADlib: pivot.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    pivot.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for pivoting.  
+More...
    
+
+
+
+
+
+
+
+
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+
+
    
+Functions
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, text aggregate_func, text fill_value, boolean keep_null, boolean output_col_dictionary, text output_type)
     Helper function that can be used to pivot tables.  More...
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, text aggregate_func, text fill_value, boolean keep_null, boolean output_col_dictionary)
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, text aggregate_func, text fill_value, boolean keep_null)
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, text aggregate_func, text fill_value)
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, text aggregate_func, boolean keep_null)
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, text aggregate_func)
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values, boolean keep_null)
     
    void pivot (text source_table, text output_table, text index, text pivot_cols, text pivot_values)
     
    varchar pivot (varchar message)
     
    varchar pivot ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    June 2016
    
+
    See also
    Creates a pivot table for data summarization. 
    
+
    Function Documentation
    
+
+
    ◆ pivot() [1/10]
    
+
+
    
+
    
+      
+        
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    text aggregate_func, 
    text fill_value, 
    boolean keep_null, 
    boolean output_col_dictionary, 
    text output_type 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    source_tableThe original data table 
    output_tableThe output table that contains the dummy variable columns 
    indexThe index columns to group by the records by 
    pivot_colsThe columns to pivot the table 
    pivot_valuesThe value columns to be summarized in the pivoted table 
    aggregate_funcThe aggregate function to be applied to the values 
    fill_valueIf specified, determines how to fill NULL values resulting from pivot operation 
    keep_nullThe flag for determining how to handle NULL values in pivot columns 
    output_col_dictionaryThe flag for enabling the creation of the output dictionary for shorter column names 
    
+  
    
+
    
+
    Returns
    Void 
    
+
+
    
+
    
+
+
    ◆ pivot() [2/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    text aggregate_func, 
    text fill_value, 
    boolean keep_null, 
    boolean output_col_dictionary 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [3/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    text aggregate_func, 
    text fill_value, 
    boolean keep_null 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [4/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    text aggregate_func, 
    text fill_value 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [5/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    text aggregate_func, 
    boolean keep_null 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [6/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    text aggregate_func 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [7/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
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+        
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values, 
    boolean keep_null 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [8/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
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+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void pivot (text source_table, 
    text output_table, 
    text index, 
    text pivot_cols, 
    text pivot_values 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [9/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar pivot (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ pivot() [10/10]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar pivot ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/pivotalr__arrayops_8sql__in.html b/docs/docs/v2.1.0/pivotalr__arrayops_8sql__in.html
new file mode 100644
index 00000000..983a5a59
--- /dev/null
+++ b/docs/docs/v2.1.0/pivotalr__arrayops_8sql__in.html
@@ -0,0 +1,273 @@
+
+
+
+
+
+
+
+
+MADlib: pivotalr_arrayops.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    pivotalr_arrayops.sql_in File Reference
      
    
+
    
+
    
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    float8 [] __pivotalr_crossprod_transition (float8[] current_state, float8[] left_arr, float8[] right_arr)
     
    float8 [] __pivotalr_crossprod_merge (float8[] left_state, float8[] right_state)
     
    aggregate float8 [] crossprod (float8[], float8[])
     
    float8 [] __pivotalr_crossprod_sym_transition (float8[] current_state, float8[] arr)
     
    aggregate float8 [] crossprod_sym (float8[])
     
    
+
    Function Documentation
    
+
+
    ◆ __pivotalr_crossprod_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __pivotalr_crossprod_merge (float8 [] left_state, 
    float8 [] right_state 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __pivotalr_crossprod_sym_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __pivotalr_crossprod_sym_transition (float8 [] current_state, 
    float8 [] arr 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __pivotalr_crossprod_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __pivotalr_crossprod_transition (float8 [] current_state, 
    float8 [] left_arr, 
    float8 [] right_arr 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ crossprod()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] crossprod (float8 [], 
    float8 [] 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ crossprod_sym()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate float8 [] crossprod_sym (float8 [])
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/porter__stemmer_8sql__in.html b/docs/docs/v2.1.0/porter__stemmer_8sql__in.html
new file mode 100644
index 00000000..d179c8ae
--- /dev/null
+++ b/docs/docs/v2.1.0/porter__stemmer_8sql__in.html
@@ -0,0 +1,229 @@
+
+
+
+
+
+
+
+
+MADlib: porter_stemmer.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    porter_stemmer.sql_in File Reference
      
    
+
    
+
    
+
+
    implementation of porter stemmer operations in SQL  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    text stem_token (text token)
     Returns stem of input token. Returns NULL if input token is NULL.  More...
     
    text [] stem_token_arr (text[] token_arr)
     Returns stems in an array of input token array. Returns NULL element for corresponding input NULL token.  More...
     
    text stem_token ()
     
    text stem_token_arr ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    September 2015 
    
+
    Function Documentation
    
+
+
    ◆ stem_token() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text stem_token (text token)
    
+
    
+
    Parameters
    
+  
+    
+  
    tokenText token 
    
+  
    
+
    
+
    Returns
    stem of token. 
    
+
+
    
+
    
+
+
    ◆ stem_token() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text stem_token ()
    
+
    
+
+
    
+
    
+
+
    ◆ stem_token_arr() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text [] stem_token_arr (text [] token_arr)
    
+
    
+
    Parameters
    
+  
+    
+  
    token_arrText[] token 
    
+  
    
+
    
+
    Returns
    stems array of input token array. 
    
+
+
    
+
    
+
+
    ◆ stem_token_arr() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text stem_token_arr ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/pred__metrics_8sql__in.html b/docs/docs/v2.1.0/pred__metrics_8sql__in.html
new file mode 100644
index 00000000..4c800198
--- /dev/null
+++ b/docs/docs/v2.1.0/pred__metrics_8sql__in.html
@@ -0,0 +1,1373 @@
+
+
+
+
+
+
+
+
+MADlib: pred_metrics.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    pred_metrics.sql_in File Reference
      
    
+
    
+
    
+
+
    A collection of summary statistics to gauge model accuracy based on predicted values vs. ground-truth values.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
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+
+
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+
+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
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+
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+
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+
+
+
+
+
+
+
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+
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+
+
+
+
+
+
+
    
+Functions
    void mean_abs_error (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     Mean Absolute Error.  More...
     
    void mean_abs_error (text table_in, text table_out, text prediction_col, text observed_col)
     
    text mean_abs_error (text message)
     
    text mean_abs_error ()
     
    void mean_abs_perc_error (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     Mean Absolute Percentage Error.  More...
     
    void mean_abs_perc_error (text table_in, text table_out, text prediction_col, text observed_col)
     
    text mean_abs_perc_error (text message)
     
    text mean_abs_perc_error ()
     
    void mean_perc_error (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     Mean Percentage Error.  More...
     
    void mean_perc_error (text table_in, text table_out, text prediction_col, text observed_col)
     
    text mean_perc_error (text message)
     
    text mean_perc_error ()
     
    void mean_squared_error (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     Mean Squared Error.  More...
     
    void mean_squared_error (text table_in, text table_out, text prediction_col, text observed_col)
     
    text mean_squared_error (text message)
     
    text mean_squared_error ()
     
    void r2_score (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     R2 Score.  More...
     
    void r2_score (text table_in, text table_out, text prediction_col, text observed_col)
     
    text r2_score (text message)
     
    text r2_score ()
     
    void adjusted_r2_score (text table_in, text table_out, text prediction_col, text observed_col, integer num_predictors, integer training_size, text grouping_cols)
     Adjusted R2 Score.  More...
     
    void adjusted_r2_score (text table_in, text table_out, text prediction_col, text observed_col, integer num_predictors, integer training_size)
     
    text adjusted_r2_score (text message)
     
    text adjusted_r2_score ()
     
    void binary_classifier (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     Binary Classifier.  More...
     
    void binary_classifier (text table_in, text table_out, text prediction_col, text observed_col)
     
    text binary_classifier (text message)
     
    text binary_classifier ()
     
    void area_under_roc (text table_in, text table_out, text prediction_col, text observed_col, text grouping_cols)
     Area under ROC Curve.  More...
     
    void area_under_roc (text table_in, text table_out, text prediction_col, text observed_col)
     
    text area_under_roc (text message)
     
    text area_under_roc ()
     
    void confusion_matrix (text table_in, text table_out, text prediction_col, text observed_col)
     Confusion Matrix.  More...
     
    text confusion_matrix (text message)
     
    text confusion_matrix ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    April 2016 
    
+
    Function Documentation
    
+
+
    ◆ adjusted_r2_score() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void adjusted_r2_score (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    integer num_predictors, 
    integer training_size, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    num_predictorsThe number of parameters in the predicting model, not counting the constant term. 
    training_sizeThe number of rows used for training, excluding any NULL rows. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ adjusted_r2_score() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void adjusted_r2_score (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    integer num_predictors, 
    integer training_size 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ adjusted_r2_score() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text adjusted_r2_score (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ adjusted_r2_score() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text adjusted_r2_score ()
    
+
    
+
+
    
+
    
+
+
    ◆ area_under_roc() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void area_under_roc (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ area_under_roc() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void area_under_roc (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ area_under_roc() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text area_under_roc (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ area_under_roc() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text area_under_roc ()
    
+
    
+
+
    
+
    
+
+
    ◆ binary_classifier() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void binary_classifier (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ binary_classifier() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void binary_classifier (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ binary_classifier() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text binary_classifier (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ binary_classifier() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text binary_classifier ()
    
+
    
+
+
    
+
    
+
+
    ◆ confusion_matrix() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void confusion_matrix (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ confusion_matrix() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text confusion_matrix (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ confusion_matrix() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text confusion_matrix ()
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_error() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_abs_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_error() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_abs_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_error() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text mean_abs_error (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_error() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text mean_abs_error ()
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_perc_error() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_abs_perc_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_perc_error() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_abs_perc_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_perc_error() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text mean_abs_perc_error (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ mean_abs_perc_error() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text mean_abs_perc_error ()
    
+
    
+
+
    
+
    
+
+
    ◆ mean_perc_error() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_perc_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ mean_perc_error() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_perc_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mean_perc_error() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text mean_perc_error (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ mean_perc_error() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text mean_perc_error ()
    
+
    
+
+
    
+
    
+
+
    ◆ mean_squared_error() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_squared_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ mean_squared_error() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void mean_squared_error (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mean_squared_error() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text mean_squared_error (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ mean_squared_error() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text mean_squared_error ()
    
+
    
+
+
    
+
    
+
+
    ◆ r2_score() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void r2_score (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col, 
    text grouping_cols 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    table_inName of the input table. 
    table_outName of the output table. 
    prediction_colName of the column of predicted values from input table. 
    observed_colName of the column of observed values from input table. 
    grouping_colsName of the column of grouping values from input table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ r2_score() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+          
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+        
+        
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void r2_score (text table_in, 
    text table_out, 
    text prediction_col, 
    text observed_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ r2_score() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text r2_score (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ r2_score() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text r2_score ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/prob_8sql__in.html b/docs/docs/v2.1.0/prob_8sql__in.html
new file mode 100644
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+MADlib: prob.sql_in File Reference
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+
    
+
    
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+ 
+  
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+   
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+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
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+  
    
+Functions  
    
+  
    
+
    prob.sql_in File Reference
      
    
+
    
+
    
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+
    SQL functions for evaluating probability functions.  
+More...
    
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+Functions
    float8 bernoulli_cdf (float8 x, float8 sp)
     Bernoulli cumulative distribution function.  More...
     
    float8 bernoulli_pmf (int4 x, float8 sp)
     Bernoulli probability mass function.  More...
     
    float8 bernoulli_quantile (float8 p, float8 sp)
     Bernoulli quantile function.  More...
     
    float8 beta_cdf (float8 x, float8 alpha, float8 beta)
     Beta cumulative distribution function.  More...
     
    float8 beta_pdf (float8 x, float8 alpha, float8 beta)
     Beta probability density function.  More...
     
    float8 beta_quantile (float8 p, float8 alpha, float8 beta)
     Beta quantile function.  More...
     
    float8 binomial_cdf (float8 x, int4 n, float8 sp)
     Binomial cumulative distribution function.  More...
     
    float8 binomial_pmf (int4 x, int4 n, float8 sp)
     Binomial probability mass function.  More...
     
    float8 binomial_quantile (float8 p, int4 n, float8 sp)
     Binomial quantile function.  More...
     
    float8 cauchy_cdf (float8 x, float8 location, float8 scale)
     Cauchy cumulative distribution function.  More...
     
    float8 cauchy_pdf (float8 x, float8 location, float8 scale)
     Cauchy probability density function.  More...
     
    float8 cauchy_quantile (float8 p, float8 location, float8 scale)
     Cauchy quantile function.  More...
     
    float8 chi_squared_cdf (float8 x, float8 df)
     Chi-squared cumulative distribution function.  More...
     
    float8 chi_squared_pdf (float8 x, float8 df)
     Chi-squared distribution probability density function.  More...
     
    float8 chi_squared_quantile (float8 p, float8 df)
     Chi-squared distribution quantile function.  More...
     
    float8 exponential_cdf (float8 x, float8 lambda)
     Exponential cumulative distribution function.  More...
     
    float8 exponential_pdf (float8 x, float8 lambda)
     Exponential probability density function.  More...
     
    float8 exponential_quantile (float8 p, float8 lambda)
     Exponential quantile function.  More...
     
    float8 extreme_value_cdf (float8 x, float8 location, float8 scale)
     Extreme Value cumulative distribution function.  More...
     
    float8 extreme_value_pdf (float8 x, float8 location, float8 scale)
     Extreme Value probability density function.  More...
     
    float8 extreme_value_quantile (float8 p, float8 location, float8 scale)
     Extreme Value quantile function.  More...
     
    float8 fisher_f_cdf (float8 x, float8 df1, float8 df2)
     Fisher F cumulative distribution function.  More...
     
    float8 fisher_f_pdf (float8 x, float8 df1, float8 df2)
     Fisher F probability density function.  More...
     
    float8 fisher_f_quantile (float8 p, float8 df1, float8 df2)
     Fisher F quantile function.  More...
     
    float8 gamma_cdf (float8 x, float8 shape, float8 scale)
     Gamma cumulative distribution function.  More...
     
    float8 gamma_pdf (float8 x, float8 shape, float8 scale)
     Gamma probability density function.  More...
     
    float8 gamma_quantile (float8 p, float8 shape, float8 scale)
     Gamma quantile function.  More...
     
    float8 geometric_cdf (float8 x, float8 sp)
     Geometric cumulative distribution function.  More...
     
    float8 geometric_pmf (int4 x, float8 sp)
     Geometric probability mass function.  More...
     
    float8 geometric_quantile (float8 p, float8 sp)
     Geometric quantile function.  More...
     
    float8 hypergeometric_cdf (float8 x, int4 r, int4 n, int4 N)
     Hypergeometric cumulative distribution function.  More...
     
    float8 hypergeometric_pmf (int4 x, int4 r, int4 n, int4 N)
     Hypergeometric probability mass function.  More...
     
    float8 hypergeometric_quantile (float8 p, int4 r, int4 n, int4 N)
     Hypergeometric quantile function.  More...
     
    float8 inverse_gamma_cdf (float8 x, float8 shape, float8 scale)
     Inverse Gamma cumulative distribution function.  More...
     
    float8 inverse_gamma_pdf (float8 x, float8 shape, float8 scale)
     Inverse Gamma probability density function.  More...
     
    float8 inverse_gamma_quantile (float8 p, float8 shape, float8 scale)
     Inverse Gamma quantile function.  More...
     
    float8 kolmogorov_cdf (float8 x)
     Kolmogorov cumulative distribution function.  More...
     
    float8 laplace_cdf (float8 x, float8 mean, float8 scale)
     Laplace cumulative distribution function.  More...
     
    float8 laplace_pdf (float8 x, float8 mean, float8 scale)
     Laplace probability density function.  More...
     
    float8 laplace_quantile (float8 p, float8 mean, float8 scale)
     Laplace quantile function.  More...
     
    float8 logistic_cdf (float8 x, float8 mean, float8 scale)
     Logistic cumulative distribution function.  More...
     
    float8 logistic_pdf (float8 x, float8 mean, float8 scale)
     Logistic probability density function.  More...
     
    float8 logistic_quantile (float8 p, float8 mean, float8 scale)
     Logistic quantile function.  More...
     
    float8 lognormal_cdf (float8 x, float8 location, float8 scale)
     Log-normal cumulative distribution function.  More...
     
    float8 lognormal_pdf (float8 x, float8 location, float8 scale)
     Log-normal probability density function.  More...
     
    float8 lognormal_quantile (float8 p, float8 location, float8 scale)
     Log-normal quantile function.  More...
     
    float8 negative_binomial_cdf (float8 x, float8 r, float8 sp)
     Negative binomial cumulative distribution function.  More...
     
    float8 negative_binomial_pmf (int4 x, float8 r, float8 sp)
     Negative binomial probability mass function.  More...
     
    float8 negative_binomial_quantile (float8 p, float8 r, float8 sp)
     Negative binomial quantile function.  More...
     
    float8 non_central_beta_cdf (float8 x, float8 alpha, float8 beta, float8 ncp)
     Noncentral beta cumulative distribution function.  More...
     
    float8 non_central_beta_pdf (float8 x, float8 alpha, float8 beta, float8 ncp)
     Noncentral beta probability density function.  More...
     
    float8 non_central_beta_quantile (float8 p, float8 alpha, float8 beta, float8 ncp)
     Noncentral beta quantile function.  More...
     
    float8 non_central_chi_squared_cdf (float8 x, float8 df, float8 ncp)
     Noncentral chi-squared cumulative distribution function.  More...
     
    float8 non_central_chi_squared_pdf (float8 x, float8 df, float8 ncp)
     Noncentral chi-squared distribution probability density function.  More...
     
    float8 non_central_chi_squared_quantile (float8 p, float8 df, float8 ncp)
     Noncentral chi-squared distribution quantile function.  More...
     
    float8 non_central_f_cdf (float8 x, float8 df1, float8 df2, float8 ncp)
     Noncentral Fisher F cumulative distribution function.  More...
     
    float8 non_central_f_pdf (float8 x, float8 df1, float8 df2, float8 ncp)
     Noncentral Fisher F probability density function.  More...
     
    float8 non_central_f_quantile (float8 p, float8 df1, float8 df2, float8 ncp)
     Noncentral Fisher F quantile function.  More...
     
    float8 non_central_t_cdf (float8 x, float8 df, float8 ncp)
     Noncentral Student-t cumulative distribution function.  More...
     
    float8 non_central_t_pdf (float8 x, float8 df, float8 ncp)
     Noncentral Student-t probability density function.  More...
     
    float8 non_central_t_quantile (float8 p, float8 df, float8 ncp)
     Noncentral Student-t quantile function.  More...
     
    float8 normal_cdf (float8 x, float8 mean=0, float8 sd=1)
     Normal cumulative distribution function.  More...
     
    float8 normal_cdf (float8 x, float8 mean)
     
    float8 normal_cdf (float8 x)
     
    float8 normal_pdf (float8 x, float8 mean=0, float8 sd=1)
     Normal probability density function.  More...
     
    float8 normal_pdf (float8 x, float8 mean)
     
    float8 normal_pdf (float8 x)
     
    float8 normal_quantile (float8 p, float8 mean=0, float8 sd=1)
     Normal quantile function.  More...
     
    float8 normal_quantile (float8 p, float8 mean)
     
    float8 normal_quantile (float8 p)
     
    float8 pareto_cdf (float8 x, float8 scale, float8 shape)
     Pareto cumulative distribution function.  More...
     
    float8 pareto_pdf (float8 x, float8 scale, float8 shape)
     Pareto probability density function.  More...
     
    float8 pareto_quantile (float8 p, float8 scale, float8 shape)
     Pareto quantile function.  More...
     
    float8 poisson_cdf (float8 x, float8 mean)
     Poisson cumulative distribution function.  More...
     
    float8 poisson_pmf (int4 x, float8 mean)
     Poisson probability mass function.  More...
     
    float8 poisson_quantile (float8 p, float8 mean)
     Poisson quantile function.  More...
     
    float8 rayleigh_cdf (float8 x, float8 scale)
     Rayleigh cumulative distribution function.  More...
     
    float8 rayleigh_pdf (float8 x, float8 scale)
     Rayleigh probability density function.  More...
     
    float8 rayleigh_quantile (float8 p, float8 scale)
     Rayleigh quantile function.  More...
     
    float8 students_t_cdf (float8 x, float8 df)
     Student's t cumulative distribution function.  More...
     
    float8 students_t_pdf (float8 x, float8 df)
     Student's t probability density function.  More...
     
    float8 students_t_quantile (float8 p, float8 df)
     Student's t quantile function.  More...
     
    float8 triangular_cdf (float8 x, float8 lower, float8 mode, float8 upper)
     Triangular cumulative distribution function.  More...
     
    float8 triangular_pdf (float8 x, float8 lower, float8 mode, float8 upper)
     Triangular probability density function.  More...
     
    float8 triangular_quantile (float8 p, float8 lower, float8 mode, float8 upper)
     Triangular quantile function.  More...
     
    float8 uniform_cdf (float8 x, float8 lower, float8 upper)
     Uniform cumulative distribution function.  More...
     
    float8 uniform_pdf (float8 x, float8 lower, float8 upper)
     Uniform probability density function.  More...
     
    float8 uniform_quantile (float8 p, float8 lower, float8 upper)
     Uniform quantile function.  More...
     
    float8 weibull_cdf (float8 x, float8 shape, float8 scale)
     Weibull cumulative distribution function.  More...
     
    float8 weibull_pdf (float8 x, float8 shape, float8 scale)
     Weibull probability density function.  More...
     
    float8 weibull_quantile (float8 p, float8 shape, float8 scale)
     Weibull quantile function.  More...
     
    
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    Detailed Description
    
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    See also
    For an overview of probability functions, see the module description Probability Functions. 
    
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    Function Documentation
    
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    ◆ bernoulli_cdf()
    
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    float8 bernoulli_cdf (float8 x, 
    float8 sp 
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    spSuccess probability \( p \in [0,1] \) 
    
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    \( \Pr[X \leq x] \) where \( X \) is a Bernoulli-distributed random variable with success probability \( \mathit{sp} \) 
    
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    ◆ bernoulli_pmf()
    
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    float8 bernoulli_pmf (int4 x, 
    float8 sp 
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    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
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    \( f(x) \) where \( f \) is the probability mass function of a Bernoulli-distributed random variable with success probability \( \mathit{sp} \) 
    
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    ◆ bernoulli_quantile()
    
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    float8 bernoulli_quantile (float8 p, 
    float8 sp 
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    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
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    0 if \( p \leq 1 - \mathit{sp} \) and 1 otherwise 
    
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    ◆ beta_cdf()
    
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    float8 beta_cdf (float8 x, 
    float8 alpha, 
    float8 beta 
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    alphaShape \( \alpha > 0 \) 
    betaShape \( \beta > 0 \) 
    
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    \( \Pr[X \leq x] \) where \( X \) is a beta distributed random variable with shape parameters \( \alpha \) and \( \beta \) 
    
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    ◆ beta_pdf()
    
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    float8 beta_pdf (float8 x, 
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    float8 beta 
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    alphaShape \( \alpha > 0 \) 
    betaShape \( \beta > 0 \) 
    
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    \( f(x) \) where \( f \) is the probability density function of a beta random variable with shape parameters \( \alpha \) and \( \beta \) 
    
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    ◆ beta_quantile()
    
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    float8 beta_quantile (float8 p, 
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    alphaShape \( \alpha > 0 \) 
    betaShape \( \beta > 0 \) 
    
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    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is beta distribution random variable with shape parameters \( \alpha \) and \( \beta \) 
    
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    ◆ binomial_cdf()
    
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    float8 binomial_cdf (float8 x, 
    int4 n, 
    float8 sp 
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    nThe number of trials \( n \in \mathbb N_0 \) 
    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
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    \( \Pr[X \leq x] \) where \( X \) is a binomially distributed random variable with \( n \) trials and success probability \( \mathit{sp} \) 
    
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    ◆ binomial_pmf()
    
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    float8 binomial_pmf (int4 x, 
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    nThe number of trials \( n \in \mathbb N_0 \) 
    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
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    \( f(x) \) where \( f \) is the probability mass function of a binomially distributed random variable with \( n \) trials and success probability \( \mathit{sp} \) 
    
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    ◆ binomial_quantile()
    
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    float8 binomial_quantile (float8 p, 
    int4 n, 
    float8 sp 
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    nThe number of trials \( n \in \mathbb N_0 \) 
    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
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    If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a binomially distributed random variable with \( n \) trials and success probability \( \mathit{sp} \). 
    
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    ◆ cauchy_cdf()
    
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    float8 cauchy_cdf (float8 x, 
    float8 location, 
    float8 scale 
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    locationLocation \( x_0 \) 
    scaleScale \( \gamma > 0 \) 
    
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    \( \Pr[X \leq x] \) where \( X \) is a Cauchy-distributed random variable with location and scale parameters \( x_0 \) and \( \gamma \), respectively 
    
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    ◆ cauchy_pdf()
    
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    float8 cauchy_pdf (float8 x, 
    float8 location, 
    float8 scale 
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    \( f(x) \) where \( f \) is the probability density function of a Cauchy-distributed random variable with location and scale parameters \( x_0 \) and \( \gamma \), respectively 
    
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    ◆ cauchy_quantile()
    
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    float8 cauchy_quantile (float8 p, 
    float8 location, 
    float8 scale 
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    locationLocation \( x_0 \) 
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    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Cauchy-distributed random variable with location and scale parameters \( x_0 \) and \( \gamma \), respectively 
    
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    ◆ chi_squared_cdf()
    
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    float8 chi_squared_cdf (float8 x, 
    float8 df 
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    dfDegrees of freedom \( \nu > 0 \) 
    
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    \( \Pr[X \leq x] \) where \( X \) is a chi-squared distributed random variable with \( \nu \) degrees of freedom 
    
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    ◆ chi_squared_pdf()
    
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    float8 chi_squared_pdf (float8 x, 
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    dfDegrees of freedom \( \nu > 0 \) 
    
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    \( f(x) \) where \( f \) is the probability density function of a chi-squared distributed random variable with \( \nu \) degrees of freedom 
    
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    ◆ chi_squared_quantile()
    
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    float8 chi_squared_quantile (float8 p, 
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    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a chi-squared distributed random variable with \( \nu \) degrees of freedom 
    
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    ◆ exponential_cdf()
    
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    float8 exponential_cdf (float8 x, 
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    lambdaRate parameter \( \lambda > 0 \) 
    
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    \( \Pr[X \leq x] \) where \( X \) is an exponentially distributed random variable with rate parameter \( \lambda \) 
    
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    ◆ exponential_pdf()
    
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    float8 exponential_pdf (float8 x, 
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    lambdaRate parameter \( \lambda > 0 \) 
    
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    \( f(x) \) where \( f \) is the probability density function of exponentially distributed random variable with rate parameter \( \lambda \) 
    
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    float8 exponential_quantile (float8 p, 
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    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a exponentially distributed random variable with rate parameter \( \lambda \) 
    
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    ◆ extreme_value_cdf()
    
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    float8 extreme_value_cdf (float8 x, 
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    locationLocation \( \alpha \) 
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    \( \Pr[X \leq x] \) where \( X \) is an extreme-value distributed random variable with location and scale parameters \( \alpha \) and \( \beta \), respectively 
    
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    float8 extreme_value_pdf (float8 x, 
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    \( f(x) \) where \( f \) is the probability density function of an extreme-value distributed random variable with location and scale parameters \( \alpha \) and \( \beta \), respectively 
    
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    float8 extreme_value_quantile (float8 p, 
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    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is an extreme-value distributed random variable with location and scale parameters \( \alpha \) and \( \beta \), respectively 
    
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    ◆ fisher_f_cdf()
    
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    float8 fisher_f_cdf (float8 x, 
    float8 df1, 
    float8 df2 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    df1Degrees of freedom in numerator \( \nu_1 > 0 \) 
    df2Degrees of freedom in denominator \( \nu_1 > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Fisher F-distributed random variable with parameters \( \nu_1 \) and \( \nu_2 \) 
    
+
+
    
+
    
+
+
    ◆ fisher_f_pdf()
    
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    float8 fisher_f_pdf (float8 x, 
    float8 df1, 
    float8 df2 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    df1Degrees of freedom in numerator \( \nu_1 > 0 \) 
    df2Degrees of freedom in denominator \( \nu_1 > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a Fisher F-distributed random variable with parameters \( \nu_1 \) and \( \nu_2 \) 
    
+
+
    
+
    
+
+
    ◆ fisher_f_quantile()
    
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    float8 fisher_f_quantile (float8 p, 
    float8 df1, 
    float8 df2 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    df1Degrees of freedom in numerator \( \nu_1 > 0 \) 
    df2Degrees of freedom in denominator \( \nu_1 > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Fisher F-distributed random variable with parameters \( \nu_1 \) and \( \nu_2 \) 
    
+
+
    
+
    
+
+
    ◆ gamma_cdf()
    
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    float8 gamma_cdf (float8 x, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    shapeShape \( k > 0 \) 
    scaleScale \( \theta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a gamma distributed random variable with shape and scale parameters \( k \) and \( \theta \), respectively 
    
+
+
    
+
    
+
+
    ◆ gamma_pdf()
    
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    float8 gamma_pdf (float8 x, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    shapeShape \( k > 0 \) 
    scaleScale \( \theta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a gamma distributed random variable with shape and scale parameters \( k \) and \( \theta \), respectively 
    
+
+
    
+
    
+
+
    ◆ gamma_quantile()
    
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    float8 gamma_quantile (float8 p, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    shapeShape \( k > 0 \) 
    scaleScale \( \theta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a gamma distributed random variable with shape and scale parameters \( k \) and \( \theta \), respectively 
    
+
+
    
+
    
+
+
    ◆ geometric_cdf()
    
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    float8 geometric_cdf (float8 x, 
    float8 sp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a geometrically distributed random variable with success probability \( \mathit{sp} \). 
    
+
+
    
+
    
+
+
    ◆ geometric_pmf()
    
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    float8 geometric_pmf (int4 x, 
    float8 sp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability mass function of a geometrically distributed random variable with success probability \( \mathit{sp} \) 
    
+
+
    
+
    
+
+
    ◆ geometric_quantile()
    
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    float8 geometric_quantile (float8 p, 
    float8 sp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    spSuccess probability \( \mathit{sp} \in [0,1] \) 
    
+  
    
+
    
+
    Returns
    If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a geometrically distributed random variable with success probability \( \mathit{sp} \). 
    
+
+
    
+
    
+
+
    ◆ hypergeometric_cdf()
    
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    float8 hypergeometric_cdf (float8 x, 
    int4 r, 
    int4 n, 
    int4 N 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    xRandom variate \( x \) 
    rNumber \( r \in \{ 0, 1, \dots, N \} \) of items with distinct property (sometimes called the number of success states in population) 
    nNumber \( n \in \{ 0, 1, \dots, N \} \) of draws (without replacement) 
    NTotal number \( N \in \mathbb N \) of items 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a hypergeometrically distributed random variable with parameters \( r, n, N \) 
    
+
+
    
+
    
+
+
    ◆ hypergeometric_pmf()
    
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    float8 hypergeometric_pmf (int4 x, 
    int4 r, 
    int4 n, 
    int4 N 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    xRandom variate \( x \) 
    rNumber \( r \in \{ 0, 1, \dots, N \} \) of items with distinct property (sometimes called the number of success states in population) 
    nNumber \( n \in \{ 0, 1, \dots, N \} \) of draws (without replacement) 
    NTotal number \( N \in \mathbb N \) of items 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability mass function of a hypergeometrically distributed random variable with parameters \( r, n, N \) 
    
+
+
    
+
    
+
+
    ◆ hypergeometric_quantile()
    
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    float8 hypergeometric_quantile (float8 p, 
    int4 r, 
    int4 n, 
    int4 N 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    rNumber \( r \in \{ 0, 1, \dots, N \} \) of items with distinct property (sometimes called the number of success states in population) 
    nNumber \( n \in \{ 0, 1, \dots, N \} \) of draws (without replacement) 
    NTotal number \( N \in \mathbb N \) of items 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a hypergeometrically distributed random variable with parameters \( r, n, N \) 
    
+
+
    
+
    
+
+
    ◆ inverse_gamma_cdf()
    
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    float8 inverse_gamma_cdf (float8 x, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    shapeShape \( \alpha > 0 \) 
    scaleScale \( \beta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is an inverse-gamma distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
+
    ◆ inverse_gamma_pdf()
    
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    float8 inverse_gamma_pdf (float8 x, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    shapeShape \( \alpha > 0 \) 
    scaleScale \( \beta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of an inverse-gamma distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
+
    ◆ inverse_gamma_quantile()
    
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    float8 inverse_gamma_quantile (float8 p, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    shapeShape \( \alpha > 0 \) 
    scaleScale \( \beta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is an inverse-gamma distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
+
    ◆ kolmogorov_cdf()
    
+
+
    
+
    
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+      
    float8 kolmogorov_cdf (float8 x)
    
+
    
+
    Parameters
    
+  
+    
+  
    xRandom variate \( x \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Kolmogorov distributed random variable
    
+
    See also
    Kolmogorov-Smirnov test: ks_test() 
    
+
+
    
+
    
+
+
    ◆ laplace_cdf()
    
+
+
    
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    float8 laplace_cdf (float8 x, 
    float8 mean, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    meanMean \( \mu \) 
    scaleScale \( b > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Laplace-distributed random variable with mean \( \mu \) and variance \( 2 b^2 \) 
    
+
+
    
+
    
+
+
    ◆ laplace_pdf()
    
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    float8 laplace_pdf (float8 x, 
    float8 mean, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    meanMean \( \mu \) 
    scaleScale \( b > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a Laplace-distributed random variable with mean \( \mu \) and variance \( 2 b^2 \) 
    
+
+
    
+
    
+
+
    ◆ laplace_quantile()
    
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    float8 laplace_quantile (float8 p, 
    float8 mean, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    meanMean \( \mu \) 
    scaleScale \( b > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Laplace-distributed random variable with mean \( \mu \) and variance \( 2 b^2 \) 
    
+
+
    
+
    
+
+
    ◆ logistic_cdf()
    
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    float8 logistic_cdf (float8 x, 
    float8 mean, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    meanMean \( \mu \) 
    scaleScale \( s > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a logistically distributed random variable with mean \( \mu \) and scale parameter \( s \) 
    
+
+
    
+
    
+
+
    ◆ logistic_pdf()
    
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    float8 logistic_pdf (float8 x, 
    float8 mean, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    meanMean \( \mu \) 
    scaleScale \( s > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a logistically distributed random variable with mean \( \mu \) and scale parameter \( s \) 
    
+
+
    
+
    
+
+
    ◆ logistic_quantile()
    
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    float8 logistic_quantile (float8 p, 
    float8 mean, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    meanMean \( \mu \) 
    scaleScale \( s > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a logistically distributed random variable with mean \( \mu \) and scale parameter \( s \) 
    
+
+
    
+
    
+
+
    ◆ lognormal_cdf()
    
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    float8 lognormal_cdf (float8 x, 
    float8 location, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    locationLocation \( m \) 
    scaleScale \( s > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a lognormally distributed random variable with location and scale parameters \( m \) and \( s \), respectively 
    
+
+
    
+
    
+
+
    ◆ lognormal_pdf()
    
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    float8 lognormal_pdf (float8 x, 
    float8 location, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    locationLocation \( m \) 
    scaleScale \( s > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a lognormally distributed random variable with location and scale parameters \( m \) and \( s \), respectively 
    
+
+
    
+
    
+
+
    ◆ lognormal_quantile()
    
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    float8 lognormal_quantile (float8 p, 
    float8 location, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    locationLocation \( m \) 
    scaleScale \( s > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a lognormally distributed random variable with location and scale parameters \( m \) and \( s \), respectively 
    
+
+
    
+
    
+
+
    ◆ negative_binomial_cdf()
    
+
+
    
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    float8 negative_binomial_cdf (float8 x, 
    float8 r, 
    float8 sp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
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    xRandom variate \( x \) 
    rTotal number \( r > 0 \) of successes in \( x + r \) trials (assuming success in the last trial) 
    spSuccess probability \( \mathit{sp} \in (0,1] \) in each trial 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a negative-binomially distributed random variable with parameters \( r, \mathit{sp} \) 
    
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+
    
+
    
+
+
    ◆ negative_binomial_pmf()
    
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    float8 negative_binomial_pmf (int4 x, 
    float8 r, 
    float8 sp 
    )
    
+
    
+
    Parameters
    
+  
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+    
+    
+  
    xRandom variate \( x \) 
    rTotal number \( r > 0 \) of successes in \( x + r \) trials (assuming success in the last trial) 
    spSuccess probability \( \mathit{sp} \in (0,1] \) in each trial 
    
+  
    
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+
    Returns
    \( f(x) \) where \( f \) is the probability mass function of a negative-binomially distributed random variable with parameters \( r, \mathit{sp} \) 
    
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+
    
+
    
+
+
    ◆ negative_binomial_quantile()
    
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    float8 negative_binomial_quantile (float8 p, 
    float8 r, 
    float8 sp 
    )
    
+
    
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    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    rTotal number \( r > 0 \) of successes in \( x + r \) trials (assuming success in the last trial) 
    spSuccess probability \( \mathit{sp} \in (0,1] \) in each trial 
    
+  
    
+
    
+
    Returns
    If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a negative-binomially distributed random variable with parameters \( r, \mathit{sp} \) 
    
+
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+
    
+
+
    ◆ non_central_beta_cdf()
    
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    float8 non_central_beta_cdf (float8 x, 
    float8 alpha, 
    float8 beta, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
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+    
+    
+    
+  
    xRandom variate \( x \) 
    alphaShape \( \alpha > 0 \) 
    betaShape \( \beta > 0 \) 
    ncpNoncentrality parameter \( \delta \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a noncentral-beta distributed random variable with shape parameters \( shape_1 \) and \( shape_2 \) and noncentrality parameter \( \delta \) 
    
+
+
    
+
    
+
+
    ◆ non_central_beta_pdf()
    
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    float8 non_central_beta_pdf (float8 x, 
    float8 alpha, 
    float8 beta, 
    float8 ncp 
    )
    
+
    
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    Parameters
    
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+  
    xRandom variate \( x \) 
    alphaShape \( \alpha > 0 \) 
    betaShape \( \beta > 0 \) 
    ncpNoncentrality parameter \( \delta \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a noncentral-beta distributed random variable with shape parameters \( shape_1 \) and \( shape_2 \) and noncentrality parameter \( \delta \) 
    
+
+
    
+
    
+
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    ◆ non_central_beta_quantile()
    
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    float8 non_central_beta_quantile (float8 p, 
    float8 alpha, 
    float8 beta, 
    float8 ncp 
    )
    
+
    
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    Parameters
    
+  
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+    
+    
+  
    pProbability \( p \in [0,1] \) 
    alphaShape \( \alpha > 0 \) 
    betaShape \( \beta > 0 \) 
    ncpNoncentrality parameter \( \delta \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral-beta distributed random variable with shape parameters \( shape_1 \) and \( shape_2 \) and noncentrality parameter \( \delta \) 
    
+
+
    
+
    
+
+
    ◆ non_central_chi_squared_cdf()
    
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    float8 non_central_chi_squared_cdf (float8 x, 
    float8 df, 
    float8 ncp 
    )
    
+
    
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    Parameters
    
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+    
+    
+  
    xRandom variate \( x \) 
    dfDegrees of freedom \( \nu > 0 \) 
    ncpThe noncentrality parameter \( \lambda \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a noncentral-chi-squared distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \lambda \) 
    
+
+
    
+
    
+
+
    ◆ non_central_chi_squared_pdf()
    
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    float8 non_central_chi_squared_pdf (float8 x, 
    float8 df, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
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+    
+    
+  
    xRandom variate \( x \) 
    dfDegrees of freedom \( \nu > 0 \) 
    ncpThe noncentrality parameter \( \lambda \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a noncentral-chi-squared distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \lambda \) 
    
+
+
    
+
    
+
+
    ◆ non_central_chi_squared_quantile()
    
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    float8 non_central_chi_squared_quantile (float8 p, 
    float8 df, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    dfDegrees of freedom \( \nu > 0 \) 
    ncpThe noncentrality parameter \( \lambda \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral-chi-squared distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \lambda \) 
    
+
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+
    
+
+
    ◆ non_central_f_cdf()
    
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    float8 non_central_f_cdf (float8 x, 
    float8 df1, 
    float8 df2, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    xRandom variate \( x \) 
    df1Degrees of freedom in numerator \( \nu_1 > 0 \) 
    df2Degrees of freedom in denominator \( \nu_1 > 0 \) 
    ncpThe noncentrality parameter \( \lambda \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a noncentral Fisher F-distributed random variable with parameters \( \nu_1, \nu_2, \lambda \) 
    
+
+
    
+
    
+
+
    ◆ non_central_f_pdf()
    
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    float8 non_central_f_pdf (float8 x, 
    float8 df1, 
    float8 df2, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    xRandom variate \( x \) 
    df1Degrees of freedom in numerator \( \nu_1 > 0 \) 
    df2Degrees of freedom in denominator \( \nu_1 > 0 \) 
    ncpThe noncentrality parameter \( \lambda \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a noncentral Fisher F-distributed random variable with parameters \( \nu_1, \nu_2, \lambda \) 
    
+
+
    
+
    
+
+
    ◆ non_central_f_quantile()
    
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    float8 non_central_f_quantile (float8 p, 
    float8 df1, 
    float8 df2, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    df1Degrees of freedom in numerator \( \nu_1 > 0 \) 
    df2Degrees of freedom in denominator \( \nu_1 > 0 \) 
    ncpThe noncentrality parameter \( \lambda \geq 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral Fisher F-distributed random variable with parameters \( \nu_1, \nu_2, \lambda \) 
    
+
+
    
+
    
+
+
    ◆ non_central_t_cdf()
    
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    float8 non_central_t_cdf (float8 x, 
    float8 df, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    dfDegrees of freedom \( \nu > 0 \) 
    ncpNoncentrality parameter \( \delta \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a noncentral Student's t-distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \delta \) 
    
+
+
    
+
    
+
+
    ◆ non_central_t_pdf()
    
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    float8 non_central_t_pdf (float8 x, 
    float8 df, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    dfDegrees of freedom \( \nu > 0 \) 
    ncpNoncentrality parameter \( \delta \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral Student's t-distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \delta \) 
    
+
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+
    
+
+
    ◆ non_central_t_quantile()
    
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    float8 non_central_t_quantile (float8 p, 
    float8 df, 
    float8 ncp 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    dfDegrees of freedom \( \nu > 0 \) 
    ncpNoncentrality parameter \( \delta \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a noncentral Student's t-distributed random variable with \( \nu \) degrees of freedom and noncentrality parameter \( \delta \) 
    
+
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+
    
+
+
    ◆ normal_cdf() [1/3]
    
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    float8 normal_cdf (float8 x, 
    float8 mean = 0, 
    float8 sd = 1 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    meanMean \( \mu \) 
    sdStandard deviation \( \sigma > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( T \) is a normally distributed random variable with mean \( \mu \) and variance \( \sigma^2 \) 
    
+
+
    
+
    
+
+
    ◆ normal_cdf() [2/3]
    
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    float8 normal_cdf (float8 x, 
    float8 mean 
    )
    
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+
    
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    ◆ normal_cdf() [3/3]
    
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    float8 normal_cdf (float8 x)
    
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    ◆ normal_pdf() [1/3]
    
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    float8 normal_pdf (float8 x, 
    float8 mean = 0, 
    float8 sd = 1 
    )
    
+
    
+
    Parameters
    
+  
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+    
+    
+  
    xRandom variate \( x \) 
    meanMean \( \mu \) 
    sdStandard deviation \( \sigma > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a normally distributed random variable with mean \( \mu \) and variance \( \sigma^2 \) 
    
+
+
    
+
    
+
+
    ◆ normal_pdf() [2/3]
    
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    float8 normal_pdf (float8 x, 
    float8 mean 
    )
    
+
    
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    ◆ normal_pdf() [3/3]
    
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    float8 normal_pdf (float8 x)
    
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    ◆ normal_quantile() [1/3]
    
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    float8 normal_quantile (float8 p, 
    float8 mean = 0, 
    float8 sd = 1 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    meanMean \( \mu \) 
    sdStandard deviation \( \sigma > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a normally distributed random variable with mean \( \mu \) and variance \( \sigma^2 \) 
    
+
+
    
+
    
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    ◆ normal_quantile() [2/3]
    
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    float8 normal_quantile (float8 p, 
    float8 mean 
    )
    
+
    
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+
    
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    ◆ normal_quantile() [3/3]
    
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    float8 normal_quantile (float8 p)
    
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    ◆ pareto_cdf()
    
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    float8 pareto_cdf (float8 x, 
    float8 scale, 
    float8 shape 
    )
    
+
    
+
    Parameters
    
+  
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+    
+  
    xRandom variate \( x \) 
    scaleScale \( \beta > 0 \) 
    shapeShape \( \alpha > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Pareto-distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
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    ◆ pareto_pdf()
    
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    float8 pareto_pdf (float8 x, 
    float8 scale, 
    float8 shape 
    )
    
+
    
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    Parameters
    
+  
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+  
    xRandom variate \( x \) 
    scaleScale \( \beta > 0 \) 
    shapeShape \( \alpha > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a Pareto-distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
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    ◆ pareto_quantile()
    
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    float8 pareto_quantile (float8 p, 
    float8 scale, 
    float8 shape 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    scaleScale \( \beta > 0 \) 
    shapeShape \( \alpha > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Pareto-distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
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+
    ◆ poisson_cdf()
    
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+          
+          
+        
+      
    float8 poisson_cdf (float8 x, 
    float8 mean 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    meanAverage occurrence rate \( \lambda > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Poisson distributed random variable with mean \( \lambda \) 
    
+
+
    
+
    
+
+
    ◆ poisson_pmf()
    
+
+
    
+
    
+      
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+          
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+        
+      
    float8 poisson_pmf (int4 x, 
    float8 mean 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    meanAverage occurrence rate \( \lambda > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability mass function of a Poisson distributed random variable with mean \( \lambda \) 
    
+
+
    
+
    
+
+
    ◆ poisson_quantile()
    
+
+
    
+
    
+      
+        
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+        
+        
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+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 poisson_quantile (float8 p, 
    float8 mean 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    meanAverage occurrence rate \( \lambda > 0 \) 
    
+  
    
+
    
+
    Returns
    If \( p < 0.5 \) the maximum \( x \) such that \( p \geq \Pr[X \leq x] \). If \( p \geq 0.5 \) the minimum \( x \) such that \( p \leq \Pr[X \leq x] \). Here, \( X \) is a Poisson distributed random variable with mean \( \lambda \) 
    
+
+
    
+
    
+
+
    ◆ rayleigh_cdf()
    
+
+
    
+
    
+      
+        
+          
+          
+          
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+        
+        
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+          
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+        
+        
+          
+          
+          
+        
+      
    float8 rayleigh_cdf (float8 x, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    scaleScale \( \sigma > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Rayleigh-distributed random variable with parameter \( \sigma \) 
    
+
+
    
+
    
+
+
    ◆ rayleigh_pdf()
    
+
+
    
+
    
+      
+        
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+        
+          
+          
+          
+        
+      
    float8 rayleigh_pdf (float8 x, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    scaleScale \( \sigma > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a Rayleigh-distributed random variable with parameter \( \sigma \) 
    
+
+
    
+
    
+
+
    ◆ rayleigh_quantile()
    
+
+
    
+
    
+      
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+        
+      
    float8 rayleigh_quantile (float8 p, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    scaleScale \( \sigma > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Rayleigh-distributed random variable with parameter \( \sigma \) 
    
+
+
    
+
    
+
+
    ◆ students_t_cdf()
    
+
+
    
+
    
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+        
+      
    float8 students_t_cdf (float8 x, 
    float8 df 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    dfDegrees of freedom \( \nu > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a Student's t-distributed random variable with \( \nu \) degrees of freedom 
    
+
+
    
+
    
+
+
    ◆ students_t_pdf()
    
+
+
    
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+      
    float8 students_t_pdf (float8 x, 
    float8 df 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    xRandom variate \( x \) 
    dfDegrees of freedom \( \nu > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a Stundent's t-distributed random variable with \( \nu \) degrees of freedom 
    
+
+
    
+
    
+
+
    ◆ students_t_quantile()
    
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+
    
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+      
    float8 students_t_quantile (float8 p, 
    float8 df 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    dfDegrees of freedom \( \nu > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a Student's t-distributed random variable with \( \nu \) degrees of freedom 
    
+
+
    
+
    
+
+
    ◆ triangular_cdf()
    
+
+
    
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+      
    float8 triangular_cdf (float8 x, 
    float8 lower, 
    float8 mode, 
    float8 upper 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    xRandom variate \( x \) 
    lowerLower bound \( a \) 
    modeMode \( c \geq a \) 
    upperUpper bound \( b \geq c \), where \( b > a \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a triangular distributed random variable with parameters \( a, b, c \) 
    
+
+
    
+
    
+
+
    ◆ triangular_pdf()
    
+
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+        
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    float8 triangular_pdf (float8 x, 
    float8 lower, 
    float8 mode, 
    float8 upper 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    xRandom variate \( x \) 
    lowerLower bound \( a \) 
    modeMode \( c \geq a \) 
    upperUpper bound \( b \geq c \), where \( b > a \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a triangular distributed random variable with parameters \( a, b, c \) 
    
+
+
    
+
    
+
+
    ◆ triangular_quantile()
    
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+      
    float8 triangular_quantile (float8 p, 
    float8 lower, 
    float8 mode, 
    float8 upper 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    lowerLower bound \( a \) 
    modeMode \( c \geq a \) 
    upperUpper bound \( b \geq c \), where \( b > a \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a trianbular distributed random variable with parameters \( a, b, c \) 
    
+
+
    
+
    
+
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    ◆ uniform_cdf()
    
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+      
    float8 uniform_cdf (float8 x, 
    float8 lower, 
    float8 upper 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    lowerLower bound \( a \) 
    upperUpper bound \( b \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a uniform distributed random variable with support \( [a, b] \) 
    
+
+
    
+
    
+
+
    ◆ uniform_pdf()
    
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    float8 uniform_pdf (float8 x, 
    float8 lower, 
    float8 upper 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    lowerLower bound \( a \) 
    upperUpper bound \( b \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a uniform distributed random variable with support \( [a, b] \) 
    
+
+
    
+
    
+
+
    ◆ uniform_quantile()
    
+
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+      
    float8 uniform_quantile (float8 p, 
    float8 lower, 
    float8 upper 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    lowerLower bound \( a \) 
    upperUpper bound \( b \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a uniform distributed random variable with support \( [a, b] \) 
    
+
+
    
+
    
+
+
    ◆ weibull_cdf()
    
+
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+
    
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+          
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+        
+      
    float8 weibull_cdf (float8 x, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    shapeShape \( \alpha > 0 \) 
    scaleScale \( \beta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( \Pr[X \leq x] \) where \( X \) is a weibull distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
+
    ◆ weibull_pdf()
    
+
+
    
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+      
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+        
+      
    float8 weibull_pdf (float8 x, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    xRandom variate \( x \) 
    shapeShape \( \alpha > 0 \) 
    scaleScale \( \beta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( f(x) \) where \( f \) is the probability density function of a weibull distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
+
+
    ◆ weibull_quantile()
    
+
+
    
+
    
+      
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+          
+          
+        
+      
    float8 weibull_quantile (float8 p, 
    float8 shape, 
    float8 scale 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    pProbability \( p \in [0,1] \) 
    shapeShape \( \alpha > 0 \) 
    scaleScale \( \beta > 0 \) 
    
+  
    
+
    
+
    Returns
    \( x \) such that \( p = \Pr[X \leq x] \) where \( X \) is a weibull distributed random variable with shape and scale parameters \( \alpha \) and \( \beta \), respectively 
    
+
+
    
+
    
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diff --git a/docs/docs/v2.1.0/random__forest_8sql__in.html b/docs/docs/v2.1.0/random__forest_8sql__in.html
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+   2.1.0
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    User Documentation for Apache MADlib
    
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+Functions |
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    random_forest.sql_in File Reference
      
    
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+Functions
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth, integer min_split, integer min_bucket, integer num_splits, text null_handling_params, boolean verbose, float8 sample_ratio)
     Training of Random Forest.  More...
     
    float8 _get_bin_value_by_index (bytea8 con_splits, integer feature_index, integer bin_index)
     
    integer _get_bin_index_by_value (float8 bin_value, bytea8 con_splits, integer feature_index)
     
    integer [] _get_bin_indices_by_values (float8[] bin_values, bytea8 con_splits)
     
    void forest_predict (text model, text source, text output, text pred_type)
     Use random forest model to make predictions.  More...
     
    void forest_predict (text model, text source, text output)
     
    text forest_predict (text message)
     
    text forest_predict ()
     
    CREATE OR REPLACE FUNCTION madlib get_var_importance (model_table TEXT, output_table TEXT) RETURNS VOID AS $$ PythonFunction(recursive_partitioning
     
    CREATE OR REPLACE FUNCTION madlib get_var_importance (message TEXT) RETURNS TEXT AS $$ PythonFunction(recursive_partitioning
     
    CREATE OR REPLACE FUNCTION madlib get_var_importance () RETURNS TEXT AS $$ BEGIN RETURN madlib.get_var_importance('')
     
    varchar get_tree (text model_table, integer gid, integer sample_id, boolean dot_format, boolean verbose)
     Display a single tree from random forest in dot or text format.  More...
     
    varchar get_tree (text model_table, integer gid, integer sample_id, boolean dot_format)
     
    varchar get_tree (text model_table, integer gid, integer sample_id)
     
    varchar get_tree ()
     
    varchar get_tree_surr (text model_table, integer gid, integer sample_id)
     Display the surrogate splits for each internal node in a single tree from random forest.  More...
     
    varchar get_tree_surr ()
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth, integer min_split, integer min_bucket, integer num_splits, text null_handling_params, boolean verbose)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth, integer min_split, integer min_bucket, integer num_splits, text null_handling_params)
     
    text forest_train (text message)
     
    text forest_train ()
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth, integer min_split, integer min_bucket, integer num_splits)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth, integer min_split, integer min_bucket)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth, integer min_split)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations, integer max_tree_depth)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance, integer num_permutations)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features, boolean importance)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees, integer num_random_features)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols, integer num_trees)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude, text grouping_cols)
     
    void forest_train (text training_table_name, text output_table_name, text id_col_name, text dependent_variable, text list_of_features, text list_of_features_to_exclude)
     
    float8 [][] _convert_to_random_forest_format (bytea8 model)
     
    float8 [][] _rf_cat_imp_score (bytea8 tree, integer[] cat_features, float8[] con_features, integer[] cat_n_levels, integer num_permutations, float8 y, boolean is_classification, float8[][] cat_feature_distributions)
     
    float8 [] _rf_con_imp_score (bytea8 tree, integer[] cat_features, float8[] con_features, bytea8 con_splits, integer num_permutations, float8 y, boolean is_classification, float8[][] con_index_distrbutions)
     
    float8 [] normalize_sum_array (float8[] input_array, float8 target_sum)
     
    
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+Variables
    CREATE OR REPLACE FUNCTION madlib random_forest
     
    CREATE OR REPLACE FUNCTION madlib get_var_importance LANGUAGE plpython3u VOLATILE
     
    CREATE OR REPLACE FUNCTION madlib _importance_help_message LANGUAGE plpython3u IMMUTABLE
     
     END
     
    
+
    Function Documentation
    
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    ◆ _convert_to_random_forest_format()
    
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    float8 [][] _convert_to_random_forest_format (bytea8 model)
    
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    ◆ _get_bin_index_by_value()
    
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    integer _get_bin_index_by_value (float8 bin_value, 
    bytea8 con_splits, 
    integer feature_index 
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    ◆ _get_bin_indices_by_values()
    
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    integer [] _get_bin_indices_by_values (float8 [] bin_values, 
    bytea8 con_splits 
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    ◆ _get_bin_value_by_index()
    
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    float8 _get_bin_value_by_index (bytea8 con_splits, 
    integer feature_index, 
    integer bin_index 
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    ◆ _rf_cat_imp_score()
    
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    float8 [][] _rf_cat_imp_score (bytea8 tree, 
    integer [] cat_features, 
    float8 [] con_features, 
    integer [] cat_n_levels, 
    integer num_permutations, 
    float8 y, 
    boolean is_classification, 
    float8 cat_feature_distributions[][] 
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    ◆ _rf_con_imp_score()
    
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    float8 [] _rf_con_imp_score (bytea8 tree, 
    integer [] cat_features, 
    float8 [] con_features, 
    bytea8 con_splits, 
    integer num_permutations, 
    float8 y, 
    boolean is_classification, 
    float8 con_index_distrbutions[][] 
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    ◆ forest_predict() [1/4]
    
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    void forest_predict (text model, 
    text source, 
    text output, 
    text pred_type 
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    modelName of the table containing the random forest model 
    sourceName of table containing prediction data 
    outputName of table to output prediction results 
    pred_typeOPTIONAL (Default = 'response'). For regression trees, 'response', implies output is the predicted value. For classification models, this can be 'response', giving the classification prediction as output, or ‘prob’, giving the class probabilities as output (for two classes, only a single probability value is output that corresponds to the first class when the two classes are sorted by name; in case of more than two classes, an array of class probabilities (a probability of each class) is output).
    
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    See Random Forest for more details. 
    
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    ◆ forest_predict() [2/4]
    
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    void forest_predict (text model, 
    text source, 
    text output 
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    ◆ forest_predict() [3/4]
    
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    text forest_predict (text message)
    
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    ◆ forest_predict() [4/4]
    
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    text forest_predict ()
    
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    ◆ forest_train() [1/15]
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth, 
    integer min_split, 
    integer min_bucket, 
    integer num_splits, 
    text null_handling_params, 
    boolean verbose, 
    float8 sample_ratio 
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    training_table_nameName of the table containing data. 
    output_table_nameName of the table to output the model. 
    id_col_nameName of column containing the id information in training data. 
    dependent_variableName of the column that contains the output for training. Boolean, integer and text are considered classification outputs, while float values are considered regression outputs. 
    list_of_featuresList of column names (comma-separated string) to use as predictors. Can also be a ‘*’ implying all columns are to be used as predictors (except the ones included in the next argument). Boolean, integer, and text columns are considered categorical columns. 
    list_of_features_to_excludeList of column names (comma-separated string) to exlude from the predictors list. 
    grouping_colsOPTIONAL. List of column names (comma-separated string) to group the data by. This will lead to creating multiple Random Forests, one for each group. 
    num_treesOPTIONAL (Default = 100). Maximum number of trees to grow in the Random forest model. 
    num_random_featuresOPTIONAL (Default = sqrt(n) for classification, n/3 for regression) Number of features to randomly select at each split. 
    max_tree_depthOPTIONAL (Default = 7). Set the maximum depth of any node of the final tree, with the root node counted as depth 0. 
    min_splitOPTIONAL (Default = 20). Minimum number of observations that must exist in a node for a split to be attempted. 
    min_bucketOPTIONAL (Default = minsplit/3). Minimum number of observations in any terminal node. If only one of minbucket or minsplit is specified, minsplit is set to minbucket*3 or minbucket to minsplit/3, as appropriate. 
    num_splitsoptional (default = 20) number of bins to use during binning. Continuous-valued features are binned into discrete bins (per the quartile values) to compute split boundaries. This global parameter is used to compute the resolution of the bins. Higher number of bins will lead to higher processing time and more memory usage. 
    verboseoptional (default = false) prints status information on the splits performed and any other information useful for debugging. 
    importanceoptional (default = false) calculates variable importance of all features if True 
    num_permutationsoptional (default = 1) number of times to permute feature values while calculating variable importance
    
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    see Random Forest for more details. 
    
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    ◆ forest_train() [2/15]
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth, 
    integer min_split, 
    integer min_bucket, 
    integer num_splits, 
    text null_handling_params, 
    boolean verbose 
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    ◆ forest_train() [3/15]
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth, 
    integer min_split, 
    integer min_bucket, 
    integer num_splits, 
    text null_handling_params 
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    text forest_train (text message)
    
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    ◆ forest_train() [5/15]
    
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    text forest_train ()
    
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    ◆ forest_train() [6/15]
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth, 
    integer min_split, 
    integer min_bucket, 
    integer num_splits 
    )
    
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    ◆ forest_train() [7/15]
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth, 
    integer min_split, 
    integer min_bucket 
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth, 
    integer min_split 
    )
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations, 
    integer max_tree_depth 
    )
    
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance, 
    integer num_permutations 
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    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features, 
    boolean importance 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ forest_train() [12/15]
    
+
+
    
+
    
+      
+        
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+          
+        
+        
+          
+          
+          
+        
+      
    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees, 
    integer num_random_features 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ forest_train() [13/15]
    
+
+
    
+
    
+      
+        
+          
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+        
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+          
+        
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+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols, 
    integer num_trees 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ forest_train() [14/15]
    
+
+
    
+
    
+      
+        
+          
+          
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+        
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude, 
    text grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ forest_train() [15/15]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void forest_train (text training_table_name, 
    text output_table_name, 
    text id_col_name, 
    text dependent_variable, 
    text list_of_features, 
    text list_of_features_to_exclude 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ get_tree() [1/4]
    
+
+
    
+
    
+      
+        
+          
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+        
+      
    varchar get_tree (text model_table, 
    integer gid, 
    integer sample_id, 
    boolean dot_format, 
    boolean verbose 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    forest_modelName of the table containing the random forest model 
    gidGroup id of the tree to display 
    sample_idSample id of the tree to display  TRUE if dot format, FALSE for text format  TRUE if the dot format output will contain additional information 
    
+  
    
+
    
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+
    
+
    
+
+
    ◆ get_tree() [2/4]
    
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+        
+      
    varchar get_tree (text model_table, 
    integer gid, 
    integer sample_id, 
    boolean dot_format 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ get_tree() [3/4]
    
+
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+        
+      
    varchar get_tree (text model_table, 
    integer gid, 
    integer sample_id 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ get_tree() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar get_tree ()
    
+
    
+
+
    
+
    
+
+
    ◆ get_tree_surr() [1/2]
    
+
+
    
+
    
+      
+        
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+        
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+          
+          
+        
+      
    varchar get_tree_surr (text model_table, 
    integer gid, 
    integer sample_id 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    forest_modelName of the table containing the random forest model 
    gidGroup id of the tree to display 
    sample_idSample id of the tree to display 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ get_tree_surr() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar get_tree_surr ()
    
+
    
+
+
    
+
    
+
+
    ◆ get_var_importance() [1/3]
    
+
+
    
+
    
+      
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+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    CREATE OR REPLACE FUNCTION madlib get_var_importance (model_table TEXT, 
    output_table TEXT 
    )
    
+
    
+
    Helper function to display variable importance scores (both oob and impurity importance scores for variables). 
    
+
+
    
+
    
+
+
    ◆ get_var_importance() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    CREATE OR REPLACE FUNCTION madlib get_var_importance (message TEXT)
    
+
    
+
+
    
+
    
+
+
    ◆ get_var_importance() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    CREATE OR REPLACE FUNCTION madlib get_var_importance ()
    
+
    
+
+
    
+
    
+
+
    ◆ normalize_sum_array()
    
+
+
    
+
    
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+        
+      
    float8 [] normalize_sum_array (float8 [] input_array, 
    float8 target_sum 
    )
    
+
    
+
+
    
+
    
+
    Variable Documentation
    
+
+
    ◆ END
    
+
+
    
+
    
+      
+        
+          
+        
+      
    END
    
+
    
+
+
    
+
    
+
+
    ◆ IMMUTABLE
    
+
+
    
+
    
+      
+        
+          
+        
+      
    LANGUAGE plpgsql IMMUTABLE
    
+
    
+
+
    
+
    
+
+
    ◆ random_forest
    
+
+
    
+
    
+      
+        
+          
+        
+      
    CREATE OR REPLACE FUNCTION madlib random_forest
    
+
    
+
+
    
+
    
+
+
    ◆ VOLATILE
    
+
+
    
+
    
+      
+        
+          
+        
+      
    CREATE OR REPLACE FUNCTION madlib get_var_importance LANGUAGE plpython3u VOLATILE
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/resize.js b/docs/docs/v2.1.0/resize.js
new file mode 100644
index 00000000..56e4a023
--- /dev/null
+++ b/docs/docs/v2.1.0/resize.js
@@ -0,0 +1,114 @@
+function initResizable()
+{
+  var cookie_namespace = 'doxygen';
+  var sidenav,navtree,content,header,collapsed,collapsedWidth=0,barWidth=6,desktop_vp=768,titleHeight;
+
+  function readCookie(cookie)
+  {
+    var myCookie = cookie_namespace+"_"+cookie+"=";
+    if (document.cookie) {
+      var index = document.cookie.indexOf(myCookie);
+      if (index != -1) {
+        var valStart = index + myCookie.length;
+        var valEnd = document.cookie.indexOf(";", valStart);
+        if (valEnd == -1) {
+          valEnd = document.cookie.length;
+        }
+        var val = document.cookie.substring(valStart, valEnd);
+        return val;
+      }
+    }
+    return 0;
+  }
+
+  function writeCookie(cookie, val, expiration)
+  {
+    if (val==undefined) return;
+    if (expiration == null) {
+      var date = new Date();
+      date.setTime(date.getTime()+(10*365*24*60*60*1000)); // default expiration is one week
+      expiration = date.toGMTString();
+    }
+    document.cookie = cookie_namespace + "_" + cookie + "=" + val + "; expires=" + expiration+"; path=/";
+  }
+
+  function resizeWidth()
+  {
+    var windowWidth = $(window).width() + "px";
+    var sidenavWidth = $(sidenav).outerWidth();
+    content.css({marginLeft:parseInt(sidenavWidth)+"px"});
+    writeCookie('width',sidenavWidth-barWidth, null);
+  }
+
+  function restoreWidth(navWidth)
+  {
+    var windowWidth = $(window).width() + "px";
+    content.css({marginLeft:parseInt(navWidth)+barWidth+"px"});
+    sidenav.css({width:navWidth + "px"});
+  }
+
+  function resizeHeight()
+  {
+    var headerHeight = header.outerHeight();
+    var footerHeight = footer.outerHeight();
+    var windowHeight = $(window).height() - headerHeight - footerHeight;
+    content.css({height:windowHeight + "px"});
+    navtree.css({height:windowHeight + "px"});
+    sidenav.css({height:windowHeight + "px"});
+    var width=$(window).width();
+    if (width!=collapsedWidth) {
+      if (width=desktop_vp) {
+        if (!collapsed) {
+          collapseExpand();
+        }
+      } else if (width>desktop_vp && collapsedWidth0) {
+      restoreWidth(0);
+      collapsed=true;
+    }
+    else {
+      var width = readCookie('width');
+      if (width>200 && width<$(window).width()) { restoreWidth(width); } else { restoreWidth(200); }
+      collapsed=false;
+    }
+  }
+
+  header  = $("#top");
+  sidenav = $("#side-nav");
+  content = $("#doc-content");
+  navtree = $("#nav-tree");
+  footer  = $("#nav-path");
+  $(".side-nav-resizable").resizable({resize: function(e, ui) { resizeWidth(); } });
+  $(sidenav).resizable({ minWidth: 0 });
+  $(window).resize(function() { resizeHeight(); });
+  var device = navigator.userAgent.toLowerCase();
+  var touch_device = device.match(/(iphone|ipod|ipad|android)/);
+  if (touch_device) { /* wider split bar for touch only devices */
+    $(sidenav).css({ paddingRight:'20px' });
+    $('.ui-resizable-e').css({ width:'20px' });
+    $('#nav-sync').css({ right:'34px' });
+    barWidth=20;
+  }
+  var width = readCookie('width');
+  if (width) { restoreWidth(width); } else { resizeWidth(); }
+  resizeHeight();
+  var url = location.href;
+  var i=url.indexOf("#");
+  if (i>=0) window.location.hash=url.substr(i);
+  var _preventDefault = function(evt) { evt.preventDefault(); };
+  $("#splitbar").bind("dragstart", _preventDefault).bind("selectstart", _preventDefault);
+  $(".ui-resizable-handle").dblclick(collapseExpand);
+  $(window).load(resizeHeight);
+}
+
+
diff --git a/docs/docs/v2.1.0/robust_8sql__in.html b/docs/docs/v2.1.0/robust_8sql__in.html
new file mode 100644
index 00000000..30bbc422
--- /dev/null
+++ b/docs/docs/v2.1.0/robust_8sql__in.html
@@ -0,0 +1,1759 @@
+
+
+
+
+
+
+
+
+MADlib: robust.sql_in File Reference
+
+
+
+
+
+
+
+
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+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
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+  
    
+
    
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+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    robust.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for robust variance linear and logistic regression.  
+More...
    
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+
    
+Functions
    bytea8 robust_linregr_transition (bytea8 state, float8 y, float8[] x, float8[] coef)
     
    bytea8 robust_linregr_merge_states (bytea8 state1, bytea8 state2)
     
    robust_linregr_result robust_linregr_final (bytea8 state)
     
    aggregate bytea8 robust_linregr (float8 dependentVariable, float8[] independentVariables, float8[] coef)
     
    varchar robust_variance_linregr (varchar message)
     
    varchar robust_variance_linregr ()
     
    void robust_variance_linregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, boolean verbose_mode)
     
    void robust_variance_linregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols)
     
    void robust_variance_linregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname)
     
    float8 [] robust_logregr_step_transition (float8[] state, boolean y, float8[] x, float8[] coef)
     
    float8 [] robust_logregr_step_merge_states (float8[] state1, float8[] state2)
     
    robust_logregr_result robust_logregr_step_final (float8[] state)
     
    aggregate robust_logregr_result robust_logregr (boolean dependentVariable, float8[] independentVariables, float8[] coef)
     
    varchar robust_variance_logregr (varchar message)
     
    varchar robust_variance_logregr ()
     
    void robust_variance_logregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, varchar grouping_cols, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose_mode)
     The robust logistic regression function.  More...
     
    void robust_variance_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer max_iter, varchar optimizer, float8 tolerance)
     
    void robust_variance_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer max_iter, varchar optimizer)
     
    void robust_variance_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols, integer max_iter)
     
    void robust_variance_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable, varchar grouping_cols)
     
    void robust_variance_logregr (varchar source_table, varchar out_table, varchar dependent_variable, varchar independent_variable)
     
    float8 [] mlogregr_robust_step_transition (float8[] state, integer y, integer numcategories, integer ref_category, float8[] x, float8[] coef)
     
    float8 [] mlogregr_robust_step_merge_states (float8[] state1, float8[] state2)
     
    robust_mlogregr_result mlogregr_robust_step_final (float8[] state)
     
    aggregate robust_mlogregr_result robust_mlogregr (integer dependentVariable, integer numCategories, integer ref_category, float8[] independentVariables, float8[] coef)
     
    varchar robust_variance_mlogregr (varchar message)
     
    varchar robust_variance_mlogregr ()
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, varchar optimizer_params, boolean verbose_mode)
     Compute robust regression diagnostic statistics for multinomial logistic regression.  More...
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, varchar optimizer_params)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer max_iter, varchar optimizer, float8 tolerance, boolean verbose_mode)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer max_iter, varchar optimizer, float8 tolerance)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer max_iter, varchar optimizer)
     
    void robust_variance_mlogregr (varchar source_table, varchar out_table, varchar dependent_varname, varchar independent_varname, integer ref_category, varchar grouping_cols, integer max_iter)
     
    
+
    Detailed Description
    
+
    Date
    2012
    
+
    See also
    For a brief introduction to robust variance, see Robust Variance 
    
+
    Function Documentation
    
+
+
    ◆ mlogregr_robust_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    robust_mlogregr_result mlogregr_robust_step_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_robust_step_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] mlogregr_robust_step_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mlogregr_robust_step_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+          
+          
+        
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] mlogregr_robust_step_transition (float8 [] state, 
    integer y, 
    integer numcategories, 
    integer ref_category, 
    float8 [] x, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_linregr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate bytea8 robust_linregr (float8 dependentVariable, 
    float8 [] independentVariables, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_linregr_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    robust_linregr_result robust_linregr_final (bytea8 state)
    
+
    
+
+
    
+
    
+
+
    ◆ robust_linregr_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 robust_linregr_merge_states (bytea8 state1, 
    bytea8 state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_linregr_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
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+        
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+          
+          
+        
+      
    bytea8 robust_linregr_transition (bytea8 state, 
    float8 y, 
    float8 [] x, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_logregr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate robust_logregr_result robust_logregr (boolean dependentVariable, 
    float8 [] independentVariables, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_logregr_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    robust_logregr_result robust_logregr_step_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ robust_logregr_step_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+          
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+        
+        
+          
+          
+          
+        
+      
    float8 [] robust_logregr_step_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_logregr_step_transition()
    
+
+
    
+
    
+      
+        
+          
+          
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+        
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+          
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+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] robust_logregr_step_transition (float8 [] state, 
    boolean y, 
    float8 [] x, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_mlogregr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate robust_mlogregr_result robust_mlogregr (integer dependentVariable, 
    integer numCategories, 
    integer ref_category, 
    float8 [] independentVariables, 
    float8 [] coef 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_linregr() [1/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar robust_variance_linregr (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_linregr() [2/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar robust_variance_linregr ()
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_linregr() [3/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_linregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols, 
    boolean verbose_mode 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_linregr() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_linregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_linregr() [5/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_linregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [1/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar robust_variance_logregr (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [2/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar robust_variance_logregr ()
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [3/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    varchar grouping_cols, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance, 
    boolean verbose_mode 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    source_tableString identifying the input table 
    out_tableString identifying the output table to be created 
    dependent_varnameColumn containing the dependent variable 
    independent_varnameColumn containing the array of independent variables 
    grouping_colsColumns to group by. 
    max_iterInteger identifying the maximum iterations used by the logistic regression solver. Default is 20. 
    optimizerString identifying the optimizer used in the logistic regression. See the documentation in the logistic regression for the available options. Default is irls. 
    toleranceFloat identifying the tolerance of the logistic regression optimizer. Default is 1e-4. 
    verbose_modeBoolean specifying if the regression fit should print any warning messages. Default is false. 
    
+  
    
+
    
+
    To include an intercept in the model, set one coordinate in the independent_varname array to 1.
    
+
    Returns
    A composite value:
      
+
    • std_err FLOAT8[] - Array of huber-white standard errors, \( \mathit{se}(c_1), \dots, \mathit{se}(c_k) \)
      • 
+
    • t_stats FLOAT8[] - Array of t-statistics, \( \boldsymbol t \)
      • 
+
    • p_values FLOAT8[] - Array of p-values, \( \boldsymbol p \)
      • 
+
    
+
    
+
    Usage
    For function summary information. Run sql> select robust_variance_logregr('help'); OR sql> select robust_variance_logregr(); OR sql> select robust_variance_logregr('?'); For function usage information. Run sql> select robust_variance_logregr('usage');
      
+
    • Compute the coefficients, and the get the robust diagnostic statistics: 
      +   select robust_variance_logregr(source_table, out_table, regression_type, dependentVariable, independentVariables, NULL );
+  
      • 
+
    • If the coefficients are already known, they can be provided directly 
      select robust_variance_logregr(source_table, out_table, regression_type, dependentVariable, independentVariables, coef );
+
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [4/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [5/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer max_iter, 
    varchar optimizer 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [6/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols, 
    integer max_iter 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [7/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_logregr() [8/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_logregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_variable, 
    varchar independent_variable 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [1/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar robust_variance_mlogregr (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [2/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar robust_variance_mlogregr ()
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [3/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    varchar optimizer_params, 
    boolean verbose_mode 
    )
    
+
    
+
    – NOTICE ---------------------------------------------------------—— – All functions calling other modeling functions should be in the format: – accept a model table created by the underlying modeling function – and extract all parameters from the model table and summary table CREATE OR REPLACE FUNCTION madlib.robust_variance_mlogregr( model_table VARCHAR – name of the mlogregr model table , out_table VARCHAR – name of output table ) RETURNS VOID AS $$ PythonFunction(regress, robust_mlogistic, robust_variance_mlogregr_new) $$ LANGUAGE plpython3u; – END OF NOTICE ---------------------------------------------------------—— 
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    source_tablename of input table, VARCHAR 
    out_tablename of output table, VARCHAR 
    dependent_varnamedependent variable, VARCHAR 
    independent_varnameindependent variables, VARCHAR 
    ref_categoryInteger specifying the reference category. Default is 0. 
    grouping_colsgrouping variables, VARCHAR. Default is NULL. Currently a placeholder. 
    max_iterInteger identifying the maximum iterations used by the logistic regression solver. Default is 20. 
    optimizerString identifying the optimizer used in the multinomial logistic regression. See the documentation in the multinomial logistic regression for the available options. Default is 'irls'. 
    toleranceFloat identifying the tolerance of the multinomial logistic regression optimizer. Default is 1e-4. 
    verbose_modeBoolean specifying if the multinomial logistic regression solver should print any warnings. Currently a placeholder.
    
+  
    
+
    
+
    To include an intercept in the model, set one coordinate in the independentVariables array to 1.
    
+
    Usage
    +SELECT  madlib.robust_variance_mlogregr(
+    'source_table',        -- name of input table, VARCHAR
+    'out_table',           -- name of output table, VARCHAR
+    'dependent_varname',   -- dependent variable, VARCHAR
+    'independent_varname', -- independent variables, VARCHAR
+    ref_category,        -- [OPTIONAL] Integer specifying the reference category. Default is 0.
+    'grouping_cols',        -- [OPTIONAL] grouping variables, VARCHAR. Default is NULL.
+    max_iter,           -- [OPTIONAL] Integer identifying the maximum iterations used by the logistic regression solver.  Default is 20.
+    'optimizer',            -- [OPTIONAL] String identifying the optimizer used in the multinomial logistic regression.  See the documentation in the multinomial logistic regression for the available options.  Default is irls.
+ tolerance,         -- [OPTIONAL] Float identifying the tolerance of the multinomial logistic regression optimizer. Default is 1e-4.
+ verbose_mode        -- [OPTIONAL] Boolean specifying if the regression fit should print any warning messages.  Default is false.
+);
+
    
+
    Returns
    A composite value:
      
+
    • ref_category INTEGER - The reference category
      • 
+
    • coef FLOAT8[]  - The coefficients for the regression
      • 
+
    • std_err FLOAT8[] - Array of huber-white standard errors,
      • 
+
    • z_stats FLOAT8[] - Array of Wald z-statistics,
      • 
+
    • p_values FLOAT8[] - Array of p-values, 
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [4/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    varchar optimizer_params 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [5/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [6/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [7/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [8/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance, 
    boolean verbose_mode 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [9/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer max_iter, 
    varchar optimizer, 
    float8 tolerance 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [10/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer max_iter, 
    varchar optimizer 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_mlogregr() [11/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_mlogregr (varchar source_table, 
    varchar out_table, 
    varchar dependent_varname, 
    varchar independent_varname, 
    integer ref_category, 
    varchar grouping_cols, 
    integer max_iter 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/robust__variance__coxph_8sql__in.html b/docs/docs/v2.1.0/robust__variance__coxph_8sql__in.html
new file mode 100644
index 00000000..1b90f73d
--- /dev/null
+++ b/docs/docs/v2.1.0/robust__variance__coxph_8sql__in.html
@@ -0,0 +1,494 @@
+
+
+
+
+
+
+
+
+MADlib: robust_variance_coxph.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    robust_variance_coxph.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for robust cox proportional hazards regression.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    varchar robust_variance_coxph ()
     
    varchar robust_variance_coxph (varchar message)
     
    void robust_variance_coxph (varchar model_table, varchar output_table)
     
    float8 [] rb_coxph_step_transition (float8[], float8[], float8, boolean, float8[], float8[], float8[], float8)
     
    __rb_coxph_result rb_coxph_step_final (float8[])
     
    float8 [] coxph_h_s_transition (float8[], float8[], float8[])
     
    float8 [] coxph_h_s_merge (float8[] left_state, float8[] right_state)
     
    __rb_coxph_hs_result coxph_h_s_final (float8[])
     
    aggregate float8 [] coxph_h_s (float8[], float8[])
     
    float8 [] rb_coxph_strata_step_final (float8[])
     
    float8 [] rb_sum_strata_transition (float8[] in_state1, float8[] in_state2)
     
    __rb_coxph_result rb_sum_strata_final (float8[] in_state)
     
    aggregate float8 [] rb_sum_strata (float8[])
     
    
+
    Detailed Description
    
+
    Date
    Oct 2013
    
+
    See also
    For a brief introduction to robust cox regression, see the module description grp_robust_cox_prop_hazards 
    
+
    Function Documentation
    
+
+
    ◆ coxph_h_s()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] coxph_h_s (float8 [], 
    float8 [] 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ coxph_h_s_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    __rb_coxph_hs_result coxph_h_s_final (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ coxph_h_s_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] coxph_h_s_merge (float8 [] left_state, 
    float8 [] right_state 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ coxph_h_s_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] coxph_h_s_transition (float8 [], 
    float8 [], 
    float8 [] 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ rb_coxph_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    __rb_coxph_result rb_coxph_step_final (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ rb_coxph_step_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] rb_coxph_step_transition (float8 [], 
    float8 [], 
    float8 , 
    boolean , 
    float8 [], 
    float8 [], 
    float8 [], 
    float8  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ rb_coxph_strata_step_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] rb_coxph_strata_step_final (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ rb_sum_strata()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate float8 [] rb_sum_strata (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ rb_sum_strata_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    __rb_coxph_result rb_sum_strata_final (float8 [] in_state)
    
+
    
+
+
    
+
    
+
+
    ◆ rb_sum_strata_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] rb_sum_strata_transition (float8 [] in_state1, 
    float8 [] in_state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_coxph() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar robust_variance_coxph ()
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_coxph() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar robust_variance_coxph (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ robust_variance_coxph() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void robust_variance_coxph (varchar model_table, 
    varchar output_table 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/sample_8sql__in.html b/docs/docs/v2.1.0/sample_8sql__in.html
new file mode 100644
index 00000000..f76af2dc
--- /dev/null
+++ b/docs/docs/v2.1.0/sample_8sql__in.html
@@ -0,0 +1,433 @@
+
+
+
+
+
+
+
+
+MADlib: sample.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    sample.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for random sampling.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    bytea8 weighted_sample_transition_int64 (bytea8 state, bigint value, float8 weight)
     
    bytea8 weighted_sample_merge_int64 (bytea8 state_left, bytea8 state_right)
     
    bigint weighted_sample_final_int64 (bytea8 state)
     
    aggregate bytea8 weighted_sample (bigint value, float8 weight)
     Sample a single row according to weights.  More...
     
    bytea8 weighted_sample_transition_vector (bytea8 state, float8[] value, float8 weight)
     
    bytea8 weighted_sample_merge_vector (bytea8 state_left, bytea8 state_right)
     
    float8 [] weighted_sample_final_vector (bytea8 state)
     
    aggregate bytea8 weighted_sample (float8[] value, float8 weight)
     
    integer poisson_random (float8 mean)
     
    float8 gamma_random (float8 alpha)
     
    integer index_weighted_sample (float8[])
     
    
+
    Detailed Description
    
+
    See also
    For an overview of random-sampling functions, see the module description Random Sampling. 
    
+
    Function Documentation
    
+
+
    ◆ gamma_random()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 gamma_random (float8 alpha)
    
+
    
+
+
    
+
    
+
+
    ◆ index_weighted_sample()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    integer index_weighted_sample (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ poisson_random()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    integer poisson_random (float8 mean)
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate bytea8 weighted_sample (bigint value, 
    float8 weight 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    valueValue of row. Uniqueness is not enforced. If a value occurs multiple times, the probability of sampling this value is proportional to the sum of its weights. 
    weightWeight for row. A negative value here is treated has zero weight. 
    
+  
    
+
    
+
    Returns
    identifier of the selected row. The probability of sampling any particular row (value, weight) is weight/SUM(weight). 
    
+
+
    
+
    
+
+
    ◆ weighted_sample() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate bytea8 weighted_sample (float8 [] value, 
    float8 weight 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample_final_int64()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bigint weighted_sample_final_int64 (bytea8 state)
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample_final_vector()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] weighted_sample_final_vector (bytea8 state)
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample_merge_int64()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 weighted_sample_merge_int64 (bytea8 state_left, 
    bytea8 state_right 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample_merge_vector()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 weighted_sample_merge_vector (bytea8 state_left, 
    bytea8 state_right 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample_transition_int64()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 weighted_sample_transition_int64 (bytea8 state, 
    bigint value, 
    float8 weight 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weighted_sample_transition_vector()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bytea8 weighted_sample_transition_vector (bytea8 state, 
    float8 [] value, 
    float8 weight 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/search/all_0.html b/docs/docs/v2.1.0/search/all_0.html
new file mode 100644
index 00000000..f25360b7
--- /dev/null
+++ b/docs/docs/v2.1.0/search/all_0.html
@@ -0,0 +1,26 @@
+
+
+
+
+
+
+
+
+
+
    
+
    Loading...
    
+
    
+
+
    Searching...
    
+
    No Matches
    
+
+
    
+
+
diff --git a/docs/docs/v2.1.0/search/all_0.js b/docs/docs/v2.1.0/search/all_0.js
new file mode 100644
index 00000000..4888931a
--- /dev/null
+++ b/docs/docs/v2.1.0/search/all_0.js
@@ -0,0 +1,330 @@
+var searchData=
+[
+  ['_5f_5farima_5fadjust',['__arima_adjust',['../arima_8sql__in.html#af6f5621d79045e8270e6785ed0d98ce3',1,'arima.sql_in']]],
+  ['_5f_5farima_5fdiff',['__arima_diff',['../arima_8sql__in.html#ab686e554403a61a5404d83e692735ada',1,'arima.sql_in']]],
+  ['_5f_5farima_5flm',['__arima_lm',['../arima_8sql__in.html#aadd3c7627043810a7e650e80b7fafd52',1,'arima.sql_in']]],
+  ['_5f_5farima_5flm_5fdelta',['__arima_lm_delta',['../arima_8sql__in.html#a6a728067ea53fcb8fcbf66bbe296a783',1,'arima.sql_in']]],
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+    right:10px;
+    top:0px;
+    width:20px;
+    height:19px;
+    background:url('search_r.png') no-repeat;
+    background-position:left;
+}
+
+#MSearchClose {
+    display: none;
+    position: absolute;
+    top: 4px;
+    background : none;
+    border: none;
+    margin: 0px 4px 0px 0px;
+    padding: 0px 0px;
+    outline: none;
+}
+
+.left #MSearchClose {
+    left: 6px;
+}
+
+.right #MSearchClose {
+    right: 2px;
+}
+
+.MSearchBoxActive #MSearchField {
+    color: #000000;
+}
+
+/*---------------- Search filter selection */
+
+#MSearchSelectWindow {
+    display: none;
+    position: absolute;
+    left: 0; top: 0;
+    border: 1px solid #90A5CE;
+    background-color: #F9FAFC;
+    z-index: 10001;
+    padding-top: 4px;
+    padding-bottom: 4px;
+    -moz-border-radius: 4px;
+    -webkit-border-top-left-radius: 4px;
+    -webkit-border-top-right-radius: 4px;
+    -webkit-border-bottom-left-radius: 4px;
+    -webkit-border-bottom-right-radius: 4px;
+    -webkit-box-shadow: 5px 5px 5px rgba(0, 0, 0, 0.15);
+}
+
+.SelectItem {
+    font: 8pt Arial, Verdana, sans-serif;
+    padding-left:  2px;
+    padding-right: 12px;
+    border: 0px;
+}
+
+span.SelectionMark {
+    margin-right: 4px;
+    font-family: monospace;
+    outline-style: none;
+    text-decoration: none;
+}
+
+a.SelectItem {
+    display: block;
+    outline-style: none;
+    color: #000000; 
+    text-decoration: none;
+    padding-left:   6px;
+    padding-right: 12px;
+}
+
+a.SelectItem:focus,
+a.SelectItem:active {
+    color: #000000; 
+    outline-style: none;
+    text-decoration: none;
+}
+
+a.SelectItem:hover {
+    color: #FFFFFF;
+    background-color: #3D578C;
+    outline-style: none;
+    text-decoration: none;
+    cursor: pointer;
+    display: block;
+}
+
+/*---------------- Search results window */
+
+iframe#MSearchResults {
+    width: 60ex;
+    height: 15em;
+}
+
+#MSearchResultsWindow {
+    display: none;
+    position: absolute;
+    left: 0; top: 0;
+    border: 1px solid #000;
+    background-color: #EEF1F7;
+    z-index:10000;
+}
+
+/* ----------------------------------- */
+
+
+#SRIndex {
+    clear:both; 
+    padding-bottom: 15px;
+}
+
+.SREntry {
+    font-size: 10pt;
+    padding-left: 1ex;
+}
+
+.SRPage .SREntry {
+    font-size: 8pt;
+    padding: 1px 5px;
+}
+
+body.SRPage {
+    margin: 5px 2px;
+}
+
+.SRChildren {
+    padding-left: 3ex; padding-bottom: .5em 
+}
+
+.SRPage .SRChildren {
+    display: none;
+}
+
+.SRSymbol {
+    font-weight: bold; 
+    color: #425E97;
+    font-family: Arial, Verdana, sans-serif;
+    text-decoration: none;
+    outline: none;
+}
+
+a.SRScope {
+    display: block;
+    color: #425E97; 
+    font-family: Arial, Verdana, sans-serif;
+    text-decoration: none;
+    outline: none;
+}
+
+a.SRSymbol:focus, a.SRSymbol:active,
+a.SRScope:focus, a.SRScope:active {
+    text-decoration: underline;
+}
+
+span.SRScope {
+    padding-left: 4px;
+}
+
+.SRPage .SRStatus {
+    padding: 2px 5px;
+    font-size: 8pt;
+    font-style: italic;
+}
+
+.SRResult {
+    display: none;
+}
+
+DIV.searchresults {
+    margin-left: 10px;
+    margin-right: 10px;
+}
+
+/*---------------- External search page results */
+
+.searchresult {
+    background-color: #F0F3F8;
+}
+
+.pages b {
+   color: white;
+   padding: 5px 5px 3px 5px;
+   background-image: url("../tab_a.png");
+   background-repeat: repeat-x;
+   text-shadow: 0 1px 1px #000000;
+}
+
+.pages {
+    line-height: 17px;
+    margin-left: 4px;
+    text-decoration: none;
+}
+
+.hl {
+    font-weight: bold;
+}
+
+#searchresults {
+    margin-bottom: 20px;
+}
+
+.searchpages {
+    margin-top: 10px;
+}
+
diff --git a/docs/docs/v2.1.0/search/search.js b/docs/docs/v2.1.0/search/search.js
new file mode 100644
index 00000000..dedce3bf
--- /dev/null
+++ b/docs/docs/v2.1.0/search/search.js
@@ -0,0 +1,791 @@
+function convertToId(search)
+{
+  var result = '';
+  for (i=0;i do a search
+    {
+      this.Search();
+    }
+  }
+
+  this.OnSearchSelectKey = function(evt)
+  {
+    var e = (evt) ? evt : window.event; // for IE
+    if (e.keyCode==40 && this.searchIndex0) // Up
+    {
+      this.searchIndex--;
+      this.OnSelectItem(this.searchIndex);
+    }
+    else if (e.keyCode==13 || e.keyCode==27)
+    {
+      this.OnSelectItem(this.searchIndex);
+      this.CloseSelectionWindow();
+      this.DOMSearchField().focus();
+    }
+    return false;
+  }
+
+  // --------- Actions
+
+  // Closes the results window.
+  this.CloseResultsWindow = function()
+  {
+    this.DOMPopupSearchResultsWindow().style.display = 'none';
+    this.DOMSearchClose().style.display = 'none';
+    this.Activate(false);
+  }
+
+  this.CloseSelectionWindow = function()
+  {
+    this.DOMSearchSelectWindow().style.display = 'none';
+  }
+
+  // Performs a search.
+  this.Search = function()
+  {
+    this.keyTimeout = 0;
+
+    // strip leading whitespace
+    var searchValue = this.DOMSearchField().value.replace(/^ +/, "");
+
+    var code = searchValue.toLowerCase().charCodeAt(0);
+    var idxChar = searchValue.substr(0, 1).toLowerCase();
+    if ( 0xD800 <= code && code <= 0xDBFF && searchValue > 1) // surrogate pair
+    {
+      idxChar = searchValue.substr(0, 2);
+    }
+
+    var resultsPage;
+    var resultsPageWithSearch;
+    var hasResultsPage;
+
+    var idx = indexSectionsWithContent[this.searchIndex].indexOf(idxChar);
+    if (idx!=-1)
+    {
+       var hexCode=idx.toString(16);
+       resultsPage = this.resultsPath + '/' + indexSectionNames[this.searchIndex] + '_' + hexCode + '.html';
+       resultsPageWithSearch = resultsPage+'?'+escape(searchValue);
+       hasResultsPage = true;
+    }
+    else // nothing available for this search term
+    {
+       resultsPage = this.resultsPath + '/nomatches.html';
+       resultsPageWithSearch = resultsPage;
+       hasResultsPage = false;
+    }
+
+    window.frames.MSearchResults.location = resultsPageWithSearch;
+    var domPopupSearchResultsWindow = this.DOMPopupSearchResultsWindow();
+
+    if (domPopupSearchResultsWindow.style.display!='block')
+    {
+       var domSearchBox = this.DOMSearchBox();
+       this.DOMSearchClose().style.display = 'inline';
+       if (this.insideFrame)
+       {
+         var domPopupSearchResults = this.DOMPopupSearchResults();
+         domPopupSearchResultsWindow.style.position = 'relative';
+         domPopupSearchResultsWindow.style.display  = 'block';
+         var width = document.body.clientWidth - 8; // the -8 is for IE :-(
+         domPopupSearchResultsWindow.style.width    = width + 'px';
+         domPopupSearchResults.style.width          = width + 'px';
+       }
+       else
+       {
+         var domPopupSearchResults = this.DOMPopupSearchResults();
+         var left = getXPos(domSearchBox) + 150; // domSearchBox.offsetWidth;
+         var top  = getYPos(domSearchBox) + 20;  // domSearchBox.offsetHeight + 1;
+         domPopupSearchResultsWindow.style.display = 'block';
+         left -= domPopupSearchResults.offsetWidth;
+         domPopupSearchResultsWindow.style.top     = top  + 'px';
+         domPopupSearchResultsWindow.style.left    = left + 'px';
+       }
+    }
+
+    this.lastSearchValue = searchValue;
+    this.lastResultsPage = resultsPage;
+  }
+
+  // -------- Activation Functions
+
+  // Activates or deactivates the search panel, resetting things to
+  // their default values if necessary.
+  this.Activate = function(isActive)
+  {
+    if (isActive || // open it
+        this.DOMPopupSearchResultsWindow().style.display == 'block'
+       )
+    {
+      this.DOMSearchBox().className = 'MSearchBoxActive';
+
+      var searchField = this.DOMSearchField();
+
+      if (searchField.value == this.searchLabel) // clear "Search" term upon entry
+      {
+        searchField.value = '';
+        this.searchActive = true;
+      }
+    }
+    else if (!isActive) // directly remove the panel
+    {
+      this.DOMSearchBox().className = 'MSearchBoxInactive';
+      this.DOMSearchField().value   = this.searchLabel;
+      this.searchActive             = false;
+      this.lastSearchValue          = ''
+      this.lastResultsPage          = '';
+    }
+  }
+}
+
+// -----------------------------------------------------------------------
+
+// The class that handles everything on the search results page.
+function SearchResults(name)
+{
+    // The number of matches from the last run of .
+    this.lastMatchCount = 0;
+    this.lastKey = 0;
+    this.repeatOn = false;
+
+    // Toggles the visibility of the passed element ID.
+    this.FindChildElement = function(id)
+    {
+      var parentElement = document.getElementById(id);
+      var element = parentElement.firstChild;
+
+      while (element && element!=parentElement)
+      {
+        if (element.nodeName == 'DIV' && element.className == 'SRChildren')
+        {
+          return element;
+        }
+
+        if (element.nodeName == 'DIV' && element.hasChildNodes())
+        {
+           element = element.firstChild;
+        }
+        else if (element.nextSibling)
+        {
+           element = element.nextSibling;
+        }
+        else
+        {
+          do
+          {
+            element = element.parentNode;
+          }
+          while (element && element!=parentElement && !element.nextSibling);
+
+          if (element && element!=parentElement)
+          {
+            element = element.nextSibling;
+          }
+        }
+      }
+    }
+
+    this.Toggle = function(id)
+    {
+      var element = this.FindChildElement(id);
+      if (element)
+      {
+        if (element.style.display == 'block')
+        {
+          element.style.display = 'none';
+        }
+        else
+        {
+          element.style.display = 'block';
+        }
+      }
+    }
+
+    // Searches for the passed string.  If there is no parameter,
+    // it takes it from the URL query.
+    //
+    // Always returns true, since other documents may try to call it
+    // and that may or may not be possible.
+    this.Search = function(search)
+    {
+      if (!search) // get search word from URL
+      {
+        search = window.location.search;
+        search = search.substring(1);  // Remove the leading '?'
+        search = unescape(search);
+      }
+
+      search = search.replace(/^ +/, ""); // strip leading spaces
+      search = search.replace(/ +$/, ""); // strip trailing spaces
+      search = search.toLowerCase();
+      search = convertToId(search);
+
+      var resultRows = document.getElementsByTagName("div");
+      var matches = 0;
+
+      var i = 0;
+      while (i < resultRows.length)
+      {
+        var row = resultRows.item(i);
+        if (row.className == "SRResult")
+        {
+          var rowMatchName = row.id.toLowerCase();
+          rowMatchName = rowMatchName.replace(/^sr\d*_/, ''); // strip 'sr123_'
+
+          if (search.length<=rowMatchName.length &&
+             rowMatchName.substr(0, search.length)==search)
+          {
+            row.style.display = 'block';
+            matches++;
+          }
+          else
+          {
+            row.style.display = 'none';
+          }
+        }
+        i++;
+      }
+      document.getElementById("Searching").style.display='none';
+      if (matches == 0) // no results
+      {
+        document.getElementById("NoMatches").style.display='block';
+      }
+      else // at least one result
+      {
+        document.getElementById("NoMatches").style.display='none';
+      }
+      this.lastMatchCount = matches;
+      return true;
+    }
+
+    // return the first item with index index or higher that is visible
+    this.NavNext = function(index)
+    {
+      var focusItem;
+      while (1)
+      {
+        var focusName = 'Item'+index;
+        focusItem = document.getElementById(focusName);
+        if (focusItem && focusItem.parentNode.parentNode.style.display=='block')
+        {
+          break;
+        }
+        else if (!focusItem) // last element
+        {
+          break;
+        }
+        focusItem=null;
+        index++;
+      }
+      return focusItem;
+    }
+
+    this.NavPrev = function(index)
+    {
+      var focusItem;
+      while (1)
+      {
+        var focusName = 'Item'+index;
+        focusItem = document.getElementById(focusName);
+        if (focusItem && focusItem.parentNode.parentNode.style.display=='block')
+        {
+          break;
+        }
+        else if (!focusItem) // last element
+        {
+          break;
+        }
+        focusItem=null;
+        index--;
+      }
+      return focusItem;
+    }
+
+    this.ProcessKeys = function(e)
+    {
+      if (e.type == "keydown")
+      {
+        this.repeatOn = false;
+        this.lastKey = e.keyCode;
+      }
+      else if (e.type == "keypress")
+      {
+        if (!this.repeatOn)
+        {
+          if (this.lastKey) this.repeatOn = true;
+          return false; // ignore first keypress after keydown
+        }
+      }
+      else if (e.type == "keyup")
+      {
+        this.lastKey = 0;
+        this.repeatOn = false;
+      }
+      return this.lastKey!=0;
+    }
+
+    this.Nav = function(evt,itemIndex)
+    {
+      var e  = (evt) ? evt : window.event; // for IE
+      if (e.keyCode==13) return true;
+      if (!this.ProcessKeys(e)) return false;
+
+      if (this.lastKey==38) // Up
+      {
+        var newIndex = itemIndex-1;
+        var focusItem = this.NavPrev(newIndex);
+        if (focusItem)
+        {
+          var child = this.FindChildElement(focusItem.parentNode.parentNode.id);
+          if (child && child.style.display == 'block') // children visible
+          {
+            var n=0;
+            var tmpElem;
+            while (1) // search for last child
+            {
+              tmpElem = document.getElementById('Item'+newIndex+'_c'+n);
+              if (tmpElem)
+              {
+                focusItem = tmpElem;
+              }
+              else // found it!
+              {
+                break;
+              }
+              n++;
+            }
+          }
+        }
+        if (focusItem)
+        {
+          focusItem.focus();
+        }
+        else // return focus to search field
+        {
+           parent.document.getElementById("MSearchField").focus();
+        }
+      }
+      else if (this.lastKey==40) // Down
+      {
+        var newIndex = itemIndex+1;
+        var focusItem;
+        var item = document.getElementById('Item'+itemIndex);
+        var elem = this.FindChildElement(item.parentNode.parentNode.id);
+        if (elem && elem.style.display == 'block') // children visible
+        {
+          focusItem = document.getElementById('Item'+itemIndex+'_c0');
+        }
+        if (!focusItem) focusItem = this.NavNext(newIndex);
+        if (focusItem)  focusItem.focus();
+      }
+      else if (this.lastKey==39) // Right
+      {
+        var item = document.getElementById('Item'+itemIndex);
+        var elem = this.FindChildElement(item.parentNode.parentNode.id);
+        if (elem) elem.style.display = 'block';
+      }
+      else if (this.lastKey==37) // Left
+      {
+        var item = document.getElementById('Item'+itemIndex);
+        var elem = this.FindChildElement(item.parentNode.parentNode.id);
+        if (elem) elem.style.display = 'none';
+      }
+      else if (this.lastKey==27) // Escape
+      {
+        parent.searchBox.CloseResultsWindow();
+        parent.document.getElementById("MSearchField").focus();
+      }
+      else if (this.lastKey==13) // Enter
+      {
+        return true;
+      }
+      return false;
+    }
+
+    this.NavChild = function(evt,itemIndex,childIndex)
+    {
+      var e  = (evt) ? evt : window.event; // for IE
+      if (e.keyCode==13) return true;
+      if (!this.ProcessKeys(e)) return false;
+
+      if (this.lastKey==38) // Up
+      {
+        if (childIndex>0)
+        {
+          var newIndex = childIndex-1;
+          document.getElementById('Item'+itemIndex+'_c'+newIndex).focus();
+        }
+        else // already at first child, jump to parent
+        {
+          document.getElementById('Item'+itemIndex).focus();
+        }
+      }
+      else if (this.lastKey==40) // Down
+      {
+        var newIndex = childIndex+1;
+        var elem = document.getElementById('Item'+itemIndex+'_c'+newIndex);
+        if (!elem) // last child, jump to parent next parent
+        {
+          elem = this.NavNext(itemIndex+1);
+        }
+        if (elem)
+        {
+          elem.focus();
+        }
+      }
+      else if (this.lastKey==27) // Escape
+      {
+        parent.searchBox.CloseResultsWindow();
+        parent.document.getElementById("MSearchField").focus();
+      }
+      else if (this.lastKey==13) // Enter
+      {
+        return true;
+      }
+      return false;
+    }
+}
+
+function setKeyActions(elem,action)
+{
+  elem.setAttribute('onkeydown',action);
+  elem.setAttribute('onkeypress',action);
+  elem.setAttribute('onkeyup',action);
+}
+
+function setClassAttr(elem,attr)
+{
+  elem.setAttribute('class',attr);
+  elem.setAttribute('className',attr);
+}
+
+function createResults()
+{
+  var results = document.getElementById("SRResults");
+  for (var e=0; ek7RCwB~R6VQOP#AvB$vH7i{6H{96zot$7cZT<7246EF5Np6N}+$IbiG6W
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literal 0
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diff --git a/docs/docs/v2.1.0/search/search_r.png b/docs/docs/v2.1.0/search/search_r.png
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index 0000000000000000000000000000000000000000..97ee8b439687084201b79c6f776a41f495c6392a
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+
+
+
+
+
+
+
+
+
    
+
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+
    
+
+
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+
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+
+
    
+
+
diff --git a/docs/docs/v2.1.0/search/variables_0.js b/docs/docs/v2.1.0/search/variables_0.js
new file mode 100644
index 00000000..5c1c8e2d
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_0.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['end',['END',['../random__forest_8sql__in.html#a1de54bd922161dd5c6a353647f448fd6',1,'random_forest.sql_in']]]
+];
diff --git a/docs/docs/v2.1.0/search/variables_1.html b/docs/docs/v2.1.0/search/variables_1.html
new file mode 100644
index 00000000..84237b6e
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_1.html
@@ -0,0 +1,26 @@
+
+
+
+
+
+
+
+
+
+
    
+
    Loading...
    
+
    
+
+
    Searching...
    
+
    No Matches
    
+
+
    
+
+
diff --git a/docs/docs/v2.1.0/search/variables_1.js b/docs/docs/v2.1.0/search/variables_1.js
new file mode 100644
index 00000000..90b7e93e
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_1.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['immutable',['IMMUTABLE',['../random__forest_8sql__in.html#a8ee741e3812ad259d3ca4c9fa489dc7e',1,'random_forest.sql_in']]]
+];
diff --git a/docs/docs/v2.1.0/search/variables_2.html b/docs/docs/v2.1.0/search/variables_2.html
new file mode 100644
index 00000000..5c9de1aa
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_2.html
@@ -0,0 +1,26 @@
+
+
+
+
+
+
+
+
+
+
    
+
    Loading...
    
+
    
+
+
    Searching...
    
+
    No Matches
    
+
+
    
+
+
diff --git a/docs/docs/v2.1.0/search/variables_2.js b/docs/docs/v2.1.0/search/variables_2.js
new file mode 100644
index 00000000..61c54c81
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_2.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['random_5fforest',['random_forest',['../random__forest_8sql__in.html#a7b9a14c36355554372b1163f7b157b88',1,'random_forest.sql_in']]]
+];
diff --git a/docs/docs/v2.1.0/search/variables_3.html b/docs/docs/v2.1.0/search/variables_3.html
new file mode 100644
index 00000000..f95e34c6
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_3.html
@@ -0,0 +1,26 @@
+
+
+
+
+
+
+
+
+
+
    
+
    Loading...
    
+
    
+
+
    Searching...
    
+
    No Matches
    
+
+
    
+
+
diff --git a/docs/docs/v2.1.0/search/variables_3.js b/docs/docs/v2.1.0/search/variables_3.js
new file mode 100644
index 00000000..07018d34
--- /dev/null
+++ b/docs/docs/v2.1.0/search/variables_3.js
@@ -0,0 +1,4 @@
+var searchData=
+[
+  ['volatile',['VOLATILE',['../random__forest_8sql__in.html#ada54f78269779a528d34057b0280b0ca',1,'random_forest.sql_in']]]
+];
diff --git a/docs/docs/v2.1.0/sessionize_8sql__in.html b/docs/docs/v2.1.0/sessionize_8sql__in.html
new file mode 100644
index 00000000..0cd6b25c
--- /dev/null
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@@ -0,0 +1,336 @@
+
+
+
+
+
+
+
+
+MADlib: sessionize.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    sessionize.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for sessionization functions.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    void sessionize (varchar source_table, varchar output_table, varchar partition_expr, varchar time_stamp, interval max_time, varchar output_cols, boolean create_view)
     
    void sessionize (varchar source_table, varchar output_table, varchar partition_expr, varchar time_stamp, interval max_time, varchar output_cols)
     
    void sessionize (varchar source_table, varchar output_table, varchar partition_expr, varchar time_stamp, interval max_time)
     
    text sessionize (text message)
     
    text sessionize ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    May 2016 
    
+
    Function Documentation
    
+
+
    ◆ sessionize() [1/5]
    
+
+
    
+
    
+      
+        
+          
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+          
+        
+        
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+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void sessionize (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar time_stamp, 
    interval max_time, 
    varchar output_cols, 
    boolean create_view 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sessionize() [2/5]
    
+
+
    
+
    
+      
+        
+          
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+          
+        
+        
+          
+          
+          
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+        
+        
+          
+          
+          
+        
+      
    void sessionize (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar time_stamp, 
    interval max_time, 
    varchar output_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sessionize() [3/5]
    
+
+
    
+
    
+      
+        
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+        
+      
    void sessionize (varchar source_table, 
    varchar output_table, 
    varchar partition_expr, 
    varchar time_stamp, 
    interval max_time 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sessionize() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text sessionize (text message)
    
+
    
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+
    
+
    
+
+
    ◆ sessionize() [5/5]
    
+
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+      
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    text sessionize ()
    
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diff --git a/docs/docs/v2.1.0/sketch_8sql__in.html b/docs/docs/v2.1.0/sketch_8sql__in.html
new file mode 100644
index 00000000..2cd9b673
--- /dev/null
+++ b/docs/docs/v2.1.0/sketch_8sql__in.html
@@ -0,0 +1,975 @@
+
+
+
+
+
+
+
+
+MADlib: sketch.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
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+            
+          
+        
    
+
    
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+
+
    
+  
    
+Functions  
    
+  
    
+
    sketch.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for sketch-based approximations of descriptive statistics.  
+More...
    
+
+
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+
    
+Functions
    bytea big_or (bytea bitmap1, bytea bitmap2)
     
    bytea __fmsketch_trans (bytea bitmaps, anyelement input)
     
    int8 __fmsketch_count_distinct (bytea bitmaps)
     
    bytea __fmsketch_merge (bytea bitmaps1, bytea bitmaps2)
     
    aggregate bytea fmsketch_dcount (anyelement column)
     Flajolet-Martin's distinct count estimation.  More...
     
    bytea __cmsketch_int8_trans (bytea bitmaps, int8 input)
     
    bytea __cmsketch_int8_trans (bytea bitmaps, int8 input, int8 arg1)
     
    bytea __cmsketch_int8_trans (bytea bitmaps, int8 input, int8 arg1, int8 arg2)
     
    bytea __cmsketch_int8_trans (bytea bitmaps, int8 input, int8 arg1, int8 arg2, int8 arg3)
     
    text __cmsketch_base64_final (bytea sketch)
     
    bytea __cmsketch_merge (bytea, bytea)
     
    aggregate bytea cmsketch (int8 column)
     cmsketch is a UDA that can be run on columns of type int8, or any column that can be cast to an int8. It produces a base64 string representing a CountMin sketch: a large array of counters that is intended to be passed into a UDF like cmsketch_width_histogram described below.  More...
     
    int8 cmsketch_count (text sketches64, int8 val)
     cmsketch_count is a scalar UDF to compute the approximate number of occurences of a value in a column summarized by a cmsketch. Takes the results of the cmsketch aggregate as its first argument, and the desired value as the second.  More...
     
    int8 cmsketch_rangecount (text sketches64, int8 bot, int8 top)
     cmsketch_rangecount is a scalar UDF to approximate the number of occurrences of values in the range [lo,hi] inclusive, given a cmsketch of a column. Takes the results of the cmsketch aggregate as its first argument, and the desired range boundaries as the second and third.  More...
     
    int8 cmsketch_centile (text sketches64, int8 centile, int8 cnt)
     cmsketch_centile is a scalar UDF to compute a centile value from a cmsketch. Takes the results of the cmsketch aggregate as its first argument, a number between 1 and 99 as the desired centile in the second, and the count of the column as the third. Produces a value from the sketched column that is approximately at the centile's position in sorted order.  More...
     
    int8 cmsketch_median (text sketches64, int8 cnt)
     cmsketch_median is a scalar UDF to compute a median value from a cmsketch. Takes the results of the cmsketch aggregate as its first argument, and the count as the second. Produces a value from the sketched column that is approximately at the halfway position in sorted order.  More...
     
    text cmsketch_width_histogram (text sketches64, int8 themin, int8 themax, int4 nbuckets)
     cmsketch_width_histogram is a scalar UDF that takes three aggregates of a column – cmsketch, min and max– as well as a number of buckets, and produces an n-bucket histogram for the column where each bucket has approximately the same width. The output is a text string containing triples {lo, hi, count} representing the buckets; counts are approximate.  More...
     
    text cmsketch_depth_histogram (text sketches64, int4 nbuckets)
     cmsketch_depth_histogram is a UDA that takes a cmsketch and a number of buckets n, and produces an n-bucket histogram for the column where each bucket has approximately the same count. The output is a text string containing triples {lo, hi, count} representing the buckets; counts are approximate. Note that an equi-depth histogram is equivalent to a spanning set of equi-spaced centiles.  More...
     
    bytea __mfvsketch_trans (bytea, anyelement, int4)
     
    text [][] __mfvsketch_final (bytea)
     
    bytea __mfvsketch_merge (bytea, bytea)
     
    integer __sketch_rightmost_one (bytea, integer, integer)
     
    integer __sketch_leftmost_zero (bytea, integer, integer)
     
    bytea __sketch_array_set_bit_in_place (bytea, integer, integer, integer, integer)
     
    aggregate text [][] mfvsketch_top_histogram (anyelement column, int4 number_of_buckets)
     Produces an n-bucket histogram for a column where each bucket counts one of the most frequent values in the column. The output is an array of doubles {value, count} in descending order of frequency; counts are approximated via CountMin sketches. Ties are handled arbitrarily.  More...
     
    aggregate bytea mfvsketch_quick_histogram (anyelement column, int4 number_of_buckets)
     On Postgres it works the same way as mfvsketch_top_histogram but, in Greenplum it does parallel aggregation to provide a "quick and dirty" answer.  More...
     
    
+
    Detailed Description
    
+
    Date
    April 2011
    
+
    See also
    For a brief introduction to sketches, see the module description Cardinality Estimators 
    
+
    Function Documentation
    
+
+
    ◆ __cmsketch_base64_final()
    
+
+
    
+
    
+      
+        
+          
+          
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+      
    text __cmsketch_base64_final (bytea sketch)
    
+
    
+
+
    
+
    
+
+
    ◆ __cmsketch_int8_trans() [1/4]
    
+
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+
    
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    bytea __cmsketch_int8_trans (bytea bitmaps, 
    int8 input 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __cmsketch_int8_trans() [2/4]
    
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    bytea __cmsketch_int8_trans (bytea bitmaps, 
    int8 input, 
    int8 arg1 
    )
    
+
    
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    ◆ __cmsketch_int8_trans() [3/4]
    
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    bytea __cmsketch_int8_trans (bytea bitmaps, 
    int8 input, 
    int8 arg1, 
    int8 arg2 
    )
    
+
    
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    ◆ __cmsketch_int8_trans() [4/4]
    
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    bytea __cmsketch_int8_trans (bytea bitmaps, 
    int8 input, 
    int8 arg1, 
    int8 arg2, 
    int8 arg3 
    )
    
+
    
+
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    ◆ __cmsketch_merge()
    
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    bytea __cmsketch_merge (bytea , 
    bytea  
    )
    
+
    
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    ◆ __fmsketch_count_distinct()
    
+
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+
    
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    int8 __fmsketch_count_distinct (bytea bitmaps)
    
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    ◆ __fmsketch_merge()
    
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    bytea __fmsketch_merge (bytea bitmaps1, 
    bytea bitmaps2 
    )
    
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    ◆ __fmsketch_trans()
    
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    bytea __fmsketch_trans (bytea bitmaps, 
    anyelement input 
    )
    
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    ◆ __mfvsketch_final()
    
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    text [][] __mfvsketch_final (bytea )
    
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    ◆ __mfvsketch_merge()
    
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    bytea __mfvsketch_merge (bytea , 
    bytea  
    )
    
+
    
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    ◆ __mfvsketch_trans()
    
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    bytea __mfvsketch_trans (bytea , 
    anyelement , 
    int4  
    )
    
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    ◆ __sketch_array_set_bit_in_place()
    
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    bytea __sketch_array_set_bit_in_place (bytea , 
    integer , 
    integer , 
    integer , 
    integer  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __sketch_leftmost_zero()
    
+
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+      
    integer __sketch_leftmost_zero (bytea , 
    integer , 
    integer  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __sketch_rightmost_one()
    
+
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    integer __sketch_rightmost_one (bytea , 
    integer , 
    integer  
    )
    
+
    
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+
    ◆ big_or()
    
+
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    bytea big_or (bytea bitmap1, 
    bytea bitmap2 
    )
    
+
    
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    ◆ cmsketch()
    
+
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    aggregate bytea cmsketch (int8 column)
    
+
    
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+
    ◆ cmsketch_centile()
    
+
+
    
+
    
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+      
    int8 cmsketch_centile (text sketches64, 
    int8 centile, 
    int8 cnt 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ cmsketch_count()
    
+
+
    
+
    
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    int8 cmsketch_count (text sketches64, 
    int8 val 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ cmsketch_depth_histogram()
    
+
+
    
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    text cmsketch_depth_histogram (text sketches64, 
    int4 nbuckets 
    )
    
+
    
+
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+
    
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    ◆ cmsketch_median()
    
+
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    int8 cmsketch_median (text sketches64, 
    int8 cnt 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ cmsketch_rangecount()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    int8 cmsketch_rangecount (text sketches64, 
    int8 bot, 
    int8 top 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ cmsketch_width_histogram()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    text cmsketch_width_histogram (text sketches64, 
    int8 themin, 
    int8 themax, 
    int4 nbuckets 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ fmsketch_dcount()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate bytea fmsketch_dcount (anyelement column)
    
+
    
+
    Parameters
    
+  
+    
+  
    columnname 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ mfvsketch_quick_histogram()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate bytea mfvsketch_quick_histogram (anyelement column, 
    int4 number_of_buckets 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ mfvsketch_top_histogram()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate text [][] mfvsketch_top_histogram (anyelement column, 
    int4 number_of_buckets 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/sparse__linear__systems_8sql__in.html b/docs/docs/v2.1.0/sparse__linear__systems_8sql__in.html
new file mode 100644
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@@ -0,0 +1,982 @@
+
+
+
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+
+
+
+
+MADlib: sparse_linear_systems.sql_in File Reference
+
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+
+
+
+
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+
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+
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+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
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+
    
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+
    
+
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+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    sparse_linear_systems.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for linear systems.  
+More...
    
+
+
+
+
+
+
+
+
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+
+
+
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+
    
+Functions
    float8 [] sparse_inmem_iterative_linear_system_transition (float8[] state, integer row_id, integer col_id, float8 value, float8 b, integer num_eqs, integer num_vars, integer nnz, integer algorithm, integer maxiter, float8 termtoler)
     
    float8 [] sparse_inmem_iterative_linear_system_merge_states (float8[] state1, float8[] state2)
     
    sparse_linear_solver_result sparse_inmem_iterative_linear_system_final (float8[] state)
     
    aggregate sparse_linear_solver_result sparse_inmem_iterative_linear_system (integer row_id, integer col_id, float8 value, float8 right_hand_side, integer numEquations, integer numVars, integer nnz, integer algorithm, integer maxIter, float8 termToler)
     Solve a system of linear equations using the inmem_iterative method.  More...
     
    float8 [] sparse_direct_linear_system_transition (float8[] state, integer row_id, integer col_id, float8 value, float8 b, integer num_eqs, integer num_vars, integer nnz, integer algorithm)
     
    float8 [] sparse_direct_linear_system_merge_states (float8[] state1, float8[] state2)
     
    sparse_linear_solver_result sparse_direct_linear_system_final (float8[] state)
     
    aggregate sparse_linear_solver_result sparse_direct_linear_system (integer row_id, integer col_id, float8 value, float8 right_hand_side, integer numEquations, integer numVars, integer nnz, integer algorithm)
     Solve a system of linear equations using the direct method.  More...
     
    varchar linear_solver_sparse (varchar input_string)
     Help function, to print out the supported families.  More...
     
    varchar linear_solver_sparse ()
     
    void linear_solver_sparse (varchar lhs_table, varchar rhs_table, varchar out_table, varchar lhs_row_id, varchar lhs_col_id, varchar lhs_value, varchar rhs_row_id, varchar rhs_value, integer num_vars, varchar grouping_cols, varchar optimizer, varchar optimizer_options)
     A wrapper function for the various marginal linear_systemsion analyzes.  More...
     
    void linear_solver_sparse (varchar lhs_table, varchar rhs_table, varchar out_table, varchar lhs_row_id, varchar lhs_col_id, varchar lhs_value, varchar rhs_row_id, varchar rhs_value, integer num_vars)
     Marginal effects with default variables.  More...
     
    void linear_solver_sparse (varchar lhs_table, varchar rhs_table, varchar out_table, varchar lhs_row_id, varchar lhs_col_id, varchar lhs_value, varchar rhs_row_id, varchar rhs_value, integer num_vars, varchar grouping_cols)
     Marginal effects with default variables.  More...
     
    void linear_solver_sparse (varchar lhs_table, varchar rhs_table, varchar out_table, varchar lhs_row_id, varchar lhs_col_id, varchar lhs_value, varchar rhs_row_id, varchar rhs_value, integer num_vars, varchar grouping_cols, varchar optimizer)
     Marginal effects with default variables.  More...
     
    
+
    Detailed Description
    
+
    Date
    January 2011
    
+
    See also
    Computes the solution of a consistent linear system 
    
+
    Function Documentation
    
+
+
    ◆ linear_solver_sparse() [1/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar linear_solver_sparse (varchar input_string)
    
+
    
+
+
    
+
    
+
+
    ◆ linear_solver_sparse() [2/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar linear_solver_sparse ()
    
+
    
+
+
    
+
    
+
+
    ◆ linear_solver_sparse() [3/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void linear_solver_sparse (varchar lhs_table, 
    varchar rhs_table, 
    varchar out_table, 
    varchar lhs_row_id, 
    varchar lhs_col_id, 
    varchar lhs_value, 
    varchar rhs_row_id, 
    varchar rhs_value, 
    integer num_vars, 
    varchar grouping_cols, 
    varchar optimizer, 
    varchar optimizer_options 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    lhs_tableString identifying the input A matrix 
    rhs_tableString identifying the input b vector 
    out_tableString identifying the output table to be created 
    lhs_row_idColumn name containing the LHS of the equations 
    lhs_col_idColumn name containing the LHS of the equations 
    lhs_valueColumn name containing the LHS of the equations 
    rhs_row_idColumn name containing the RHS of the equations 
    rhs_valueColumn name containing the RHS of the equations 
    num_varsNumber of variables in the system 
    grouping_colsColumns to group the linear systems by 
    optimizerOptimizer to be used 
    optimizer_optionsOptimizer options used
    
+  
    
+
    
+
    Returns
    void
    
+
    Usage
    For function summary information. Run sql> select linear_solver_sparse('help'); OR sql> select linear_solver_sparse(); OR sql> select linear_solver_sparse('?'); For function usage information. Run sql> select linear_solver_sparse('usage'); 
    
+
+
    
+
    
+
+
    ◆ linear_solver_sparse() [4/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void linear_solver_sparse (varchar lhs_table, 
    varchar rhs_table, 
    varchar out_table, 
    varchar lhs_row_id, 
    varchar lhs_col_id, 
    varchar lhs_value, 
    varchar rhs_row_id, 
    varchar rhs_value, 
    integer num_vars 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ linear_solver_sparse() [5/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void linear_solver_sparse (varchar lhs_table, 
    varchar rhs_table, 
    varchar out_table, 
    varchar lhs_row_id, 
    varchar lhs_col_id, 
    varchar lhs_value, 
    varchar rhs_row_id, 
    varchar rhs_value, 
    integer num_vars, 
    varchar grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ linear_solver_sparse() [6/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void linear_solver_sparse (varchar lhs_table, 
    varchar rhs_table, 
    varchar out_table, 
    varchar lhs_row_id, 
    varchar lhs_col_id, 
    varchar lhs_value, 
    varchar rhs_row_id, 
    varchar rhs_value, 
    integer num_vars, 
    varchar grouping_cols, 
    varchar optimizer 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_direct_linear_system()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate sparse_linear_solver_result sparse_direct_linear_system (integer row_id, 
    integer col_id, 
    float8 value, 
    float8 right_hand_side, 
    integer numEquations, 
    integer numVars, 
    integer nnz, 
    integer algorithm 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+  
    row_idColumn containing the row_id 
    col_idColumn containing the col_id 
    valueValue of the LHS matrix 
    right_hand_sideColumn containing the right hand side of the system 
    numEquationsNumber of equations 
    numVarsNumber of variables 
    nnzNumber of non-zero values 
    algorithmAlgorithm used for the sparse linear solver
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • solution FLOAT8[]  - Array of marginal effects
      • 
+
    • residual_norm FLOAT8 - Norm of the residual
      • 
+
    • iters INTEGER - Iterations taken
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+ 
      SELECT linear_system_sparse(<em>row_id</em>,
+*                                    <em>left_hand_side</em>,
+*                                    <em> right_hand_side </em>,
+*                                    <em> numEquations </em>)
+*   FROM <em>dataTable</em>;
+* 
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_direct_linear_system_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    sparse_linear_solver_result sparse_direct_linear_system_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_direct_linear_system_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] sparse_direct_linear_system_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_direct_linear_system_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] sparse_direct_linear_system_transition (float8 [] state, 
    integer row_id, 
    integer col_id, 
    float8 value, 
    float8 b, 
    integer num_eqs, 
    integer num_vars, 
    integer nnz, 
    integer algorithm 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_inmem_iterative_linear_system()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate sparse_linear_solver_result sparse_inmem_iterative_linear_system (integer row_id, 
    integer col_id, 
    float8 value, 
    float8 right_hand_side, 
    integer numEquations, 
    integer numVars, 
    integer nnz, 
    integer algorithm, 
    integer maxIter, 
    float8 termToler 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+    
+    
+    
+    
+    
+  
    row_idColumn containing the row_id 
    col_idColumn containing the col_id 
    valueValue of the LHS matrix 
    right_hand_sideColumn containing the right hand side of the system 
    numEquationsNumber of equations 
    numVarsNumber of variables 
    nnzNumber of non-zero values 
    algorithmAlgorithm used for the sparse linear solver 
    maxIterMaximum number of iterations 
    termTolerTermination tolerance
    
+  
    
+
    
+
    Returns
    A composite value:
      
+
    • solution FLOAT8[]  - Array of marginal effects
      • 
+
    • residual_norm FLOAT8 - Norm of the residual
      • 
+
    • iters INTEGER - Iterations taken
      • 
+
    
+
    
+
    Usage
      
+
    • Get all the diagnostic statistics:
      
+ 
      SELECT linear_system_sparse(<em>row_id</em>,
+*                                    <em>left_hand_side</em>,
+*                                    <em> right_hand_side </em>,
+*                                    <em> numEquations </em>)
+*   FROM <em>dataTable</em>;
+* 
       
      • 
+
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_inmem_iterative_linear_system_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    sparse_linear_solver_result sparse_inmem_iterative_linear_system_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_inmem_iterative_linear_system_merge_states()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] sparse_inmem_iterative_linear_system_merge_states (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ sparse_inmem_iterative_linear_system_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] sparse_inmem_iterative_linear_system_transition (float8 [] state, 
    integer row_id, 
    integer col_id, 
    float8 value, 
    float8 b, 
    integer num_eqs, 
    integer num_vars, 
    integer nnz, 
    integer algorithm, 
    integer maxiter, 
    float8 termtoler 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/splitbar.png b/docs/docs/v2.1.0/splitbar.png
new file mode 100644
index 0000000000000000000000000000000000000000..fe895f2c58179b471a22d8320b39a4bd7312ec8e
GIT binary patch
literal 314
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diff --git a/docs/docs/v2.1.0/sssp_8sql__in.html b/docs/docs/v2.1.0/sssp_8sql__in.html
new file mode 100644
index 00000000..da0d6e55
--- /dev/null
+++ b/docs/docs/v2.1.0/sssp_8sql__in.html
@@ -0,0 +1,475 @@
+
+
+
+
+
+
+
+
+MADlib: sssp.sql_in File Reference
+
+
+
+
+
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+
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+
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+
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+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
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+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
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+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    sssp.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for graph analytics.  
+More...
    
+
+
+
+
+
+
+
+
+
+
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+
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+
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+
+
+
+
    
+Functions
    void graph_sssp (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint source_vertex, text out_table, text grouping_cols)
     
    void graph_sssp (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint[] source_vertex, text out_table, text grouping_cols)
     
    void graph_sssp (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint source_vertex, text out_table)
     
    void graph_sssp (text vertex_table, text vertex_id, text edge_table, text edge_args, bigint[] source_vertex, text out_table)
     
    void graph_sssp_get_path (text sssp_table, bigint dest_vertex, text path_table)
     
    void graph_sssp_get_path (text sssp_table, bigint[] dest_vertex, text path_table)
     
    varchar graph_sssp (varchar message)
     
    varchar graph_sssp ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    Nov 2016
    
+
    See also
    Provides single source shortest path algorithm. 
    
+
    Function Documentation
    
+
+
    ◆ graph_sssp() [1/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
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+        
+        
+          
+          
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+        
+        
+          
+          
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+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_sssp (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    bigint source_vertex, 
    text out_table, 
    text grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp() [2/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_sssp (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    bigint [] source_vertex, 
    text out_table, 
    text grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp() [3/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_sssp (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    bigint source_vertex, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp() [4/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_sssp (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    bigint [] source_vertex, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp() [5/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar graph_sssp (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp() [6/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar graph_sssp ()
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp_get_path() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_sssp_get_path (text sssp_table, 
    bigint dest_vertex, 
    text path_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_sssp_get_path() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_sssp_get_path (text sssp_table, 
    bigint [] dest_vertex, 
    text path_table 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/stratified__sample_8sql__in.html b/docs/docs/v2.1.0/stratified__sample_8sql__in.html
new file mode 100644
index 00000000..6f3f0852
--- /dev/null
+++ b/docs/docs/v2.1.0/stratified__sample_8sql__in.html
@@ -0,0 +1,355 @@
+
+
+
+
+
+
+
+
+MADlib: stratified_sample.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    stratified_sample.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL functions for stratified sampling.  
+More...
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    void stratified_sample (text source_table, text output_table, float8 proportion, text grouping_cols, text target_cols, boolean with_replacement)
     
    void stratified_sample (text source_table, text output_table, float8 proportion, text grouping_cols, text target_cols)
     
    void stratified_sample (text source_table, text output_table, float8 proportion, text grouping_cols)
     
    void stratified_sample (text source_table, text output_table, float8 proportion)
     
    varchar stratified_sample (varchar message)
     
    varchar stratified_sample ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    07/19/2017
    
+
    See also
    Given a table, stratified sampling returns a proportion of records for each group (strata). 
    
+
    Function Documentation
    
+
+
    ◆ stratified_sample() [1/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void stratified_sample (text source_table, 
    text output_table, 
    float8 proportion, 
    text grouping_cols, 
    text target_cols, 
    boolean with_replacement 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ stratified_sample() [2/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void stratified_sample (text source_table, 
    text output_table, 
    float8 proportion, 
    text grouping_cols, 
    text target_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ stratified_sample() [3/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void stratified_sample (text source_table, 
    text output_table, 
    float8 proportion, 
    text grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ stratified_sample() [4/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void stratified_sample (text source_table, 
    text output_table, 
    float8 proportion 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ stratified_sample() [5/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar stratified_sample (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ stratified_sample() [6/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar stratified_sample ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/summary_8sql__in.html b/docs/docs/v2.1.0/summary_8sql__in.html
new file mode 100644
index 00000000..15e46a4a
--- /dev/null
+++ b/docs/docs/v2.1.0/summary_8sql__in.html
@@ -0,0 +1,657 @@
+
+
+
+
+
+
+
+
+MADlib: summary.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    summary.sql_in File Reference
      
    
+
    
+
    
+
+
    Summary function for descriptive statistics.  
+More...
    
+
+
+
+
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+
+
+
    
+Functions
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols, boolean get_distinct, boolean get_quartiles, float8[] ntile_array, integer how_many_mfv, boolean get_estimates, integer n_cols_per_run)
     
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols, boolean get_distinct, boolean get_quartiles, float8[] ntile_array, integer how_many_mfv, boolean get_estimates)
     
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols, boolean get_distinct, boolean get_quartiles, float8[] ntile_array, integer how_many_mfv)
     
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols, boolean get_distinct, boolean get_quartiles, float8[] ntile_array)
     
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols, boolean get_distinct, boolean get_quartiles)
     
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols, boolean get_distinct)
     
    summary_result summary (text source_table, text output_table, text target_cols, text grouping_cols)
     
    summary_result summary (text source_table, text output_table, text target_cols)
     
    summary_result summary (text source_table, text output_table)
     
    text summary (text input_message)
     
    text summary ()
     
    
+
    Detailed Description
    
+
    Date
    Mar 2013 
    
+
    Function Documentation
    
+
+
    ◆ summary() [1/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols, 
    boolean get_distinct, 
    boolean get_quartiles, 
    float8 [] ntile_array, 
    integer how_many_mfv, 
    boolean get_estimates, 
    integer n_cols_per_run 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ summary() [2/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols, 
    boolean get_distinct, 
    boolean get_quartiles, 
    float8 [] ntile_array, 
    integer how_many_mfv, 
    boolean get_estimates 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ summary() [3/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols, 
    boolean get_distinct, 
    boolean get_quartiles, 
    float8 [] ntile_array, 
    integer how_many_mfv 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ summary() [4/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols, 
    boolean get_distinct, 
    boolean get_quartiles, 
    float8 [] ntile_array 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ summary() [5/11]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols, 
    boolean get_distinct, 
    boolean get_quartiles 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ summary() [6/11]
    
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+      
    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols, 
    boolean get_distinct 
    )
    
+
    
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    ◆ summary() [7/11]
    
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    summary_result summary (text source_table, 
    text output_table, 
    text target_cols, 
    text grouping_cols 
    )
    
+
    
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    ◆ summary() [8/11]
    
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    summary_result summary (text source_table, 
    text output_table, 
    text target_cols 
    )
    
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    ◆ summary() [9/11]
    
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    summary_result summary (text source_table, 
    text output_table 
    )
    
+
    
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    ◆ summary() [10/11]
    
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    text summary (text input_message)
    
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    ◆ summary() [11/11]
    
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    text summary ()
    
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diff --git a/docs/docs/v2.1.0/svd_8sql__in.html b/docs/docs/v2.1.0/svd_8sql__in.html
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+MADlib: svd.sql_in File Reference
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
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+  
    
+Functions  
    
+  
    
+
    svd.sql_in File Reference
      
    
+
    
+
    
+
+
    Singular Value Decomposition.  
+More...
    
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+Functions
    void svd (text source_table, text output_table_prefix, text row_id, integer k, integer n_iterations, text result_summary_table)
     
    void svd_block (text source_table, text output_table_prefix, integer k, integer n_iterations, text result_summary_table)
     
    void svd_block (text source_table, text output_table_prefix, integer k, integer n_iterations)
     
    void svd_block (text source_table, text output_table_prefix, integer k)
     
    void svd_sparse (text source_table, text output_table_prefix, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, integer n_iterations, text result_summary_table)
     
    void svd_sparse_native (text source_table, text output_table_prefix, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, integer n_iterations, text result_summary_table)
     
    void svd (text source_table, text output_table_prefix, text row_id, integer k)
     
    void svd_sparse (text source_table, text output_table_prefix, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k)
     
    void svd (text source_table, text output_table_prefix, text row_id, integer k, integer n_iterations)
     
    void svd_sparse (text source_table, text output_table_prefix, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, integer n_iterations)
     
    void svd_sparse_native (text source_table, text output_table_prefix, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k)
     
    void svd_sparse_native (text source_table, text output_table_prefix, text row_id, text col_id, text val_id, integer row_dim, integer col_dim, integer k, integer n_iterations)
     
    float8 [] __svd_unit_vector (int dim)
     
    float8 [] __svd_lanczos_sfunc (float8[] state, int row_id, float8[] row_array, float8[] vector, int dimension)
     
    float8 [] __svd_block_lanczos_sfunc (float8[] state, int4 row_id, int4 col_id, float8[] block, float8[] vector, int4 dimension)
     
    float8 [] __svd_sparse_lanczos_sfunc (float8[] state, int4 row_id, int4 col_id, float8 val, float8[] vector, int4 dimension)
     
    float8 [] __svd_lanczos_prefunc (float8[] state1, float8[] state2)
     
    aggregate float8 [] __svd_lanczos_agg (int, float8[], float8[], int)
     
    aggregate float8 [] __svd_block_lanczos_agg (int, int4, float8[], float8[], int)
     
    aggregate float8 [] __svd_sparse_lanczos_agg (int4, int4, float8, float8[], int4)
     
    __svd_lanczos_result __svd_lanczos_pvec (float8[] vector, float8[] pvec, float8 beta)
     
    float8 [] __svd_lanczos_qvec (float8[] vector, float8[] qvec, float8 alpha)
     
    float8 [] __svd_gram_schmidt_orthogonalize_sfunc (float8[] state, float8[] vec_unorthogonalized, float8[] vec_orthogonalized)
     
    float8 [] __svd_gram_schmidt_orthogonalize_prefunc (float8[] state1, float8[] state2)
     
    __svd_lanczos_result __svd_gram_schmidt_orthogonalize_ffunc (float8[] state)
     
    aggregate float8 [] __svd_gram_schmidt_orthogonalize_agg (float8[], float8[])
     
    void __svd_lanczos_bidiagonalize (text source_table, text output_table_prefix, int n_iterations, int k, boolean is_block)
     
    void __svd_lanczos_bidiagonalize_sparse (text source_table, text row_id, text col_id, text val, text output_table_prefix, int n_iterations, int k)
     
    __svd_bidiagonal_matrix_result __svd_decompose_bidiag (int[] row_ids, int[] col_ids, float8[] vals)
     
    float8 [] __svd_vec_mult_matrix (float8[] vector, float8[][] matrix, int4 k)
     
    set< __svd_vec_mat_mult_result > __svd_vec_trans_mult_matrix_internal (float8[] vector, float8[][] matrix, int4 col_id, int4 k)
     
    void __svd_vec_trans_mult_matrix (text vec_table, text mat_table, int4 k, boolean is_left, text res_table)
     
    text svd (text input_message)
     
    text svd ()
     
    
+
    Detailed Description
    
+
    See also
    For a brief introduction to singular value decomposition, see the module description Singular Value Decomposition. 
    
+
    Function Documentation
    
+
+
    ◆ __svd_block_lanczos_agg()
    
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    aggregate float8 [] __svd_block_lanczos_agg (int , 
    int4 , 
    float8 [], 
    float8 [], 
    int  
    )
    
+
    
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    ◆ __svd_block_lanczos_sfunc()
    
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    float8 [] __svd_block_lanczos_sfunc (float8 [] state, 
    int4 row_id, 
    int4 col_id, 
    float8 [] block, 
    float8 [] vector, 
    int4 dimension 
    )
    
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    ◆ __svd_decompose_bidiag()
    
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    __svd_bidiagonal_matrix_result __svd_decompose_bidiag (int [] row_ids, 
    int [] col_ids, 
    float8 [] vals 
    )
    
+
    
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    ◆ __svd_gram_schmidt_orthogonalize_agg()
    
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    aggregate float8 [] __svd_gram_schmidt_orthogonalize_agg (float8 [], 
    float8 [] 
    )
    
+
    
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+
    
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    ◆ __svd_gram_schmidt_orthogonalize_ffunc()
    
+
+
    
+
    
+      
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    __svd_lanczos_result __svd_gram_schmidt_orthogonalize_ffunc (float8 [] state)
    
+
    
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    ◆ __svd_gram_schmidt_orthogonalize_prefunc()
    
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    float8 [] __svd_gram_schmidt_orthogonalize_prefunc (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
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    ◆ __svd_gram_schmidt_orthogonalize_sfunc()
    
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    float8 [] __svd_gram_schmidt_orthogonalize_sfunc (float8 [] state, 
    float8 [] vec_unorthogonalized, 
    float8 [] vec_orthogonalized 
    )
    
+
    
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    ◆ __svd_lanczos_agg()
    
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    aggregate float8 [] __svd_lanczos_agg (int , 
    float8 [], 
    float8 [], 
    int  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __svd_lanczos_bidiagonalize()
    
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+
    
+      
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    void __svd_lanczos_bidiagonalize (text source_table, 
    text output_table_prefix, 
    int n_iterations, 
    int k, 
    boolean is_block 
    )
    
+
    
+
+
    
+
    
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    ◆ __svd_lanczos_bidiagonalize_sparse()
    
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    void __svd_lanczos_bidiagonalize_sparse (text source_table, 
    text row_id, 
    text col_id, 
    text val, 
    text output_table_prefix, 
    int n_iterations, 
    int k 
    )
    
+
    
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    ◆ __svd_lanczos_prefunc()
    
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    float8 [] __svd_lanczos_prefunc (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
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    ◆ __svd_lanczos_pvec()
    
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    __svd_lanczos_result __svd_lanczos_pvec (float8 [] vector, 
    float8 [] pvec, 
    float8 beta 
    )
    
+
    
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    ◆ __svd_lanczos_qvec()
    
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    float8 [] __svd_lanczos_qvec (float8 [] vector, 
    float8 [] qvec, 
    float8 alpha 
    )
    
+
    
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    ◆ __svd_lanczos_sfunc()
    
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    float8 [] __svd_lanczos_sfunc (float8 [] state, 
    int row_id, 
    float8 [] row_array, 
    float8 [] vector, 
    int dimension 
    )
    
+
    
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    ◆ __svd_sparse_lanczos_agg()
    
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    aggregate float8 [] __svd_sparse_lanczos_agg (int4 , 
    int4 , 
    float8 , 
    float8 [], 
    int4  
    )
    
+
    
+
+
    
+
    
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    ◆ __svd_sparse_lanczos_sfunc()
    
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    float8 [] __svd_sparse_lanczos_sfunc (float8 [] state, 
    int4 row_id, 
    int4 col_id, 
    float8 val, 
    float8 [] vector, 
    int4 dimension 
    )
    
+
    
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    ◆ __svd_unit_vector()
    
+
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    float8 [] __svd_unit_vector (int dim)
    
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+
    
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    ◆ __svd_vec_mult_matrix()
    
+
+
    
+
    
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    float8 [] __svd_vec_mult_matrix (float8 [] vector, 
    float8 matrix[][], 
    int4 k 
    )
    
+
    
+
    Multiplication of a row vector with an in-memory matrix vector: 1 x l matrix: l x l k: Sub-matrix of the size l x k 
    
+
+
    
+
    
+
+
    ◆ __svd_vec_trans_mult_matrix()
    
+
+
    
+
    
+      
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    void __svd_vec_trans_mult_matrix (text vec_table, 
    text mat_table, 
    int4 k, 
    boolean is_left, 
    text res_table 
    )
    
+
    
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+
    
+
    
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    ◆ __svd_vec_trans_mult_matrix_internal()
    
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    set<__svd_vec_mat_mult_result> __svd_vec_trans_mult_matrix_internal (float8 [] vector, 
    float8 matrix[][], 
    int4 col_id, 
    int4 k 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd() [1/5]
    
+
+
    
+
    
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    void svd (text source_table, 
    text output_table_prefix, 
    text row_id, 
    integer k, 
    integer n_iterations, 
    text result_summary_table 
    )
    
+
    
+
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+
    
+
+
    ◆ svd() [2/5]
    
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+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd (text source_table, 
    text output_table_prefix, 
    text row_id, 
    integer k 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd() [3/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd (text source_table, 
    text output_table_prefix, 
    text row_id, 
    integer k, 
    integer n_iterations 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text svd (text input_message)
    
+
    
+
+
    
+
    
+
+
    ◆ svd() [5/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text svd ()
    
+
    
+
+
    
+
    
+
+
    ◆ svd_block() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_block (text source_table, 
    text output_table_prefix, 
    integer k, 
    integer n_iterations, 
    text result_summary_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_block() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_block (text source_table, 
    text output_table_prefix, 
    integer k, 
    integer n_iterations 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_block() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_block (text source_table, 
    text output_table_prefix, 
    integer k 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_sparse() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_sparse (text source_table, 
    text output_table_prefix, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    integer n_iterations, 
    text result_summary_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_sparse() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_sparse (text source_table, 
    text output_table_prefix, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_sparse() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_sparse (text source_table, 
    text output_table_prefix, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    integer n_iterations 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_sparse_native() [1/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_sparse_native (text source_table, 
    text output_table_prefix, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    integer n_iterations, 
    text result_summary_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_sparse_native() [2/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_sparse_native (text source_table, 
    text output_table_prefix, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svd_sparse_native() [3/3]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svd_sparse_native (text source_table, 
    text output_table_prefix, 
    text row_id, 
    text col_id, 
    text val_id, 
    integer row_dim, 
    integer col_dim, 
    integer k, 
    integer n_iterations 
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/svec_8sql__in.html b/docs/docs/v2.1.0/svec_8sql__in.html
new file mode 100644
index 00000000..b72e7824
--- /dev/null
+++ b/docs/docs/v2.1.0/svec_8sql__in.html
@@ -0,0 +1,1731 @@
+
+
+
+
+
+
+
+
+MADlib: svec.sql_in File Reference
+
+
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+
+
+
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+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
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+
    
+
    
+  
+  
    
+  
    
+
    
+
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+
    
+
    
+
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+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    svec.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL type definitions and functions for sparse vector data type svec  
+More...
    
+
+
+
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+
    
+Functions
    svec svec_in (cstring)
     
    cstring svec_out (svec)
     
    svec svec_recv (internal)
     
    bytea svec_send (svec)
     
    svec svec_plus (svec, svec)
     
    svec svec_minus (svec, svec)
     
    svec svec_div (svec, svec)
     
    svec svec_mult (svec, svec)
     
    svec svec_pow (svec, svec)
     
    integer svec_cmp (svec, svec)
     
    boolean svec_ge (svec, svec)
     
    boolean svec_lt (svec, svec)
     
    boolean svec_le (svec, svec)
     
    boolean svec_gt (svec, svec)
     
    boolean svec_ne (svec, svec)
     
    boolean svec_eq (svec, svec)
     
    boolean float8arr_eq (float8[], float8[])
     
    svec float8arr_minus_float8arr (float8[], float8[])
     
    svec float8arr_minus_svec (float8[], svec)
     
    svec svec_minus_float8arr (svec, float8[])
     
    svec float8arr_plus_float8arr (float8[], float8[])
     
    svec float8arr_plus_svec (float8[], svec)
     
    svec svec_plus_float8arr (svec, float8[])
     
    svec float8arr_mult_float8arr (float8[], float8[])
     
    svec float8arr_mult_svec (float8[], svec)
     
    svec svec_mult_float8arr (svec, float8[])
     
    svec float8arr_div_float8arr (float8[], float8[])
     
    svec float8arr_div_svec (float8[], svec)
     
    svec svec_div_float8arr (svec, float8[])
     
    float8 svec_dot (svec, svec)
     
    float8 svec_dot (float8[], float8[])
     
    float8 svec_dot (svec, float8[])
     
    float8 svec_dot (float8[], svec)
     
    svec svec_cast_int2 (int2)
     
    svec svec_cast_int4 (int4)
     
    svec svec_cast_int8 (bigint)
     
    svec svec_cast_float4 (float4)
     
    svec svec_cast_float8 (float8)
     
    svec svec_cast_numeric (numeric)
     
    float8 [] float8arr_cast_int2 (int2)
     
    float8 [] float8arr_cast_int4 (int4)
     
    float8 [] float8arr_cast_int8 (bigint)
     
    float8 [] float8arr_cast_float4 (float4)
     
    float8 [] float8arr_cast_float8 (float8)
     
    float8 [] float8arr_cast_numeric (numeric)
     
    svec svec_cast_float8arr (float8[])
     
    svec svec_cast_positions_float8arr (int8[], float8[], int8, float8)
     
    float8 [] svec_return_array (svec)
     
    svec svec_concat (svec, svec)
     
    svec svec_concat_replicate (int4, svec)
     
    bool svec_l2_lt (svec, svec)
     
    bool svec_l2_le (svec, svec)
     
    bool svec_l2_eq (svec, svec)
     
    bool svec_l2_ne (svec, svec)
     
    bool svec_l2_gt (svec, svec)
     
    bool svec_l2_ge (svec, svec)
     
    integer svec_l2_cmp (svec, svec)
     
    
+
    Detailed Description
    
+
    See also
    For an introduction to the sparse vector implementation, see the module description Sparse Vectors.
    
+
    Function Documentation
    
+
+
    ◆ float8arr_cast_float4()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] float8arr_cast_float4 (float4 )
    
+
    
+
    Casts a float4 into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ float8arr_cast_float8()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] float8arr_cast_float8 (float8 )
    
+
    
+
    Casts a float8 into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ float8arr_cast_int2()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] float8arr_cast_int2 (int2 )
    
+
    
+
    Casts an int2 into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ float8arr_cast_int4()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] float8arr_cast_int4 (int4 )
    
+
    
+
    Casts an int4 into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ float8arr_cast_int8()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] float8arr_cast_int8 (bigint )
    
+
    
+
    Casts an int8 into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ float8arr_cast_numeric()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] float8arr_cast_numeric (numeric )
    
+
    
+
    Casts a numeric into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ float8arr_div_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_div_float8arr (float8 [], 
    float8 [] 
    )
    
+
    
+
    Divides a float8 array by another, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_div_svec()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_div_svec (float8 [], 
    svec  
    )
    
+
    
+
    Divides a float8 array by an SVEC, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_eq()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean float8arr_eq (float8 [], 
    float8 [] 
    )
    
+
    
+
    Returns true if two float8 arrays are equal 
    
+
+
    
+
    
+
+
    ◆ float8arr_minus_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_minus_float8arr (float8 [], 
    float8 [] 
    )
    
+
    
+
    Minus second array from the first array, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_minus_svec()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_minus_svec (float8 [], 
    svec  
    )
    
+
    
+
    Minus second SVEC from the first array, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_mult_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_mult_float8arr (float8 [], 
    float8 [] 
    )
    
+
    
+
    Multiplies two float8 arrays, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_mult_svec()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_mult_svec (float8 [], 
    svec  
    )
    
+
    
+
    Multiplies an array and an SVEC, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_plus_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_plus_float8arr (float8 [], 
    float8 [] 
    )
    
+
    
+
    Adds two arrays together, element by element. 
    
+
+
    
+
    
+
+
    ◆ float8arr_plus_svec()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec float8arr_plus_svec (float8 [], 
    svec  
    )
    
+
    
+
    Adds an array and an SVEC, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_float4()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_float4 (float4 )
    
+
    
+
    Casts a float4 into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_float8()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_float8 (float8 )
    
+
    
+
    Casts a float8 into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_float8arr (float8 [])
    
+
    
+
    Casts a float8 into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_int2()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_int2 (int2 )
    
+
    
+
    Casts an int2 into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_int4()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_int4 (int4 )
    
+
    
+
    Casts an int4 into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_int8()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_int8 (bigint )
    
+
    
+
    Casts an int8 into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_numeric()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_cast_numeric (numeric )
    
+
    
+
    Casts a numeric into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cast_positions_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_cast_positions_float8arr (int8 [], 
    float8 [], 
    int8 , 
    float8  
    )
    
+
    
+
    Casts an array of int8 positions, float8 values into an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_cmp()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    integer svec_cmp (svec , 
    svec  
    )
    
+
    
+
    Compare two SVECs, -1 for left side smaller, 1 for greater, 0 for equal 
    
+
+
    
+
    
+
+
    ◆ svec_concat()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_concat (svec , 
    svec  
    )
    
+
    
+
    Concatenates two SVECs. 
    
+
+
    
+
    
+
+
    ◆ svec_concat_replicate()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_concat_replicate (int4 , 
    svec  
    )
    
+
    
+
    Replicates n copies of an SVEC and concatenates them together. 
    
+
+
    
+
    
+
+
    ◆ svec_div()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_div (svec , 
    svec  
    )
    
+
    
+
    Divides the first SVEC by the second, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_div_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_div_float8arr (svec , 
    float8 [] 
    )
    
+
    
+
    Divides an SVEC by a float8 array, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_dot() [1/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_dot (svec , 
    svec  
    )
    
+
    
+
    Computes the dot product of two SVECs. 
    
+
+
    
+
    
+
+
    ◆ svec_dot() [2/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_dot (float8 [], 
    float8 [] 
    )
    
+
    
+
    Computes the dot product of two float8 arrays. 
    
+
+
    
+
    
+
+
    ◆ svec_dot() [3/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_dot (svec , 
    float8 [] 
    )
    
+
    
+
    Computes the dot product of an SVEC and a float8 array. 
    
+
+
    
+
    
+
+
    ◆ svec_dot() [4/4]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_dot (float8 [], 
    svec  
    )
    
+
    
+
    Computes the dot product of a float8 array and an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_eq()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_eq (svec , 
    svec  
    )
    
+
    
+
    Returns true if two SVECs are equal. If the two SVECs are of different size, then will return false. 
    
+
+
    
+
    
+
+
    ◆ svec_ge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_ge (svec , 
    svec  
    )
    
+
    
+
    Returns true if the left SVEC is greater or equal to the right. 
    
+
+
    
+
    
+
+
    ◆ svec_gt()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_gt (svec , 
    svec  
    )
    
+
    
+
    Returns true if the left SVEC is greater. 
    
+
+
    
+
    
+
+
    ◆ svec_in()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_in (cstring )
    
+
    
+
    SVEC constructor from CSTRING. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_cmp()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    integer svec_l2_cmp (svec , 
    svec  
    )
    
+
    
+
    Returns a value indicating the relative values of the l2 norms of two SVECs. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_eq()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bool svec_l2_eq (svec , 
    svec  
    )
    
+
    
+
    Returns true if the l2 norm of the first SVEC is equal to that of the second SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_ge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bool svec_l2_ge (svec , 
    svec  
    )
    
+
    
+
    Returns true if the l2 norm of the first SVEC is greater than or equal to that of the second SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_gt()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bool svec_l2_gt (svec , 
    svec  
    )
    
+
    
+
    Returns true if the l2 norm of the first SVEC is greater than that of the second SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_le()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bool svec_l2_le (svec , 
    svec  
    )
    
+
    
+
    Returns true if the l2 norm of the first SVEC is less than or equal to that of the second SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_lt()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bool svec_l2_lt (svec , 
    svec  
    )
    
+
    
+
    Returns true if the l2 norm of the first SVEC is less than that of the second SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l2_ne()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    bool svec_l2_ne (svec , 
    svec  
    )
    
+
    
+
    Returns true if the l2 norm of the first SVEC is not equal to that of the second SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_le()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_le (svec , 
    svec  
    )
    
+
    
+
    Returns true if the left SVEC is less or equal to the right. 
    
+
+
    
+
    
+
+
    ◆ svec_lt()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_lt (svec , 
    svec  
    )
    
+
    
+
    Returns true if the left SVEC is less than the right. 
    
+
+
    
+
    
+
+
    ◆ svec_minus()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_minus (svec , 
    svec  
    )
    
+
    
+
    Minus second SVEC from the first, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_minus_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_minus_float8arr (svec , 
    float8 [] 
    )
    
+
    
+
    Minus second array from the first SVEC, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_mult()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_mult (svec , 
    svec  
    )
    
+
    
+
    Multiplies two SVEVs together, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_mult_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_mult_float8arr (svec , 
    float8 [] 
    )
    
+
    
+
    Multiplies an SVEC and an array, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_ne()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_ne (svec , 
    svec  
    )
    
+
    
+
    Returns true if two SVECs are not equal. If the two SVECs are of different size, then will return true. 
    
+
+
    
+
    
+
+
    ◆ svec_out()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    cstring svec_out (svec )
    
+
    
+
    Converts SVEC to CSTRING. 
    
+
+
    
+
    
+
+
    ◆ svec_plus()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_plus (svec , 
    svec  
    )
    
+
    
+
    Adds two SVECs together, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_plus_float8arr()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_plus_float8arr (svec , 
    float8 [] 
    )
    
+
    
+
    Adds an SVEC and an array, element by element. 
    
+
+
    
+
    
+
+
    ◆ svec_pow()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_pow (svec , 
    svec  
    )
    
+
    
+
    Raises each element of the first SVEC to the power given by second SVEC, which must have dimension 1 (a scalar). 
    
+
+
    
+
    
+
+
    ◆ svec_recv()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_recv (internal )
    
+
    
+
    Converts SVEC internal representation to SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_return_array()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] svec_return_array (svec )
    
+
    
+
    Casts an SVEC into a float8 array. 
    
+
+
    
+
    
+
+
    ◆ svec_send()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bytea svec_send (svec )
    
+
    
+
    Converts SVEC to BYTEA. 
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/svec__util_8sql__in.html b/docs/docs/v2.1.0/svec__util_8sql__in.html
new file mode 100644
index 00000000..27dcbf78
--- /dev/null
+++ b/docs/docs/v2.1.0/svec__util_8sql__in.html
@@ -0,0 +1,1356 @@
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+MADlib: svec_util.sql_in File Reference
+
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
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+  
    
+  
    
+
    
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+
    
+
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+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    svec_util.sql_in File Reference
      
    
+
    
+
    
+
+
    SQL utility functions for sparse vector data type svec  
+More...
    
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+Functions
    svec __gen_svec (bigint[], float8[], bigint)
     
    text gen_doc_svecs (text output_tbl, text dictionary_tbl, text dict_id_col, text dict_term_col, text documents_tbl, text doc_id_col, text doc_term_col, text doc_term_info_col)
     
    text gen_doc_svecs ()
     
    float8 svec_dmin (float8, float8)
     
    float8 svec_dmax (float8, float8)
     
    svec svec_count (svec, svec)
     
    svec svec_log (svec)
     Computes the logarithm of each element of the input SVEC.  More...
     
    boolean svec_eq_non_zero (svec, svec)
     
    boolean svec_contains (svec, svec)
     
    float8 svec_l2norm (svec)
     
    float8 svec_l2norm (float8[])
     
    float8 l2norm (svec, svec)
     
    float8 l1norm (svec, svec)
     
    float8 svec_l1norm (svec)
     
    float8 svec_l1norm (float8[])
     
    float8 angle (svec, svec)
     
    float8 tanimoto_distance (svec, svec)
     
    set< float8 > svec_unnest (svec)
     
    svec svec_pivot (svec, float8)
     
    float8 svec_elsum (svec)
     
    float8 svec_elsum (float8[])
     
    float8 svec_median (float8[])
     
    float8 svec_median (svec)
     
    int8 [] svec_nonbase_positions (svec, float8)
     
    float8 [] svec_nonbase_values (svec, float8)
     
    integer svec_dimension (svec)
     
    svec svec_lapply (text, svec)
     
    svec svec_append (svec, float8, int8)
     
    float8 svec_proj (svec, int4)
     
    svec svec_subvec (svec, int4, int4)
     
    svec svec_reverse (svec)
     
    svec svec_change (svec, int4, svec)
     
    int4 svec_hash (svec)
     
    svec svec_sfv (text[], text[])
     
    text [] svec_sort (text[])
     
    text svec_to_string (svec)
     
    svec svec_from_string (text)
     
    float [] svec_mean_transition (float[], svec)
     
    float [] svec_mean_prefunc (float[], float[])
     
    svec svec_mean_final (float[])
     
    aggregate float [] mean (svec)
     
    aggregate svec svec_sum (svec)
     
    aggregate svec svec_count_nonzero (svec)
     
    aggregate svec svec_median_inmemory (float8)
     
    svec normalize (svec)
     
    
+
    Detailed Description
    
+
    See also
    For an introduction to the sparse vector implementation, see the module description Sparse Vectors. 
    
+
    Function Documentation
    
+
+
    ◆ __gen_svec()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
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+        
+          
+          
+          
+        
+      
    svec __gen_svec (bigint [], 
    float8 [], 
    bigint  
    )
    
+
    
+
    Creates sparse vector representation given an array of indexes, respective values and size of the required vector. The function just does the bucket filling with the values at the respective indexes for the vector given the length. 
    
+
+
    
+
    
+
+
    ◆ angle()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 angle (svec , 
    svec  
    )
    
+
    
+
    Computes the angle between two SVECs in radians. 
    
+
+
    
+
    
+
+
    ◆ gen_doc_svecs() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
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+        
+        
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+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    text gen_doc_svecs (text output_tbl, 
    text dictionary_tbl, 
    text dict_id_col, 
    text dict_term_col, 
    text documents_tbl, 
    text doc_id_col, 
    text doc_term_col, 
    text doc_term_info_col 
    )
    
+
    
+
    Creates the output table containing the sparse vector representation for the documents given the dictionary table, documents tables and names of the respective columns. 
    
+
+
    
+
    
+
+
    ◆ gen_doc_svecs() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text gen_doc_svecs ()
    
+
    
+
    Helper function for madlib.gen_doc_svec UDF. 
    
+
+
    
+
    
+
+
    ◆ l1norm()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 l1norm (svec , 
    svec  
    )
    
+
    
+
    Computes the l1norm distance between two SVECs. 
    
+
+
    
+
    
+
+
    ◆ l2norm()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 l2norm (svec , 
    svec  
    )
    
+
    
+
    Computes the l2norm distance between two SVECs. 
    
+
+
    
+
    
+
+
    ◆ mean()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate float [] mean (svec )
    
+
    
+
    Aggregate that computes the element-wise mean of a list of vectors. 
    
+
+
    
+
    
+
+
    ◆ normalize()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec normalize (svec )
    
+
    
+
    Normalizes an SVEC that is divides all elements by its norm/magnitude. 
    
+
+
    
+
    
+
+
    ◆ svec_append()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_append (svec , 
    float8 , 
    int8  
    )
    
+
    
+
    Appends a run-length block to the back of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_change()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_change (svec , 
    int4 , 
    svec  
    )
    
+
    
+
    Replaces the subvector of a given SVEC at a given start index with another SVEC. Note that element index should start at 1. 
    
+
+
    
+
    
+
+
    ◆ svec_contains()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_contains (svec , 
    svec  
    )
    
+
    
+
    Returns true if left svec contains right one, meaning that every non-zero value in the right svec equals left one 
    
+
+
    
+
    
+
+
    ◆ svec_count()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_count (svec , 
    svec  
    )
    
+
    
+
    Counts the number of non-zero entries in the input vector; the second argument is capped at 1, then added to the first; used as the sfunc in the svec_count_nonzero() aggregate below. 
    
+
+
    
+
    
+
+
    ◆ svec_count_nonzero()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate svec svec_count_nonzero (svec )
    
+
    
+
    Aggregate that provides a tally of nonzero entries in a list of vectors. 
    
+
+
    
+
    
+
+
    ◆ svec_dimension()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    integer svec_dimension (svec )
    
+
    
+
    Returns the dimension of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_dmax()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_dmax (float8 , 
    float8  
    )
    
+
    
+
    Basic floating point scalar operator: MAX. 
    
+
+
    
+
    
+
+
    ◆ svec_dmin()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_dmin (float8 , 
    float8  
    )
    
+
    
+
    Basic floating point scalar operator: MIN. 
    
+
+
    
+
    
+
+
    ◆ svec_elsum() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_elsum (svec )
    
+
    
+
    Sums the elements of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_elsum() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_elsum (float8 [])
    
+
    
+
    Sums the elements of a float8 array. 
    
+
+
    
+
    
+
+
    ◆ svec_eq_non_zero()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean svec_eq_non_zero (svec , 
    svec  
    )
    
+
    
+
    Returns true if two SVECs are equal, not counting zeros (zero equals anything). If the two SVECs are of different size, then the function essentially zero-pads the shorter one and performs the comparison. 
    
+
+
    
+
    
+
+
    ◆ svec_from_string()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_from_string (text )
    
+
    
+
    Converts a text string to an svec 
    
+
+
    
+
    
+
+
    ◆ svec_hash()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    int4 svec_hash (svec )
    
+
    
+
    Computes the hash of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l1norm() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_l1norm (svec )
    
+
    
+
    Computes the l1norm of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l1norm() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_l1norm (float8 [])
    
+
    
+
    Computes the l1norm of a float8 array. 
    
+
+
    
+
    
+
+
    ◆ svec_l2norm() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_l2norm (svec )
    
+
    
+
    Computes the l2norm of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_l2norm() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_l2norm (float8 [])
    
+
    
+
    Computes the l2norm of a float8 array. 
    
+
+
    
+
    
+
+
    ◆ svec_lapply()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_lapply (text , 
    svec  
    )
    
+
    
+
    Applies a given function to each element of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_log()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_log (svec )
    
+
    
+
+
    
+
    
+
+
    ◆ svec_mean_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_mean_final (float [])
    
+
    
+
    Final function for mean(svec) aggregate 
    
+
+
    
+
    
+
+
    ◆ svec_mean_prefunc()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float [] svec_mean_prefunc (float [], 
    float [] 
    )
    
+
    
+
    Preliminary merge function for mean(svec) aggregate 
    
+
+
    
+
    
+
+
    ◆ svec_mean_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float [] svec_mean_transition (float [], 
    svec  
    )
    
+
    
+
    Transition function for mean(svec) aggregate 
    
+
+
    
+
    
+
+
    ◆ svec_median() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_median (float8 [])
    
+
    
+
    Computes the median element of a float8 array. 
    
+
+
    
+
    
+
+
    ◆ svec_median() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 svec_median (svec )
    
+
    
+
    Computes the median element of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_median_inmemory()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate svec svec_median_inmemory (float8 )
    
+
    
+
    Aggregate that turns a list of float8 values into an SVEC.Aggregate that computes the median element of a list of float8 values. 
    
+
+
    
+
    
+
+
    ◆ svec_nonbase_positions()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    int8 [] svec_nonbase_positions (svec , 
    float8  
    )
    
+
    
+
    Compares an SVEC to a float8, and returns positions of all elements not equal to the float as an array. Element index here starts at 0. 
    
+
+
    
+
    
+
+
    ◆ svec_nonbase_values()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] svec_nonbase_values (svec , 
    float8  
    )
    
+
    
+
    Compares an SVEC to a float8, and returns values of all elements not equal to the float as an array. 
    
+
+
    
+
    
+
+
    ◆ svec_pivot()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_pivot (svec , 
    float8  
    )
    
+
    
+
    Appends an element to the back of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_proj()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 svec_proj (svec , 
    int4  
    )
    
+
    
+
    Projects onto an element of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_reverse()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    svec svec_reverse (svec )
    
+
    
+
    Reverses the elements of an SVEC. 
    
+
+
    
+
    
+
+
    ◆ svec_sfv()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_sfv (text [], 
    text [] 
    )
    
+
    
+
    Computes the word-occurence vector of a document 
    
+
+
    
+
    
+
+
    ◆ svec_sort()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text [] svec_sort (text [])
    
+
    
+
    Sorts an array of texts. This function should be in MADlib common. 
    
+
+
    
+
    
+
+
    ◆ svec_subvec()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    svec svec_subvec (svec , 
    int4 , 
    int4  
    )
    
+
    
+
    Extracts a subvector of an SVEC given the subvector's start and end indices. 
    
+
+
    
+
    
+
+
    ◆ svec_sum()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate svec svec_sum (svec )
    
+
    
+
    Aggregate that provides the element-wise sum of a list of vectors. 
    
+
+
    
+
    
+
+
    ◆ svec_to_string()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text svec_to_string (svec )
    
+
    
+
    Converts an svec to a text string 
    
+
+
    
+
    
+
+
    ◆ svec_unnest()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    set<float8> svec_unnest (svec )
    
+
    
+
    Unnests an SVEC into a table of uncompressed values 
    
+
+
    
+
    
+
+
    ◆ tanimoto_distance()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 tanimoto_distance (svec , 
    svec  
    )
    
+
    
+
    Computes the Tanimoto distance between two SVECs. 
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/svm_8sql__in.html b/docs/docs/v2.1.0/svm_8sql__in.html
new file mode 100644
index 00000000..6226b0cd
--- /dev/null
+++ b/docs/docs/v2.1.0/svm_8sql__in.html
@@ -0,0 +1,1607 @@
+
+
+
+
+
+
+
+
+MADlib: svm.sql_in File Reference
+
+
+
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+
+
+
+
+
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+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
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    svm.sql_in File Reference
      
    
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    SQL functions for SVM (Poisson)  
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    float8 [] linear_svm_igd_transition (float8[] state, float8[] ind_var, float8 dep_var, float8[] previous_state, integer dimension, float8 stepsize, float8 reg, boolean is_l2, integer n_tuples, float8 epsilon, boolean is_svc, float8 tuple_weight)
     
    float8 [] linear_svm_igd_merge (float8[] state1, float8[] state2)
     
    float8 [] linear_svm_igd_final (float8[] state)
     
    aggregate float8 [] linear_svm_igd_step (float8[] ind_var, float8 dep_var, float8[] previous_state, integer dimension, float8 stepsize, float8 reg, boolean is_l2, integer n_tuples, float8 epsilon, boolean is_svc, float8 tuple_weight)
     
    float8 internal_linear_svm_igd_distance (float8[] state1, float8[] state2)
     
    linear_svm_result internal_linear_svm_igd_result (float8[] state)
     
    void svm_regression (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params, text grouping_col, text params, bool verbose)
     
    void svm_regression (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params, text grouping_col, text params)
     
    void svm_regression (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params, text grouping_col)
     
    void svm_regression (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params)
     
    void svm_regression (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func)
     
    void svm_regression (text source_table, text model_table, text dependent_varname, text independent_varname)
     
    void svm_classification (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params, text grouping_col, text params, bool verbose)
     
    void svm_classification (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params, text grouping_col, text params)
     
    void svm_classification (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params, text grouping_col)
     
    void svm_classification (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func, text kernel_params)
     
    void svm_classification (text source_table, text model_table, text dependent_varname, text independent_varname, text kernel_func)
     
    void svm_classification (text source_table, text model_table, text dependent_varname, text independent_varname)
     
    void svm_one_class (text source_table, text model_table, text independent_varname, text kernel_func, text kernel_params, text grouping_col, text params, bool verbose)
     
    void svm_one_class (text source_table, text model_table, text independent_varname, text kernel_func, text kernel_params, text grouping_col, text params)
     
    void svm_one_class (text source_table, text model_table, text independent_varname, text kernel_func, text kernel_params, text grouping_col)
     
    void svm_one_class (text source_table, text model_table, text independent_varname, text kernel_func, text kernel_params)
     
    void svm_one_class (text source_table, text model_table, text independent_varname, text kernel_func)
     
    void svm_one_class (text source_table, text model_table, text independent_varname)
     
    void svm_predict (text model_table, text new_data_table, text id_col_name, text output_table)
     Scores the data points stored in a table using a learned linear support-vector model.  More...
     
    text svm_predict (text message)
     Help function.  More...
     
    text svm_predict ()
     
    text svm_classification (text message)
     
    text svm_classification ()
     
    text svm_one_class (text message)
     
    text svm_one_class ()
     
    text svm_regression (text message)
     
    text svm_regression ()
     
    
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    Detailed Description
    
+
    Date
    July 2015
    
+
    See also
    For a brief introduction to SVM (Poisson), see the module description Support Vector Machines. 
    
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    Function Documentation
    
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    ◆ internal_linear_svm_igd_distance()
    
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    float8 internal_linear_svm_igd_distance (float8 [] state1, 
    float8 [] state2 
    )
    
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    ◆ internal_linear_svm_igd_result()
    
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    linear_svm_result internal_linear_svm_igd_result (float8 [] state)
    
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    ◆ linear_svm_igd_final()
    
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    float8 [] linear_svm_igd_final (float8 [] state)
    
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    ◆ linear_svm_igd_merge()
    
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    float8 [] linear_svm_igd_merge (float8 [] state1, 
    float8 [] state2 
    )
    
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    ◆ linear_svm_igd_step()
    
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    aggregate float8 [] linear_svm_igd_step (float8 [] ind_var, 
    float8 dep_var, 
    float8 [] previous_state, 
    integer dimension, 
    float8 stepsize, 
    float8 reg, 
    boolean is_l2, 
    integer n_tuples, 
    float8 epsilon, 
    boolean is_svc, 
    float8 tuple_weight 
    )
    
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    ◆ linear_svm_igd_transition()
    
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    float8 [] linear_svm_igd_transition (float8 [] state, 
    float8 [] ind_var, 
    float8 dep_var, 
    float8 [] previous_state, 
    integer dimension, 
    float8 stepsize, 
    float8 reg, 
    boolean is_l2, 
    integer n_tuples, 
    float8 epsilon, 
    boolean is_svc, 
    float8 tuple_weight 
    )
    
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    void svm_classification (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col, 
    text params, 
    bool verbose 
    )
    
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    void svm_classification (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col, 
    text params 
    )
    
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    void svm_classification (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col 
    )
    
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    void svm_classification (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params 
    )
    
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    void svm_classification (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func 
    )
    
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    void svm_classification (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname 
    )
    
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    text svm_classification (text message)
    
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    ◆ svm_classification() [8/8]
    
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    text svm_classification ()
    
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    ◆ svm_one_class() [1/8]
    
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    void svm_one_class (text source_table, 
    text model_table, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col, 
    text params, 
    bool verbose 
    )
    
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    void svm_one_class (text source_table, 
    text model_table, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col, 
    text params 
    )
    
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    ◆ svm_one_class() [3/8]
    
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    void svm_one_class (text source_table, 
    text model_table, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col 
    )
    
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    ◆ svm_one_class() [4/8]
    
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    void svm_one_class (text source_table, 
    text model_table, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params 
    )
    
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    ◆ svm_one_class() [5/8]
    
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    void svm_one_class (text source_table, 
    text model_table, 
    text independent_varname, 
    text kernel_func 
    )
    
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    void svm_one_class (text source_table, 
    text model_table, 
    text independent_varname 
    )
    
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    ◆ svm_one_class() [7/8]
    
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    text svm_one_class (text message)
    
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    ◆ svm_one_class() [8/8]
    
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    text svm_one_class ()
    
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    void svm_predict (text model_table, 
    text new_data_table, 
    text id_col_name, 
    text output_table 
    )
    
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    Parameters
    
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    model_tableName of table where the learned model to be used is stored 
    new_data_tableName of table/view containing the data points to be scored 
    id_colName of column in new_data_table containing the integer identifier of data points
    output_tableName of table to store the results
    
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    Returns
    Textual summary of the algorithm run 
    
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    ◆ svm_predict() [2/3]
    
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    text svm_predict (text message)
    
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    ◆ svm_predict() [3/3]
    
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    text svm_predict ()
    
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    ◆ svm_regression() [1/8]
    
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    void svm_regression (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col, 
    text params, 
    bool verbose 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svm_regression() [2/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svm_regression (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col, 
    text params 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svm_regression() [3/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
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+          
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+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svm_regression (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params, 
    text grouping_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svm_regression() [4/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svm_regression (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func, 
    text kernel_params 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svm_regression() [5/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svm_regression (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname, 
    text kernel_func 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svm_regression() [6/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
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+          
+          
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void svm_regression (text source_table, 
    text model_table, 
    text dependent_varname, 
    text independent_varname 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ svm_regression() [7/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text svm_regression (text message)
    
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+
    
+
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    ◆ svm_regression() [8/8]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text svm_regression ()
    
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diff --git a/docs/docs/v2.1.0/sync_off.png b/docs/docs/v2.1.0/sync_off.png
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diff --git a/docs/docs/v2.1.0/table__to__pmml_8sql__in.html b/docs/docs/v2.1.0/table__to__pmml_8sql__in.html
new file mode 100644
index 00000000..13472dad
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+++ b/docs/docs/v2.1.0/table__to__pmml_8sql__in.html
@@ -0,0 +1,253 @@
+
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+MADlib: table_to_pmml.sql_in File Reference
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+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
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+  
    
+Functions  
    
+  
    
+
    table_to_pmml.sql_in File Reference
      
    
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+
    
+Functions
    xml pmml (varchar model_table)
     Given the model constructed from a data mining algorithm, this function converts the model into PMML format.  More...
     
    xml pmml (varchar model_table, varchar name_spec)
     Given the model constructed from a data mining algorithm, this function converts the model into PMML format.  More...
     
    xml pmml (varchar model_table, varchar[] name_spec)
     Given the model constructed from a data mining algorithm, this function converts the model into PMML format.  More...
     
    text pmml ()
     
    
+
    Function Documentation
    
+
+
    ◆ pmml() [1/4]
    
+
+
    
+
    
+      
+        
+          
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+          
+          
+          
+        
+      
    xml pmml (varchar model_table)
    
+
    
+
    Parameters
    
+  
+    
+  
    model_tableModel table that contains the output of a training algorithm.
    
+  
    
+
    
+
    Returns
    An XML document corresponding to the PMML of the input model.
    
+
    The names in the Data Dictionary are generated based on the names used in the model table. If the fields are represented as an array of expressions without array concatenation, the names in the Data Dictionary will match the source table, except that a suffix '_pmml_prediction' is added to the predicted variable. If the field is an array of FLOAT8 values, the names in the Data Dictionary will be indexed using the array name, like 'ind[1]', 'ind[2]', etc. In all other cases, the names will simply be 'x[1]', 'x[2]', and so on. 
    
+
+
    
+
    
+
+
    ◆ pmml() [2/4]
    
+
+
    
+
    
+      
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+      
    xml pmml (varchar model_table, 
    varchar name_spec 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    model_tableModel table that contains the output of a training algorithm. 
    name_specNames to be used in the Data Dictionary, given as a string containing an expression such as 'y ~ x1 + x2 + x3'.
    
+  
    
+
    
+
    Returns
    An XML document corresponding to the PMML of the input model. 
    
+
+
    
+
    
+
+
    ◆ pmml() [3/4]
    
+
+
    
+
    
+      
+        
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+        
+      
    xml pmml (varchar model_table, 
    varchar [] name_spec 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    model_tableModel table that contains the output of a training algorithm. 
    name_specNames to be used in the Data Dictionary given as an array of strings, such as ARRAY['y', 'x1', 'x2', ...].
    
+  
    
+
    
+
    Returns
    An XML document corresponding to the PMML of the input model. 
    
+
+
    
+
    
+
+
    ◆ pmml() [4/4]
    
+
+
    
+
    
+      
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    text pmml ()
    
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diff --git a/docs/docs/v2.1.0/tabs.css b/docs/docs/v2.1.0/tabs.css
new file mode 100644
index 00000000..a28614b8
--- /dev/null
+++ b/docs/docs/v2.1.0/tabs.css
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li{border-top:0}.sm-dox>li>ul:before,.sm-dox>li>ul:after{content:'';position:absolute;top:-18px;left:30px;width:0;height:0;overflow:hidden;border-width:9px;border-style:dashed dashed solid dashed;border-color:transparent transparent #bbb transparent}.sm-dox>li>ul:after{top:-16px;left:31px;border-width:8px;border-color:transparent transparent #fff transparent}.sm-dox ul{border:1px solid #bbb;padding:5px 0;background:#fff;-moz-border-radius:5px!important;-webkit-border-radius:5px;border-radius:5px!important;-moz-box-shadow:0 5px 9px rgba(0,0,0,0.2);-webkit-box-shadow:0 5px 9px rgba(0,0,0,0.2);box-shadow:0 5px 9px rgba(0,0,0,0.2)}.sm-dox ul a span.sub-arrow{right:8px;top:50%;margin-top:-5px;border-width:5px;border-color:transparent transparent transparent #555;border-style:dashed dashed dashed solid}.sm-dox ul a,.sm-dox ul a:hover,.sm-dox ul a:focus,.sm-dox ul a:active,.sm-dox ul a.highlighted{color:#555;background-image:none;border:0!important;color:#555;background-image:none}.sm-dox ul a:hover{background-image:url("tab_a.png");background-repeat:repeat-x;color:white;text-shadow:0 1px 1px black}.sm-dox ul a:hover span.sub-arrow{border-color:transparent transparent transparent white}.sm-dox span.scroll-up,.sm-dox span.scroll-down{position:absolute;display:none;visibility:hidden;overflow:hidden;background:#fff;height:36px}.sm-dox span.scroll-up:hover,.sm-dox span.scroll-down:hover{background:#eee}.sm-dox span.scroll-up:hover span.scroll-up-arrow,.sm-dox span.scroll-up:hover span.scroll-down-arrow{border-color:transparent transparent #d23600 transparent}.sm-dox span.scroll-down:hover span.scroll-down-arrow{border-color:#d23600 transparent transparent transparent}.sm-dox span.scroll-up-arrow,.sm-dox span.scroll-down-arrow{position:absolute;top:0;left:50%;margin-left:-6px;width:0;height:0;overflow:hidden;border-width:6px;border-style:dashed dashed solid dashed;border-color:transparent transparent #555 transparent}.sm-dox span.scroll-down-arrow{top:8px;border-style:solid dashed dashed dashed;border-color:#555 transparent transparent transparent}.sm-dox.sm-rtl a.has-submenu{padding-right:12px;padding-left:24px}.sm-dox.sm-rtl a span.sub-arrow{right:auto;left:12px}.sm-dox.sm-rtl.sm-vertical a.has-submenu{padding:10px 20px}.sm-dox.sm-rtl.sm-vertical a span.sub-arrow{right:auto;left:8px;border-style:dashed solid dashed dashed;border-color:transparent #555 transparent transparent}.sm-dox.sm-rtl>li>ul:before{left:auto;right:30px}.sm-dox.sm-rtl>li>ul:after{left:auto;right:31px}.sm-dox.sm-rtl ul a.has-submenu{padding:10px 20px!important}.sm-dox.sm-rtl ul a span.sub-arrow{right:auto;left:8px;border-style:dashed solid dashed dashed;border-color:transparent #555 transparent transparent}.sm-dox.sm-vertical{padding:10px 0;-moz-border-radius:5px;-webkit-border-radius:5px;border-radius:5px}.sm-dox.sm-vertical a{padding:10px 20px}.sm-dox.sm-vertical a:hover,.sm-dox.sm-vertical a:focus,.sm-dox.sm-vertical a:active,.sm-dox.sm-vertical a.highlighted{background:#fff}.sm-dox.sm-vertical a.disabled{background-image:url("tab_b.png")}.sm-dox.sm-vertical a span.sub-arrow{right:8px;top:50%;margin-top:-5px;border-width:5px;border-style:dashed dashed dashed solid;border-color:transparent transparent transparent #555}.sm-dox.sm-vertical>li>ul:before,.sm-dox.sm-vertical>li>ul:after{display:none}.sm-dox.sm-vertical ul a{padding:10px 20px}.sm-dox.sm-vertical ul a:hover,.sm-dox.sm-vertical ul a:focus,.sm-dox.sm-vertical ul a:active,.sm-dox.sm-vertical ul a.highlighted{background:#eee}.sm-dox.sm-vertical ul a.disabled{background:#fff}}
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diff --git a/docs/docs/v2.1.0/text__utilities_8sql__in.html b/docs/docs/v2.1.0/text__utilities_8sql__in.html
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+MADlib: text_utilities.sql_in File Reference
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    User Documentation for Apache MADlib
    
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    text_utilities.sql_in File Reference
      
    
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    SQL functions for carrying out routine text operations.  
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    text term_frequency (text input_table, text doc_id_col, text word_vec_col, text output_table, boolean compute_vocab)
     Compute the term frequency for each term in a collection of documents.  More...
     
    text term_frequency (text input_table, text doc_id_col, text word_vec_col, text output_table)
     
    
+
    Detailed Description
    
+
    See also
    For a brief overview of utility functions, see the module description Database Functions. 
    
+
    Function Documentation
    
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    ◆ term_frequency() [1/2]
    
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    text term_frequency (text input_table, 
    text doc_id_col, 
    text word_vec_col, 
    text output_table, 
    boolean compute_vocab 
    )
    
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    Returns
    Names of tables created 
    
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    ◆ term_frequency() [2/2]
    
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    text term_frequency (text input_table, 
    text doc_id_col, 
    text word_vec_col, 
    text output_table 
    )
    
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diff --git a/docs/docs/v2.1.0/train__test__split_8sql__in.html b/docs/docs/v2.1.0/train__test__split_8sql__in.html
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+MADlib: train_test_split.sql_in File Reference
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+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
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    SQL functions for test train split.  
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    void train_test_split (text source_table, text output_table, float8 train_proportion, float8 test_proportion, text grouping_cols, text target_cols, boolean with_replacement, boolean separate_output_tables)
     
    void train_test_split (text source_table, text output_table, float8 train_proportion, float8 test_proportion, text grouping_cols, text target_cols, boolean with_replacement)
     
    void train_test_split (text source_table, text output_table, float8 train_proportion, float8 test_proportion, text grouping_cols, text target_cols)
     
    void train_test_split (text source_table, text output_table, float8 train_proportion, float8 test_proportion, text grouping_cols)
     
    void train_test_split (text source_table, text output_table, float8 train_proportion, float8 test_proportion)
     
    void train_test_split (text source_table, text output_table, float8 train_proportion)
     
    varchar train_test_split (varchar message)
     
    varchar train_test_split ()
     
    
+
    Detailed Description
    
+
    Licensed to the Apache Software Foundation (ASF) under one or more contributor license agreements. See the NOTICE file distributed with this work for additional information regarding copyright ownership. The ASF licenses this file to you under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
    
+
    http://www.apache.org/licenses/LICENSE-2.0
    
+
    Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
    
+
    Date
    07/19/2017
    
+
    See also
    Given a table, test train split returns a proportion of records for each group (strata). 
    
+
    Function Documentation
    
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    ◆ train_test_split() [1/8]
    
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    void train_test_split (text source_table, 
    text output_table, 
    float8 train_proportion, 
    float8 test_proportion, 
    text grouping_cols, 
    text target_cols, 
    boolean with_replacement, 
    boolean separate_output_tables 
    )
    
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    ◆ train_test_split() [2/8]
    
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    void train_test_split (text source_table, 
    text output_table, 
    float8 train_proportion, 
    float8 test_proportion, 
    text grouping_cols, 
    text target_cols, 
    boolean with_replacement 
    )
    
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    ◆ train_test_split() [3/8]
    
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    void train_test_split (text source_table, 
    text output_table, 
    float8 train_proportion, 
    float8 test_proportion, 
    text grouping_cols, 
    text target_cols 
    )
    
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    ◆ train_test_split() [4/8]
    
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    void train_test_split (text source_table, 
    text output_table, 
    float8 train_proportion, 
    float8 test_proportion, 
    text grouping_cols 
    )
    
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    ◆ train_test_split() [5/8]
    
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    void train_test_split (text source_table, 
    text output_table, 
    float8 train_proportion, 
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    )
    
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    varchar train_test_split (varchar message)
    
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diff --git a/docs/docs/v2.1.0/utilities_8sql__in.html b/docs/docs/v2.1.0/utilities_8sql__in.html
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+   
    User Documentation for Apache MADlib
    
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    utilities.sql_in File Reference
      
    
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    SQL functions for carrying out routine tasks.  
+More...
    
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+Functions
    void cleanup_madlib_temp_tables (text target_schema)
     Drop all tables matching pattern 'madlib_temp' in a given schema.  More...
     
    text cleanup_madlib_temp_tables_script (text target_schema)
     
    void cleanup_madlib_temp_views (text target_schema)
     
    text version ()
     Return MADlib build information.  More...
     
    void assert (boolean condition, varchar msg)
     Raise an exception if the given condition is not satisfied.  More...
     
    float8 relative_error (float8 approx, float8 value)
     Compute the relative error of an approximate value.  More...
     
    float8 relative_error (float8[] approx, float8[] value)
     Compute the relative error (w.r.t. the 2-norm) of an apprixmate vector.  More...
     
    boolean check_if_raises_error (text sql)
     Check if a SQL statement raises an error.  More...
     
    boolean check_if_col_exists (text source_table, text column_name)
     Check if a column exists in a table.  More...
     
    boolean isnan (float8 number)
     Check if a floating-point number is NaN (not a number)  More...
     
    void create_schema_pg_temp ()
     Create the temporary schema if it does not exist yet.  More...
     
    void noop ()
     Create volatile noop function.  More...
     
    bytea8 bytea8in (cstring)
     
    cstring bytea8out (bytea8)
     
    bytea8 bytea8recv (internal)
     
    bytea bytea8send (bytea8)
     
    varchar __internal_get_col_names_except_dep_variable (varchar source_table, varchar dependent_varname)
     Get all column names except dependent variable.  More...
     
    varchar __unique_string ()
     Generate random remporary names for temp table and other names.  More...
     
    varchar [] _string_to_array (varchar s)
     Takes a string of comma separated values and puts it into an array.  More...
     
    text bool_to_text (boolean)
     Cast boolean into text.  More...
     
    text __to_char (anyelement val)
     Cast any value to text.  More...
     
    set< _grp_state_type > _gen_state (text[] grp_key, integer[] iteration, float8[] state)
     
    float8 _final_mode (float8[])
     
    aggregate float8 mode (float8)
     
    void dropcols (varchar source_table, varchar out_table, varchar cols_to_drop)
     Creates a new table with a subset of columns dropped from another source table.  More...
     
    boolean is_pg_major_version_less_than (integer compare_version)
     
    integer trap_error (text stmt)
     
    boolean test_error_msg (text stmt, text msg)
     
    boolean test_input_table (text stmt)
     
    boolean test_output_table (text stmt)
     
    boolean is_ver_gp_640_700_or_pg_11 ()
     
    void assert_guc_value (text guc_name, text expected_guc_value)
     
    boolean is_table_unlogged (text tbl_name)
     
    
+
    Detailed Description
    
+
    See also
    For a brief overview of utility functions, see the module description Database Functions. 
    
+
    Function Documentation
    
+
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    ◆ __internal_get_col_names_except_dep_variable()
    
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+        
+      
    varchar __internal_get_col_names_except_dep_variable (varchar source_table, 
    varchar dependent_varname 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __to_char()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text __to_char (anyelement val)
    
+
    
+
    Parameters
    
+  
+    
+  
    valA value with any specific type.
    
+  
    
+
    
+
    Returns
    The text format string for the value.
    
+
    Note
    Greenplum doesn't support bit/boolean to text casting. 
    
+
+
    
+
    
+
+
    ◆ __unique_string()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar __unique_string ()
    
+
    
+
+
    
+
    
+
+
    ◆ _final_mode()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 _final_mode (float8 [])
    
+
    
+
+
    
+
    
+
+
    ◆ _gen_state()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    set<_grp_state_type> _gen_state (text [] grp_key, 
    integer [] iteration, 
    float8 [] state 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ _string_to_array()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar [] _string_to_array (varchar s)
    
+
    
+
+
    
+
    
+
+
    ◆ assert()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void assert (boolean condition, 
    varchar msg 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ assert_guc_value()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void assert_guc_value (text guc_name, 
    text expected_guc_value 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ bool_to_text()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text bool_to_text (boolean )
    
+
    
+
+
    
+
    
+
+
    ◆ bytea8in()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bytea8 bytea8in (cstring )
    
+
    
+
+
    
+
    
+
+
    ◆ bytea8out()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    cstring bytea8out (bytea8 )
    
+
    
+
+
    
+
    
+
+
    ◆ bytea8recv()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bytea8 bytea8recv (internal )
    
+
    
+
+
    
+
    
+
+
    ◆ bytea8send()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    bytea bytea8send (bytea8 )
    
+
    
+
+
    
+
    
+
+
    ◆ check_if_col_exists()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean check_if_col_exists (text source_table, 
    text column_name 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+  
    source_tableSource table 
    column_nameColumn name in the table 
    
+  
    
+
    
+
    Returns
    TRUE if it exists and FALSE if not 
    
+
+
    
+
    
+
+
    ◆ check_if_raises_error()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    boolean check_if_raises_error (text sql)
    
+
    
+
    Parameters
    
+  
+    
+  
    sqlThe SQL statement 
    
+  
    
+
    
+
    Returns
    TRUE if an exception is raised while executing sql, FALSE otherwise. 
    
+
+
    
+
    
+
+
    ◆ cleanup_madlib_temp_tables()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    void cleanup_madlib_temp_tables (text target_schema)
    
+
    
+
    Parameters
    
+  
+    
+  
    target_schemaTEXT. The schema that takes affect. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ cleanup_madlib_temp_tables_script()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text cleanup_madlib_temp_tables_script (text target_schema)
    
+
    
+
+
    
+
    
+
+
    ◆ cleanup_madlib_temp_views()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    void cleanup_madlib_temp_views (text target_schema)
    
+
    
+
+
    
+
    
+
+
    ◆ create_schema_pg_temp()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    void create_schema_pg_temp ()
    
+
    
+
+
    
+
    
+
+
    ◆ dropcols()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void dropcols (varchar source_table, 
    varchar out_table, 
    varchar cols_to_drop 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    source_tableName of the table containing the source data. 
    out_tableName of the generated table containing the output. If a table with the same name already exists, an error will be returned. 
    cols_to_dropComma-separated string of column names from the source table to drop. An error is returned if the output table does not contain any columns or if a requested column is not present in the source table. 
    
+  
    
+
    
+
+
    
+
    
+
+
    ◆ is_pg_major_version_less_than()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    boolean is_pg_major_version_less_than (integer compare_version)
    
+
    
+
+
    
+
    
+
+
    ◆ is_table_unlogged()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    boolean is_table_unlogged (text tbl_name)
    
+
    
+
+
    
+
    
+
+
    ◆ is_ver_gp_640_700_or_pg_11()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    boolean is_ver_gp_640_700_or_pg_11 ()
    
+
    
+
+
    
+
    
+
+
    ◆ isnan()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    boolean isnan (float8 number)
    
+
    
+
    This function exists for portability. Some DBMSs like PostgreSQL treat floating-point numbers as fully ordered – contrary to IEEE 754. (See, e.g., the PostgreSQL documentation. For portability, MADlib code should not make use of such "features" directly, but only use isnan() instead.
    
+
    Parameters
    
+  
+    
+  
    number
    
+  
    
+
    
+
    Returns
    TRUE if number is NaN, FALSE otherwise 
    
+
+
    
+
    
+
+
    ◆ mode()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    aggregate float8 mode (float8 )
    
+
    
+
+
    
+
    
+
+
    ◆ noop()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    void noop ()
    
+
    
+
    The only use of this function is as an optimization fence when used in the SELECT list of a query. See, e.g., http://archives.postgresql.org/pgsql-sql/2012-07/msg00030.php 
    
+
+
    
+
    
+
+
    ◆ relative_error() [1/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 relative_error (float8 approx, 
    float8 value 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ relative_error() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 relative_error (float8 [] approx, 
    float8 [] value 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ test_error_msg()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    boolean test_error_msg (text stmt, 
    text msg 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ test_input_table()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    boolean test_input_table (text stmt)
    
+
    
+
+
    
+
    
+
+
    ◆ test_output_table()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    boolean test_output_table (text stmt)
    
+
    
+
+
    
+
    
+
+
    ◆ trap_error()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    integer trap_error (text stmt)
    
+
    
+
+
    
+
    
+
+
    ◆ version()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text version ()
    
+
    
+
    Returns
    Summary of MADlib build information, consisting of MADlib version, git revision, cmake configuration time, build type, build system, C compiler, and C++ compiler 
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/utils__regularization_8sql__in.html b/docs/docs/v2.1.0/utils__regularization_8sql__in.html
new file mode 100644
index 00000000..0c96661c
--- /dev/null
+++ b/docs/docs/v2.1.0/utils__regularization_8sql__in.html
@@ -0,0 +1,349 @@
+
+
+
+
+
+
+
+
+MADlib: utils_regularization.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    utils_regularization.sql_in File Reference
      
    
+
    
+
    
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    __utils_scales __utils_var_scales_result (float8[] in_state)
     
    float8 [] __utils_var_scales_transition (float8[] state, float8[] ind_var, integer dimension)
     
    float8 [] __utils_var_scales_merge (float8[] state1, float8[] state2)
     
    float8 [] __utils_var_scales_final (float8[] state)
     
    float8 [] __utils_var_scales_non_zero_std_final (float8[] state)
     
    aggregate float8 [] utils_var_scales (float8[], integer)
     
    aggregate float8 [] utils_var_scales_non_zero_std (float8[], integer)
     
    float8 [] utils_normalize_data (float8[] x, float8[] mean, float8[] std)
     
    
+
    Function Documentation
    
+
+
    ◆ __utils_var_scales_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __utils_var_scales_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __utils_var_scales_merge()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __utils_var_scales_merge (float8 [] state1, 
    float8 [] state2 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ __utils_var_scales_non_zero_std_final()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    float8 [] __utils_var_scales_non_zero_std_final (float8 [] state)
    
+
    
+
+
    
+
    
+
+
    ◆ __utils_var_scales_result()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    __utils_scales __utils_var_scales_result (float8 [] in_state)
    
+
    
+
+
    
+
    
+
+
    ◆ __utils_var_scales_transition()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] __utils_var_scales_transition (float8 [] state, 
    float8 [] ind_var, 
    integer dimension 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ utils_normalize_data()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    float8 [] utils_normalize_data (float8 [] x, 
    float8 [] mean, 
    float8 [] std 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ utils_var_scales()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] utils_var_scales (float8 [], 
    integer  
    )
    
+
    
+
+
    
+
    
+
+
    ◆ utils_var_scales_non_zero_std()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    aggregate float8 [] utils_var_scales_non_zero_std (float8 [], 
    integer  
    )
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/docs/v2.1.0/vec2cols_8sql__in.html b/docs/docs/v2.1.0/vec2cols_8sql__in.html
new file mode 100644
index 00000000..9922297b
--- /dev/null
+++ b/docs/docs/v2.1.0/vec2cols_8sql__in.html
@@ -0,0 +1,292 @@
+
+
+
+
+
+
+
+
+MADlib: vec2cols.sql_in File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+
    
+
+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
+
+
+
+
    
+
    
+  
+  
    
+  
    
+
    
+
+
    
+
+
    
+
    
+
+
+
    
+
+
    
+
+
    
+  
    
+Functions  
    
+  
    
+
    vec2cols.sql_in File Reference
      
    
+
    
+
    
+
+
+
+
+
+
+
+
+
+
+
+
+
    
+Functions
    void vec2cols (varchar source_table, varchar output_table, varchar vector_col, text[] feature_names, varchar cols_to_output)
     
    void vec2cols (varchar source_table, varchar output_table, varchar vector_col, text[] feature_names)
     
    void vec2cols (varchar source_table, varchar output_table, varchar vector_col)
     
    text vec2cols (text message)
     
    text vec2cols ()
     
    
+
    Function Documentation
    
+
+
    ◆ vec2cols() [1/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void vec2cols (varchar source_table, 
    varchar output_table, 
    varchar vector_col, 
    text [] feature_names, 
    varchar cols_to_output 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ vec2cols() [2/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void vec2cols (varchar source_table, 
    varchar output_table, 
    varchar vector_col, 
    text [] feature_names 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ vec2cols() [3/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void vec2cols (varchar source_table, 
    varchar output_table, 
    varchar vector_col 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ vec2cols() [4/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    text vec2cols (text message)
    
+
    
+
+
    
+
    
+
+
    ◆ vec2cols() [5/5]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    text vec2cols ()
    
+
    
+
+
    
+
    
+
    
+
    
+
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+
diff --git a/docs/docs/v2.1.0/viterbi_8sql__in.html b/docs/docs/v2.1.0/viterbi_8sql__in.html
new file mode 100644
index 00000000..7b34766d
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+++ b/docs/docs/v2.1.0/viterbi_8sql__in.html
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+
+
+
+
+
+
+
+
+MADlib: viterbi.sql_in File Reference
+
+
+
+
+
+
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+
+
+
+
+
+
+
+
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
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+  
    
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+
    
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+
    
+  
    
+Functions  
    
+  
    
+
    viterbi.sql_in File Reference
      
    
+
    
+
    
+
+
    concatenate a set of input values into arrays to feed into viterbi c function and create a human readable view of the output  
+More...
    
+
+
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+
    
+Functions
    text vcrf_top1_table (text segment_tbl, text label_tbl, text resulttbl_raw, text result_tbl)
     This function creates the specified result_tbl containing top1 labels for the sequence.  More...
     
    int [] vcrf_top1_label (float8[] marray, float8[] rarray, int nlabel)
     This function implements the Viterbi algorithm which takes the sentence to be label as input and return the top1 labeling for that sentence.  More...
     
    text vcrf_label (text segment_tbl, text factor_mtbl, text factor_rtbl, text label_tbl, text result_tbl)
     This function prepares the inputs for the c function 'vcrf_top1_label' and invoke the c function.  More...
     
    
+
    Detailed Description
    
+
    Date
    February 2012 
    
+
    Function Documentation
    
+
+
    ◆ vcrf_label()
    
+
+
    
+
    
+      
+        
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+        
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+          
+          
+        
+      
    text vcrf_label (text segment_tbl, 
    text factor_mtbl, 
    text factor_rtbl, 
    text label_tbl, 
    text result_tbl 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+    
+    
+  
    segment_tblName of table containing all the testing sentences. 
    factor_mtblName of table containing all the m factors. 
    factor_rtblName of table containing all the r factors. 
    label_tblName of table containing all the labels in the label space. 
    result_tblName of table to store the output 
    
+  
    
+
    
+
    Returns
    the top1 label sequence, the last two elements in the array is used to calculate the top1 probability 
    
+
+
    
+
    
+
+
    ◆ vcrf_top1_label()
    
+
+
    
+
    
+      
+        
+          
+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    int [] vcrf_top1_label (float8 [] marray, 
    float8 [] rarray, 
    int nlabel 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    marrayName of arrays containing m factors 
    rarrayName of arrays containing r factors 
    nlabelTotal number of labels in the label space 
    
+  
    
+
    
+
    Returns
    the top1 label sequence, the last two elements in the array is used to calculate the top1 probability 
    
+
+
    
+
    
+
+
    ◆ vcrf_top1_table()
    
+
+
    
+
    
+      
+        
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+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    text vcrf_top1_table (text segment_tbl, 
    text label_tbl, 
    text resulttbl_raw, 
    text result_tbl 
    )
    
+
    
+
    Parameters
    
+  
+    
+    
+    
+  
    segment_tblName of table containing all the testing sentences. 
    label_tblName of table containing all the labels in the label space. 
    result_tblName of table storing the best label sequence and the conditional probability. 
    
+  
    
+
    
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diff --git a/docs/docs/v2.1.0/wcc_8sql__in.html b/docs/docs/v2.1.0/wcc_8sql__in.html
new file mode 100644
index 00000000..734edc88
--- /dev/null
+++ b/docs/docs/v2.1.0/wcc_8sql__in.html
@@ -0,0 +1,592 @@
+
+
+
+
+
+
+
+
+MADlib: wcc.sql_in File Reference
+
+
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+
    
+
    
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+ 
+ 
+  
+  
+   
+ 
+ 
+
    
+   
    
+   2.1.0
+   
    
+   
    User Documentation for Apache MADlib
    
+      		        
    
+        
+          
+          
+          
+            
+          
+        
    
+
    
+
    
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+Functions  
    
+  
    
+
    wcc.sql_in File Reference
      
    
+
    
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+Functions
    void weakly_connected_components (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, text grouping_cols, integer iteration_limit, boolean warm_start)
     
    void weakly_connected_components (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, text grouping_cols, integer iteration_limit)
     
    void weakly_connected_components (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table, text grouping_cols)
     
    void weakly_connected_components (text vertex_table, text vertex_id, text edge_table, text edge_args, text out_table)
     
    void graph_wcc_largest_cpt (text wcc_table, text largest_cpt_table)
     
    void graph_wcc_histogram (text wcc_table, text histogram_table)
     
    void graph_wcc_vertex_check (text wcc_table, bigint[] vertex_pair, text pair_table)
     
    void graph_wcc_reachable_vertices (text wcc_table, bigint src, text reachable_vertices_table)
     
    void graph_wcc_reachable_vertices (text wcc_table, bigint[] src, text reachable_vertices_table)
     
    void graph_wcc_num_cpts (text wcc_table, text count_table)
     
    varchar weakly_connected_components (varchar message)
     
    varchar weakly_connected_components ()
     
    
+
    Function Documentation
    
+
+
    ◆ graph_wcc_histogram()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_wcc_histogram (text wcc_table, 
    text histogram_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_wcc_largest_cpt()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_wcc_largest_cpt (text wcc_table, 
    text largest_cpt_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_wcc_num_cpts()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_wcc_num_cpts (text wcc_table, 
    text count_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_wcc_reachable_vertices() [1/2]
    
+
+
    
+
    
+      
+        
+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_wcc_reachable_vertices (text wcc_table, 
    bigint src, 
    text reachable_vertices_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_wcc_reachable_vertices() [2/2]
    
+
+
    
+
    
+      
+        
+          
+          
+          
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+        
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+          
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+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_wcc_reachable_vertices (text wcc_table, 
    bigint [] src, 
    text reachable_vertices_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ graph_wcc_vertex_check()
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void graph_wcc_vertex_check (text wcc_table, 
    bigint [] vertex_pair, 
    text pair_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weakly_connected_components() [1/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
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+        
+        
+          
+          
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+        
+        
+          
+          
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+        
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+          
+        
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+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void weakly_connected_components (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    text grouping_cols, 
    integer iteration_limit, 
    boolean warm_start 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weakly_connected_components() [2/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void weakly_connected_components (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    text grouping_cols, 
    integer iteration_limit 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weakly_connected_components() [3/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void weakly_connected_components (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table, 
    text grouping_cols 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weakly_connected_components() [4/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+          
+        
+        
+          
+          
+          
+        
+      
    void weakly_connected_components (text vertex_table, 
    text vertex_id, 
    text edge_table, 
    text edge_args, 
    text out_table 
    )
    
+
    
+
+
    
+
    
+
+
    ◆ weakly_connected_components() [5/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+          
+        
+      
    varchar weakly_connected_components (varchar message)
    
+
    
+
+
    
+
    
+
+
    ◆ weakly_connected_components() [6/6]
    
+
+
    
+
    
+      
+        
+          
+          
+          
+          
+        
+      
    varchar weakly_connected_components ()
    
+
    
+
+
    
+
    
+
    
+
    
+
+
+
+
diff --git a/docs/documentation/examples.md b/docs/documentation/examples.md
new file mode 100644
index 00000000..fcbbb02c
--- /dev/null
+++ b/docs/documentation/examples.md
@@ -0,0 +1,49 @@
+# Example Use Cases
+
+This page provides examples of common machine learning tasks using Apache MADlib.
+
+## Linear Regression
+Linear regression is used to model the linear relationship of a scalar dependent variable to one or more explanatory independent variables.
+
+[View Example](../../docs/latest/group__grp__linreg.html#examples)
+
+## Logistic Regression  
+Logistic regression is used to predict a binary outcome of a dependent variable from one or more explanatory independent variables.
+
+[View Example](../../docs/latest/group__grp__logreg.html#examples)
+
+## Association Rules (Apriori)
+Apriori is a technique for evaluating frequent item-sets, which allows analysis of what events tend to occur together.
+
+[View Example](../../docs/latest/group__grp__assoc__rules.html#examples)
+
+## Latent Dirichlet Allocation
+Latent Dirichlet Allocation is a topic modeling function used to identify recurring themes in a large document corpus.
+
+[View Example](../../docs/latest/group__grp__lda.html#examples)
+
+## Elastic Net Regularization
+Elastic Net regularization is a technique that can be applied to either linear or logistic regression to build a more robust model, in the event of large numbers of explanatory independent variables.
+
+[View Example](../../docs/latest/group__grp__elasticnet.html#examples)
+
+## k-Means Clustering
+k-Means is a clustering method used to identify regions of similarity within a dataset. It can be used for many types of analysis including customer segmentation.
+
+[View Example](../../docs/latest/group__grp__kmeans.html#examples)
+
+## Summary Statistics
+The summary function provides summary statistics for any data table including distinct values, missing values, mean, variance, min, max, quantiles, etc.
+
+[View Example](../../docs/latest/group__grp__summary.html#examples)
+
+## Principal Component Analysis
+Principal Component Analysis is a dimensional reduction technique that can be used to transform a high dimensional space into a lower dimensional space.
+
+[View Example](../../docs/latest/group__grp__pca__train.html#examples)
+
+## Shortest Path in a Graph
+Finds a path from a source vertex to every other vertex in the graph. Example uses include vehicle routing/navigation, degrees of separation in a social network and minimum delay path in a telecommunications network.
+[View Example](../../docs/latest/group__grp__sssp.html#examples)
+
+For more detailed examples and complete API documentation, visit the [latest user guide](../../docs/latest/index.html).
\ No newline at end of file
diff --git a/docs/documentation/index.md b/docs/documentation/index.md
new file mode 100644
index 00000000..cda473f8
--- /dev/null
+++ b/docs/documentation/index.md
@@ -0,0 +1,41 @@
+# Documentation & Resources
+
+## Latest User Guide
+
+The primary documentation reference material providing detailed information on the functions and algorithms within MADlib as well as background theory and references into the literature.
+
+[Latest User Guide](../../docs/latest/index.html){ .md-button .md-button--primary }
+
+[View All Documentation Versions](versions.md){ .md-button }
+
+---
+
+## Installation Guide
+
+Information on initial installation and deployment of MADlib into a database instance.
+
+[Installation Guide](https://cwiki.apache.org/confluence/display/MADLIB/Installation+Guide){ .md-button }
+
+---
+
+## Quick Start Guide for Users
+
+Introduction to themes and concepts in MADlib. The guide walks the user through an initial data load, training a model, inspecting a model, and scoring a model.
+
+[Quick Start Guide for Users](https://cwiki.apache.org/confluence/display/MADLIB/Quick+Start+Guide+for+Users){ .md-button }
+
+---
+
+## Quick Start Guide for Developers
+
+For developers who are interested in contributing to MADlib. Includes instructions for an available Docker image with necessary dependencies to compile and test MADlib.
+
+[Quick Start Guide for Developers](https://cwiki.apache.org/confluence/display/MADLIB/Quick+Start+Guide+for+Developers){ .md-button }
+
+---
+
+## Jupyter Notebooks for Getting Started
+
+Includes many commonly used algorithms by data scientists.
+
+[Jupyter Notebooks](https://github.com/apache/madlib-site/tree/asf-site/community-artifacts){ .md-button }
\ No newline at end of file
diff --git a/docs/documentation/installation.md b/docs/documentation/installation.md
new file mode 100644
index 00000000..899c57f4
--- /dev/null
+++ b/docs/documentation/installation.md
@@ -0,0 +1,35 @@
+# Installation Guide
+
+Information on initial installation and deployment of MADlib into a database instance.
+
+For detailed installation instructions, please visit the [MADlib Wiki Installation Guide](https://cwiki.apache.org/confluence/display/MADLIB/Installation+Guide).
+
+## Quick Installation
+
+### Prerequisites
+- PostgreSQL 11+ or Greenplum Database 5.x/6.x/7.x
+- Python 3.x
+- Required system libraries
+
+### Installation Steps
+
+1. **Download MADlib**
+   ```bash
+   wget https://dist.apache.org/repos/dist/release/madlib/2.1.0/apache-madlib-2.1.0-src.tar.gz
+   ```
+
+2. **Install MADlib**
+   ```bash
+   tar -xzf apache-madlib-2.1.0-src.tar.gz
+   cd apache-madlib-2.1.0-src
+   ./configure
+   make
+   make install
+   ```
+
+3. **Deploy to Database**
+   ```sql
+   SELECT madlib.install_madlib();
+   ```
+
+For complete installation instructions, platform-specific guides, and troubleshooting, please refer to the [official installation documentation](https://cwiki.apache.org/confluence/display/MADLIB/Installation+Guide).
\ No newline at end of file
diff --git a/docs/documentation/quick-start.md b/docs/documentation/quick-start.md
new file mode 100644
index 00000000..9fdca110
--- /dev/null
+++ b/docs/documentation/quick-start.md
@@ -0,0 +1,42 @@
+# Quick Start Guide
+
+Introduction to themes and concepts in MADlib. This guide walks you through an initial data load, training a model, inspecting a model, and scoring a model.
+
+For the complete quick start guide, please visit the [MADlib Wiki Quick Start Guide for Users](https://cwiki.apache.org/confluence/display/MADLIB/Quick+Start+Guide+for+Users).
+
+## Your First MADlib Model
+
+### 1. Create Sample Data
+```sql
+CREATE TABLE sample_data AS
+SELECT 
+    random() * 100 as feature1,
+    random() * 50 as feature2,
+    random() * 200 + 100 as target
+FROM generate_series(1, 1000);
+```
+
+### 2. Train a Model
+```sql
+SELECT madlib.linregr_train(
+    'sample_data',
+    'my_model', 
+    'target',
+    'ARRAY[1, feature1, feature2]'
+);
+```
+
+### 3. View Results
+```sql
+SELECT * FROM my_model;
+```
+
+### 4. Make Predictions
+```sql
+SELECT madlib.linregr_predict(
+    (SELECT coef FROM my_model),
+    ARRAY[1, 75, 25]
+) as prediction;
+```
+
+For detailed examples and advanced usage, please refer to the [complete quick start guide](https://cwiki.apache.org/confluence/display/MADLIB/Quick+Start+Guide+for+Users).
\ No newline at end of file
diff --git a/docs/documentation/versions.md b/docs/documentation/versions.md
new file mode 100644
index 00000000..798837ac
--- /dev/null
+++ b/docs/documentation/versions.md
@@ -0,0 +1,85 @@
+# Documentation Versions
+
+Apache MADlib maintains documentation for all major releases. Choose the version that matches your MADlib installation.
+
+!!! info "Legacy Documentation"
+    The version-specific documentation links below point to the complete API reference documentation generated from the source code. These have a different interface than this site but contain comprehensive technical details.
+
+## Current Versions
+
+### Latest Stable Release
+- [MADlib Latest](../../docs/latest/index.html) - Always points to the most recent stable release
+
+### Recent Releases
+- [MADlib v2.1.0](../../docs/v2.1.0/index.html) - September 2023
+- [MADlib v2.0.0](../../docs/v2.0.0/index.html) - June 2023 (Major Release)
+- [MADlib v1.21.0](../../docs/v1.21.0/index.html) - March 2023
+- [MADlib v1.20.0](../../docs/v1.20.0/index.html) - August 2022
+- [MADlib v1.19.0](../../docs/v1.19.0/index.html) - March 2022
+- [MADlib v1.18.0](../../docs/v1.18.0/index.html) - April 2021
+
+## Historical Versions
+
+
    
+Click to expand historical versions
+
+- [MADlib v1.17.0](../../docs/v1.17.0/index.html) - April 2020
+- [MADlib v1.16](../../docs/v1.16/index.html) - September 2019
+- [MADlib v1.15.1](../../docs/v1.15.1/index.html) - February 2019
+- [MADlib v1.15](../../docs/v1.15/index.html) - September 2018
+- [MADlib v1.14](../../docs/v1.14/index.html) - January 2018
+- [MADlib v1.13](../../docs/v1.13/index.html) - July 2017
+- [MADlib v1.12](../../docs/v1.12/index.html) - September 2016
+- [MADlib v1.11](../../docs/v1.11/index.html) - July 2016
+- [MADlib v1.10](../../docs/v1.10/index.html) - February 2016
+- [MADlib v1.9.1](../../docs/v1.9.1/index.html) - September 2015
+- [MADlib v1.9](../../docs/v1.9/index.html) - July 2015
+- [MADlib v1.8](../../docs/v1.8/index.html) - February 2015
+- [MADlib v1.7.1](../../docs/v1.7.1/index.html) - October 2014
+- [MADlib v1.7](../../docs/v1.7/index.html) - July 2014
+- [MADlib v1.6](../../docs/v1.6/index.html) - December 2013
+- [MADlib v1.5](../../docs/v1.5/index.html) - July 2013
+- [MADlib v1.4](../../docs/v1.4/index.html) - February 2013
+- [MADlib v1.3](../../docs/v1.3/index.html) - October 2012
+- [MADlib v1.2](../../docs/v1.2/index.html) - July 2012
+- [MADlib v1.1](../../docs/v1.1/index.html) - March 2012
+- [MADlib v1.0](../../docs/v1.0/index.html) - October 2011
+
+
    
+
+## Version Compatibility
+
+| MADlib Version | PostgreSQL | Greenplum | Python | Release Date |
+|----------------|------------|-----------|---------|--------------|
+| 2.1.0 | 11-15 | 6.x, 7.x | 3.x | Sep 2023 |
+| 2.0.0 | 11-15 | 6.x, 7.x | 3.x | Jun 2023 |
+| 1.21.0 | 9.6-12 | 5.x, 6.x | 2.7, 3.x | Mar 2023 |
+| 1.20.0 | 9.6-12 | 5.x, 6.x | 2.7, 3.x | Aug 2022 |
+| 1.19.0 | 9.6-12 | 5.x, 6.x | 2.7 | Mar 2022 |
+| 1.18.0 | 9.6-12 | 5.x, 6.x | 2.7 | Apr 2021 |
+
+## Finding the Right Version
+
+1. **Check your MADlib installation**:
+   ```sql
+   SELECT madlib.version();
+   ```
+
+2. **Match the documentation version** to your installed version
+
+3. **For new installations**, use the [latest stable release](../../docs/latest/index.html)
+
+## Migration Guides
+
+When upgrading between major versions, please refer to:
+
+- [MADlib 2.0 Migration Guide](../blog/posts/madlib-2.0.0-release.md) - For upgrading from 1.x to 2.x
+- [Release Notes](https://github.com/apache/madlib/blob/master/RELEASE_NOTES) - Detailed changes for each version
+
+## Need Help?
+
+If you can't find the documentation version you need or have questions about compatibility:
+
+- Visit our [community forums](../community/index.md)
+- Check the [installation guide](installation.md)
+- Review [supported platforms](https://cwiki.apache.org/confluence/display/MADLIB/Database+and+OS+Support)
\ No newline at end of file
diff --git a/docs/download.md b/docs/download.md
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+++ b/docs/download.md
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+# Download
+
+## Release Integrity
+
+You must [verify](https://www.apache.org/info/verification.html) the integrity of the downloaded files. We provide OpenPGP signatures for every release file. This signature should be matched against the [KEYS file](https://www.apache.org/dist/madlib/KEYS) which contains the OpenPGP keys of MADlib's Release Managers. We also provide MD5 and SHA-512 checksums for every release file. After you download the file, you should calculate a checksum for your download, and make sure it is the same as ours.
+
+---
+
+## MADlib Development Code
+
+The latest development code is available in source from the main source repository.
+
+**Apache GitHub mirror:**
+
+- [https://github.com/apache/madlib](https://github.com/apache/madlib)
+
+---
+
+## Current Release
+
+### v2.1.0
+
+#### Source Code
+
+MADlib® source code is available from the Apache distribution site.
+
+**Latest stable release:**
+
+- [Source code tar.gz](https://dist.apache.org/repos/dist/release/madlib/2.1.0/apache-madlib-2.1.0-src.tar.gz) ([pgp](https://dist.apache.org/repos/dist/release/madlib/2.1.0/apache-madlib-2.1.0-src.tar.gz.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/2.1.0/apache-madlib-2.1.0-src.tar.gz.sha512))
+
+---
+
+## Previous Apache Releases
+
+### v2.0.0
+
+#### Source Code
+
+MADlib® source code is available from the Apache distribution site.
+
+**Latest stable release:**
+
+- [Source code tar.gz](https://dist.apache.org/repos/dist/release/madlib/2.0.0/apache-madlib-2.0.0-src.tar.gz) ([pgp](https://dist.apache.org/repos/dist/release/madlib/2.0.0/apache-madlib-2.0.0-src.tar.gz.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/2.0.0/apache-madlib-2.0.0-src.tar.gz.sha512))
+
+### v1.21.0
+
+#### Source Code
+
+MADlib® source code is available from the Apache distribution site.
+
+**Latest stable release:**
+
+- [Source code tar.gz](https://dist.apache.org/repos/dist/release/madlib/1.21.0/apache-madlib-1.21.0-src.tar.gz) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.21.0/apache-madlib-1.21.0-src.tar.gz.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.21.0/apache-madlib-1.21.0-src.tar.gz.sha512))
+
+### v1.20.0
+
+#### Source Code and Convenience Binaries
+
+MADlib® source code is available from the Apache distribution site.
+
+**Release artifacts:**
+
+- [Source code tar.gz](https://dist.apache.org/repos/dist/release/madlib/1.20.0/apache-madlib-1.20.0-src.tar.gz) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.20.0/apache-madlib-1.20.0-src.tar.gz.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.20.0/apache-madlib-1.20.0-src.tar.gz.sha512))
+- [Linux](https://dist.apache.org/repos/dist/release/madlib/1.20.0/apache-madlib-1.20.0-CentOS7.rpm) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.20.0/apache-madlib-1.20.0-CentOS7.rpm.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.20.0/apache-madlib-1.20.0-CentOS7.rpm.sha512)) — CentOS7 / Red Hat 7 (64 bit). GPDB 5.x, GPDB 6.x, PostgreSQL 11.x and 12.x.
+
+### v1.19.0
+
+#### Source Code and Convenience Binaries
+
+MADlib® source code is available from the Apache distribution site.
+
+**Release artifacts:**
+
+- [Source code tar.gz](https://dist.apache.org/repos/dist/release/madlib/1.19.0/apache-madlib-1.19.0-src.tar.gz) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.19.0/apache-madlib-1.19.0-src.tar.gz.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.19.0/apache-madlib-1.19.0-src.tar.gz.sha512))
+
+### v1.18.0
+
+#### Source Code and Convenience Binaries
+
+MADlib® source code and convenience binaries are available from the Apache distribution site.
+
+**Release artifacts:**
+
+- [Source code tar.gz](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-src.tar.gz) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-src.tar.gz.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-src.tar.gz.sha512))
+- [Linux](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-CentOS6.rpm) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-CentOS6.rpm.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-CentOS6.rpm.sha512)) — CentOS6 / Red Hat 6 (64 bit). GPDB 5.x, GPDB 6.x, PostgreSQL 11.x and 12.x. Please refer to the [notes about CentOS6 dependencies](https://cwiki.apache.org/confluence/display/MADLIB/Database+and+OS+Support).
+- [Linux](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-CentOS7.rpm) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-CentOS7.rpm.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-CentOS7.rpm.sha512)) — CentOS7 / Red Hat 7 (64 bit). GPDB 5.x, GPDB 6.x, PostgreSQL 11.x and 12.x.
+- [Linux](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-Ubuntu18.deb) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-Ubuntu18.deb.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Linux-Ubuntu18.deb.sha512)) — Ubuntu 18.04. GPDB 5.x, GPDB 6.x, PostgreSQL 11.x and 12.x.
+- [Mac OS X](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Darwin.dmg) ([pgp](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Darwin.dmg.asc), [sha512](https://dist.apache.org/repos/dist/release/madlib/1.18.0/apache-madlib-1.18.0-bin-Darwin.dmg.sha512)) — macOS 10.14.6 and higher. PostgreSQL 11.x and 12.x.
+
+### v1.17.0
+
+#### Source Code and Convenience Binaries
+
+MADlib® source code and convenience binaries are available from the Apache distribution site.
+
+**Release artifacts:**
+
+- [Source code tar.gz](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-src.tar.gz) ([pgp](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-src.tar.gz.asc), [sha512](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-src.tar.gz.sha512))
+- [Linux](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux-GPDB43.rpm) ([pgp](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux-GPDB43.rpm.asc), [sha512](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux-GPDB43.rpm.sha512)) — CentOS / Red Hat 5 and higher (64 bit). GPDB 4.3.x.
+- [Linux](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux.rpm) ([pgp](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux.rpm.asc), [sha512](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux.rpm.sha512)) — CentOS / Red Hat 6 and higher (64 bit). GPDB 5.x, GPDB 6.x, PostgreSQL 11.x and 12.x.
+- [Linux](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux.deb) ([pgp](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux.deb.asc), [sha512](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Linux.deb.sha512)) — Ubuntu 18.04. GPDB 5.x, GPDB 6.x, PostgreSQL 11.x and 12.x.
+- [Mac OS X](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Darwin.dmg) ([pgp](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Darwin.dmg.asc), [sha512](https://archive.apache.org/dist/madlib/1.17.0/apache-madlib-1.17.0-bin-Darwin.dmg.sha512)) — OS 10.6 and higher. PostgreSQL 11.x and 12.x.
+
+!!! note "More Historical Releases"
+    Additional historical releases are available in the [Apache archive](https://archive.apache.org/dist/madlib/) and include versions back to v1.0.
\ No newline at end of file
diff --git a/docs/index.md b/docs/index.md
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--- /dev/null
+++ b/docs/index.md
@@ -0,0 +1,158 @@
+---
+hide:
+  - navigation
+  - toc
+---
+
+
    
+
+
    
+
+# Welcome to Apache MADlib, Big Data Machine Learning in SQL
+
+
+
+
    
+
+
    
+
+**Apache MADlib** is an open source machine learning library designed for big data analytics that runs directly in PostgreSQL and Greenplum Database®.
+
+[Download](download.md){ .md-button .md-button--primary }
+[View Documentation](documentation/user-guide.md){ .md-button }
+
+
    
+
+
+
    
+
+### 📢 Latest News: [MADlib 2.1.0 Release](blog/posts/madlib-2.1.0-release.md)
+
+
    
+
+## Hightlights
+
+
    
+
+-   __Open Source, Commercially Friendly Apache License__
+
+    ---
+
+    Apache License, commercially friendly open source license
+
+-   __For PostgreSQL and Greenplum Database®__
+
+    ---
+
+    Supports PostgreSQL and Greenplum Database®, process data in-place
+
+-   __Powerful Machine Learning, Graph, Statistics and Analytics__
+
+    ---
+
+    Provides powerful machine learning, graph, statistics and analytics for data scientists
+
+
    
+
+## Product Overview
+
+
    
+
+In a world of ever increasing data size, many existing analytics solutions are not up to the task. The MADlib project seeks to address this need by creating a framework built to take advantage of modern computing capabilities to provide robust solutions that scale with the needs of the business.
+
+Our approach is to leverage the efforts of commercial practice, academic research, and the open-source development community.
+
+
    
+
+### Key Philosophies Driving the Architecture of MADlib
+
+
    
+
+-   __Operate on the data locally in-database__
+
+    ---
+
+    Do not move data between multiple runtime environments unnecessarily.
+
+-   __Utilize best of breed database engines__
+
+    ---
+
+    But separate the machine learning logic from database specific implementation details.
+
+-   __Leverage MPP shared nothing technology__
+
+    ---
+
+    Such as the Greenplum Database, to provide parallelism and scalability.
+
+-   __Open implementation__
+
+    ---
+
+    Maintaining active ties into Apache community and ongoing academic research.
+
+
    
+
+## Features & Capabilities
+
+
    
+
+-   ![Classification](assets/classification.png){ align=left width=64 } __Classification__
+
+    ---
+
+    When the desired output is categorical in nature, we use classification methods to build a model that predicts which of the various categories a new result would fall into.
+
+-   ![Regression](assets/regression.png){ align=left width=64 } __Regression__
+
+    ---
+
+    When the desired output is continuous in nature, we use regression methods to build a model that predicts the output value.
+
+-   ![Deep Learning](assets/neural-net.png){ align=left width=64 } __Deep Learning__
+
+    ---
+
+    Deep learning uses artificial neural networks inspired by biology of the brain. GPU acceleration is widely used to speed training.
+
+-   ![Clustering](assets/clustering.png){ align=left width=64 } __Clustering__
+
+    ---
+
+    Identify groups of data such that items within one cluster are more similar to each other than to items in other clusters.
+
+-   ![Topic Modeling](assets/topic-modelling.png){ align=left width=64 } __Topic Modeling__
+
+    ---
+
+    Similar to clustering but specific to text domain, attempting to identify clusters of documents and their main themes.
+
+-   ![Association Rule Mining](assets/rule-mining.png){ align=left width=64 } __Association Rule Mining__
+
+    ---
+
+    Also called market basket analysis, this identifies which items tend to occur together more frequently than random chance.
+
+-   ![Descriptive Statistics](assets/descriptive-statistics.png){ align=left width=64 } __Descriptive Statistics__
+
+    ---
+
+    Provide valuable insights into data that may influence choice of data model and help analysts understand underlying patterns.
+
+-   ![Validation](assets/validation.png){ align=left width=64 } __Validation__
+
+    ---
+
+    Evaluate model accuracy on test data using techniques like N-fold cross validation to ensure models are not over-fitting.
+
+
    
+
+## Getting Started with Apache MADlib using Jupyter Notebooks
+
+
    
+
+We have created a [library of Jupyter Notebooks](https://github.com/apache/madlib-site/tree/asf-site/community-artifacts) to help you get started quickly with MADlib. It includes many commonly used algorithms by data scientists.
+
+
    
+
     
\ No newline at end of file
diff --git a/docs/latest b/docs/latest
deleted file mode 120000
index 852700e1..00000000
--- a/docs/latest
+++ /dev/null
@@ -1 +0,0 @@
-v2.1.0
\ No newline at end of file
diff --git a/docs/mathjax/CONTRIBUTING.md b/docs/mathjax/CONTRIBUTING.md
deleted file mode 100644
index 96ad9b62..00000000
--- a/docs/mathjax/CONTRIBUTING.md
+++ /dev/null
@@ -1,259 +0,0 @@
-# Contributing to MathJax
-
-You are interested in giving us a hand? That's awesome! We've put together some brief guidelines that should help you get started quickly and easily.
-
-There are lots and lots of ways to get involved, this document covers:
-
-* [reporting an issue](#reporting-an-issue)
-    * [bug reports](#bug-reports)
-    * [feature requests](#feature-requests)
-    * [change requests](#change-requests)
-* [working on MathJax core](#working-on-mathjax-core)
-    * [key branches and tags](#key-branches--tags)
-    * [submitting pull requests](#submitting-pull-requests)
-    * [testing and quality assurance](#testing-and-quality-assurance)
-    * [writing documentation](#writing-documentation)
-    * [translation](#translation)
-* [Conduct](#conduct)
-
-
-## Reporting An Issue
-
-If you're about to raise an issue because you think you've found a
-problem with MathJax, or you'd like to make a request for a new
-feature in the codebase, or any other reason… please read this first.
-
-The GitHub issue tracker is the preferred channel for [bug reports](#bug-reports),
-[feature requests](#feature-requests), [change requests](#change-requests) and [submitting pull
-requests](#submitting-pull-requests), but please respect the following restrictions:
-
-* Please **search for existing issues**. Help us keep duplicate issues
-  to a minimum by checking to see if someone has already reported your
-  problem or requested your idea.
-
-* Please **do not** use the issue tracker for personal support
-  requests (use [the MathJax User Group](https://groups.google.com/forum/#!forum/mathjax-users)).
-
-* Please **be civil**. Keep the discussion on topic and respect the
-  opinions of others. See also our [Conduct Guidelines](#conduct)
-
-### Bug Reports
-
-A bug is a _demonstrable problem_ that is caused by the code in the repository.
-Good bug reports are extremely helpful - thank you!
-
-Guidelines for bug reports:
-
-1. **Use the GitHub issue search** — check if the issue has already been
-   reported.
-
-2. **Check if the issue has been fixed** — look for [closed issues in the
-   current milestone](https://github.com/MathJax/MathJax/issues?&page=1&state=closed) or try to reproduce it
-   using the latest `develop` branch. Please note that we only pack MathJax for releases, so on the `develop` branch you have to use `/unpacked/MathJax.js` etc. to test.
-
-3. **Share a live sample of the problem** — without a live page it is usually impossible to debug problems; see also the Bug Report Template below.
-
-4. **Isolate the problem** — a live sample is a starting point but if you want to speed things up create a [reduced test
-   case](http://css-tricks.com/6263-reduced-test-cases/). Be specific about your setup (browser, OS versions etc). Use services like [jsbin](http://jsbin.com), [CodePen](http://codepen.io), [JSfiddle](http://jsfiddle.com) to make collaboration on minimal test cases easier for everyone. Use the unpacked copy of MathJax (`[...]/unpacked/MathJax.js` etc.) for better debugging.
-
-5. **Include a screenshot/cast as a last resort** — Is your issue about a layout
-   or design feature / bug but hard to reproduce or isolate? Then please provide a screenshot or screencast. Tools like [LICEcap](http://www.cockos.com/licecap/) or [SauceLabs](http://www.saucelabs.com) allow you to quickly and easily record a screencasts. Make it an animated gif, embed it directly into your GitHub issue -- kapow!
-
-6. Use the Bug Report template below or [click this
-   link](https://github.com/MathJax/MathJax/issues/new?title=Bug%3A&body=%23%23%23%20Issue%20Summary%0A%0A%23%23%23%20Steps%20to%20Reproduce%0A%0A1.%20This%20is%20the%20first%20step%0A%0AThis%20is%20a%20bug%20because...%0A%0A%23%23%23%20Technical%20details%0A%0A*%20MathJax%20Version%3A%20master%20-%20latest%20commit%3A%20%20INSERT%20COMMIT%20REF%0A*%20Client%20OS%3A%20%0A*%20Browser%3A%20%0A*%20)
-   to start creating a bug report with the template automatically.
-
-A good bug report shouldn't leave others needing to chase you up for
-more information. Be sure to include the details of your environment.
-
-Here is a [real example](https://github.com/mathjax/MathJax/issues/820)
-
-Template Example ([click to use](https://github.com/MathJax/MathJax/issues/new?title=Bug%3A&body=%23%23%23%20Issue%20Summary%0A%0A%23%23%23%20Steps%20to%20Reproduce%0A%0A1.%20This%20is%20the%20first%20step%0A%0AThis%20is%20a%20bug%20because...%0A%0A%23%23%23%20Technical%20details%0A%0A*%20MathJax%20Version%3A%20master%20-%20latest%20commit%3A%20%20INSERT%20COMMIT%20REF%0A*%20Client%20OS%3A%20%0A*%20Browser%3A%20%0A*%20)):
-```
-Short and descriptive example bug report title
-
-### Issue Summary
-
-A summary of the issue and the browser/OS environment in which it occurs. If
-suitable, include the steps required to reproduce the bug.
-
-### Steps to Reproduce
-
-1. This is the first step
-2. This is the second step
-3. Further steps, etc.
-
-Any other information you want to share that is relevant to the issue
-being reported. Especially, why do you consider this to be a bug? What
-do you expect to happen instead?
-
-### Technical details:
-
-* MathJax Version: 2.3 (latest commit: f3aaf3a2a3e964df2770dc4aaaa9c87ce5f47e2c)
-* Client OS: Mac OS X 10.8.4
-* Browser: Chrome 29.0.1547.57
-```
-
-
-### Feature Requests
-
-Feature requests are welcome. Before you submit one be sure to have:
-
-1. Read the
-   [Roadmaps](https://github.com/mathjax/MathJax/wiki/Mathjax-roadmap),
-   **use the GitHub search** and check the feature hasn't already been
-   requested.
-2. Take a moment to think about whether your idea fits with the scope
-   and aims of the project, or if it might better fit being a [custom
-   extension](https://github.com/mathjax/MathJax-third-party-extensions).
-3. Remember, it's up to *you* to make a strong case to convince the
-   project's leaders of the merits of this feature. Please provide as
-   much detail and context as possible, this means explaining the use
-   case and why it is likely to be common.
-4. Clearly indicate whether this is a feature request for MathJax
-   core, input & output jax, or extensions.
-
-
-### Change Requests
-
-Change requests cover both architectural and functional changes to how
-MathJax works. If you have an idea for a new or different dependency,
-a refactor, or an improvement to a feature, etc - please be sure to:
-
-1. **Use the GitHub search** and check someone else didn't get there first
-2. Take a moment to think about the best way to make a case for, and
-   explain what you're thinking. Are you sure this shouldn't really be
-   a [bug report](#bug-reports) or a [feature
-   request](#feature-requests)?  Is it really one idea or is it many?
-   What's the context? What problem are you solving? Why is what you
-   are suggesting better than what's already there? Does it fit with
-   the Roadmap?
-
-## Working on MathJax core
-
-You want to contribute code? Fantastic! Let's get you started.
-
-### Key Branches & Tags
-
-To get it out of the way:
-
-- **[develop](https://github.com/MathJax/MathJax/tree/develop)** is
-  the development branch. All work on the next release happens here so
-  you should generally branch off `develop`. Do **NOT** use this branch
-  for a production site. 
-- **[master](https://github.com/MathJax/MathJax)** contains the latest
-  release of MathJax. This branch may be used in production. Do 
-  **NOT** use this branch to work on MathJax's source.
-
-### Submitting Pull Requests
-
-Pull requests are awesome. If you're looking to raise a PR for
-something which doesn't have an open issue, please think carefully
-about [raising an issue](#reporting-an-issue) which your PR can close,
-especially if you're fixing a bug. This makes it more likely that
-there will be enough information available for your PR to be properly
-tested and merged.
-
-##### Need Help?
-
-If you're not completely clear on how to submit / update / *do* Pull
-Requests, please check out our [source control
-policies](https://github.com/mathjax/MathJax/wiki/Source-control-policies). For
-more insights, chech the excellent in depth [Git Workflow
-guide](https://github.com/TryGhost/Ghost/wiki/Git-Workflow) from
-Ghost, in particular
-
-* [Ghost Workflow guide: commit messages](https://github.com/TryGhost/Ghost/wiki/Git-workflow#commit-messages)
-
-### Testing and Quality Assurance
-
-Never underestimate just how useful quality assurance is. If you're
-looking to get involved with the code base and don't know where to
-start, checking out and testing a pull request is one of the most
-useful things you could do.
-
-If you want to get involved with testing MathJax, there is a set of QA
-Documentation [in our testing
-framework](https://github.com/MathJax/MathJax-testing).
-
-Essentially though, [check out the latest develop
-branch](#working-on-mathJax-core), take it for a spin, and if you find
-anything odd, please follow the [bug report guidelines](#bug-reports)
-and let us know!
-
-#### Checking out a Pull Request
-
-These are some [excellent
-instructions](https://gist.github.com/piscisaureus/3342247) on
-configuring your GitHub repository to allow you to checkout pull
-requests in the same way as branches:
-.
-
-
-### Writing documentation
-
-MathJax's main documentation can be found at [docs.mathjax.org](http://docs.mathjax.org).
-The source of the docs is hosted in the
-[mathjax/mathjax-docs](http://github.com/mathjax/mathjax-docs) repo here on GitHub.
-
-The documentation is generated using [Sphinx-doc](http://sphinx-doc.org/) and hosted on 
-[Read the docs](http://readthedocs.org).
-You can clone the repo and submit pull requests following the
-[pull-request](#submitting-pull-requests) guidelines.
-
-
-### Translation
-
-If you wish to add or update translations of MathJax, please do it on
-[TranslateWiki.net](https://translatewiki.net/w/i.php?title=Special:Translate&group=out-mathjax-0-all)
-(and while you're there you can help other open source projects,
-too, because you're awesome!).
-
-For bug reports and other questions that don't fit on
-TranslateWiki.net, head over to the
-[mathjax/mathjax-i18n](https://github.com/mathjax/MathJax-i18n)
-repository.
-
-## Conduct
-
-We are committed to providing a friendly, safe and welcoming environment for
-all, regardless of gender, sexual orientation, disability, ethnicity, religion,
-or similar personal characteristic.
-
-Please be kind and courteous. There's no need to be mean or rude.
-Respect that people have differences of opinion and that every design or
-implementation choice carries a trade-off and numerous costs. There is seldom
-a right answer, merely an optimal answer given a set of values and
-circumstances.
-
-Please keep unstructured critique to a minimum. If you have solid ideas you
-want to experiment with, make a fork and see how it works.
-
-We will exclude you from interaction if you insult, demean or harass anyone.
-That is not welcome behaviour. We interpret the term "harassment" as
-including the definition in the
-[Citizen Code of Conduct](http://citizencodeofconduct.org/);
-if you have any lack of clarity about what might be included in that concept,
-please read their definition. In particular, we don't tolerate behavior that
-excludes people in socially marginalized groups.
-
-Private harassment is also unacceptable. No matter who you are, if you feel
-you have been or are being harassed or made uncomfortable by a community
-member, please contact one of the channel ops or any of the
-[MathJax](https://github.com/MathJax/MathJax) core team
-immediately. Whether you're a regular contributor or a newcomer, we care about
-making this community a safe place for you and we've got your back.
-
-Likewise any spamming, trolling, flaming, baiting or other attention-stealing
-behaviour is not welcome.
-
-We also suggest to read [discourse's
-rules](http://blog.discourse.org/2013/03/the-universal-rules-of-civilized-discourse/)
-
-## References
-
-* We heavily borrowed from Mozilla and Ghost -- thank you!
-  * https://github.com/TryGhost/Ghost/blob/master/CONTRIBUTING.md
-  * https://github.com/mozilla/rust/wiki/Note-development-policy
-* https://github.com/jden/CONTRIBUTING.md/blob/master/CONTRIBUTING.md
-* http://blog.discourse.org/2013/03/the-universal-rules-of-civilized-discourse/
diff --git a/docs/mathjax/README.md b/docs/mathjax/README.md
deleted file mode 100644
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--- a/docs/mathjax/README.md
+++ /dev/null
@@ -1,59 +0,0 @@
-# MathJax
-
-## Beautiful math in all browsers
-
-MathJax is an open-source JavaScript display engine for LaTeX, MathML, and
-AsciiMath notation that works in all modern browsers.  It was designed with
-the goal of consolidating the recent advances in web technologies into a
-single, definitive, math-on-the-web platform supporting the major browsers
-and operating systems.  It requires no setup on the part of the user (no
-plugins to download or software to install), so the page author can write
-web documents that include mathematics and be confident that users will be
-able to view it naturally and easily.  Simply include MathJax and some
-mathematics in a web page, and MathJax does the rest.
-
-Some of the main features of MathJax include:
-
-- High-quality display of LaTeX, MathML, and AsciiMath notation in HTML pages
-
-- Supported in most browsers with no plug-ins, extra fonts, or special
-  setup for the reader
-
-- Easy for authors, flexible for publishers, extensible for developers
-
-- Supports math accessibility, cut-and-paste interoperability, and other
-  advanced functionality
-
-- Powerful API for integration with other web applications
-
-See  for additional details.
-
-
-## Installation and Usage
-
-The MathJax installation and usage documentation is available in a
-separate GitHub repository at
-
-      https://github.com/mathjax/mathjax-docs
-
-The HTML versions are now available at
-
-      http://docs.mathjax.org/
-
-where it is possible for you to submit corrections and modifications
-directly to the documentation on line.
-
-
-## Community
-
-The main MathJax website is , and it includes
-announcements and other important information.  MathJax is maintained and
-distributed on GitHub at .  A user forum
-for asking questions and getting assistance is hosted at Google, and the
-bug tracker is hosted at GitHub:
-
-Bug tracker:           
-MathJax-Users Group: 
-
-Before reporting a bug, please check that it has not already been reported.
-Also, please use the bug tracker for reporting bugs rather than the help forum.
diff --git a/docs/team/history.md b/docs/team/history.md
new file mode 100644
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+++ b/docs/team/history.md
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+# Project History
+
+Apache MADlib is an open source project that endeavors to adhere in all respects to the principles of [The Apache Way](https://apache.org/foundation/governance/).
+
+## Origins
+
+MADlib grew out of discussions between database engine developers, data scientists, IT architects and academics interested in new approaches to scalable, sophisticated in-database analytics. These discussions were written up in a paper in VLDB 2009 that coined the term "MAD Skills" for data analysis. The MADlib software project began the following year as a collaboration between researchers at UC Berkeley and engineers and data scientists at EMC/Greenplum (later Pivotal).
+
+## Apache Journey
+
+In September 2015 MADlib was accepted into the Apache Software Foundation Incubator and graduated to a Top Level Project in July 2017.
+
+## Key Contributors
+
+Some of the past and present participants in this project are:
+
+
    
+
+-   ![VMware](../assets/partners/vmw.png){ width=150 }
+    
+    **VMware**
+    
+    Providing core development and scalability testing
+    
+    [Learn More](https://pivotal.io/)
+
+-   ![UC Berkeley](../assets/partners/berkeley.png){ width=150 }
+    
+    **UC Berkeley**
+    
+    Providing key research and development of scalable estimators
+    
+    [Learn More](https://db.cs.berkeley.edu/jmh/)
+
+-   ![Stanford](../assets/partners/stanford.png){ width=150 }
+    
+    **Stanford**
+    
+    Providing key research in the area of convex optimization
+    
+    [Learn More](https://cs.stanford.edu/people/chrismre/)
+
+-   ![University of Florida](../assets/partners/florida.png){ width=150 }
+    
+    **University of Florida**
+    
+    Providing key research into text analytics
+    
+    [Learn More](https://www.cise.ufl.edu/people/faculty/daisyw)
+
+-   ![UC San Diego](../assets/partners/ucsd.png){ width=150 }
+    
+    **UC San Diego**
+    
+    Providing key research in artificial neural networks on distributed systems
+    
+    [Learn More](https://cseweb.ucsd.edu/~arunkk/)
+
+
    
+
+## Get Involved
+
+If you are interested in joining our project please consider joining our [User](../community/index.md#user-resources) or [Developer](../community/index.md#developer-resources) mailing lists. Everyone is welcome.
+
+---
+
+[Back to Community](../community/index.md){ .md-button }
+[View Project Team](index.md){ .md-button .md-button--primary }
diff --git a/docs/team/index.md b/docs/team/index.md
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+# Project Team
+
+Apache MADlib is developed and maintained by a dedicated team of committers and contributors from around the world.
+
+## Project Management Committee (PMC)
+
+The Project Management Committee (PMC) is responsible for the oversight of the Apache MADlib project. PMC members have write access to the code repository and binding votes on project decisions.
+
+### PMC Members
+
+
    
+
+-   **Atri Sharma**
+    
+    Apache ID: `atri`
+
+-   **Ed Espino**
+    
+    Apache ID: `espino`
+
+-   **Gregory Chase**
+    
+    Apache ID: `gregchase`
+
+-   **Orhan Kislal**
+    
+    Apache ID: `okislal`
+
+-   **Roman Shaposhnik**
+    
+    Apache ID: `rvs`
+
+
    
+
+## Committers
+
+Committers have write access to the code repository and have demonstrated a sustained commitment to the project through code contributions, reviews, and community participation.
+
+
    
+
+-   **Aaron Feng**
+
+    Apache ID: `aaronfeng`
+
+-   **Anirudh Kondaveeti**
+
+    Apache ID: `akondave`
+
+-   **Domino Valdano**
+
+    Apache ID: `domino`
+
+-   **Frank McQuillan**
+
+    Apache ID: `fmcquillan`
+
+-   **Himanshu Pandey**
+
+    Apache ID: `hpandey`
+
+-   **Jingyi Mei**
+
+    Apache ID: `jingyimei`
+
+-   **Ekta Khanna**
+
+    Apache ID: `khannaekta`
+
+-   **Nandish Jayaram**
+
+    Apache ID: `njayaram`
+
+-   **Rashmi Raghu**
+
+    Apache ID: `rashmiraghu`
+
+-   **Rahul Iyer**
+
+    Apache ID: `riyer`
+
+-   **Sarah Joann Aerni**
+
+    Apache ID: `saerni`
+
+-   **Srivatsan Ramanujam**
+
+    Apache ID: `vatsan`
+
+
    
+
+## How to Become a Committer
+
+The Apache MADlib project follows the standard Apache process for recognizing contributors and promoting them to committers and PMC members.
+
+### Path to Committership
+
+1. **Contribute**: Start by contributing code, documentation, or helping with reviews
+2. **Engage**: Participate actively in mailing lists and community discussions
+3. **Demonstrate**: Show sustained commitment and understanding of the project
+4. **Nomination**: Existing committers may nominate contributors who have demonstrated merit
+5. **Vote**: The PMC votes on new committer nominations
+
+### What We Look For
+
+- Quality and quantity of contributions
+- Understanding of the project's architecture and goals
+- Ability to work collaboratively with the community
+- Commitment to the Apache Way
+- Willingness to help others and review contributions
+
+## Contact the Team
+
+- **Mailing Lists**: See our [Community page](../community/index.md) for mailing list information
+- **Project Info**: Visit the [Apache MADlib project page](https://projects.apache.org/committee.html?madlib)
+- **Report Issues**: Use our [issue tracker](https://github.com/apache/madlib/issues)
+
+---
+
+*Last updated: November 2024*
+
+*For the most current list of PMC members and committers, please visit the [official Apache project roster](https://projects.apache.org/committee.html?madlib).*
diff --git a/docs/v1.19.0/latest b/docs/v1.19.0/latest
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\ No newline at end of file
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-
-
-
-  
-  
-  Apache MADlib
-  
-  
-  
-  
-
-
-	
    
-		
    
-			
-			
    
-				
    
-				
    
-			
    
-		
    
-	
    
-	
    
-	
    
-		
    
-			
    Documentation
    
-		
    
-			
    
-			
-
-
    
-
    
-
    
-
    
-
    
-
    Latest User Guide
    
-
    The primary documentation reference material providing detailed information on the functions and algorithms within MADlib as well as background theory and references into the literature.
    
-
-
    
-
    
-
    
-
    
-
    
-
    
-
    Installation Guide
    
-
    Information on initial installation and deployment of MADlib into a database instance.
    
-
-
    
-
    
-
    
-
    
-
    
-
    Quick Start Guide for Users
    
-
    Introduction to themes and concepts in MADlib. The guide walks the user through an initial data load, training a model, inspecting a model, and scoring a model.
    
-
-
    
-
    
-
    
-
    
-
    
-
    Quick Start Guide for Developers
    
-
    For developers who are interested in contributing to MADlib.  Includes instructions for an available Docker image with necessary dependencies to compile and test MADlib.
    
-
-
    
-
    
-
    
-
    
-
    
-
    Jupyter Notebooks for Getting Started
    
-
    Includes many commonly used algorithms by data scientists.
    
-
-
    
-
    
-
    
-
    
-
    
-
    Community Portal
    
-
    Additional material for individuals looking to contribute to the project is available on our community portal.
    
-
    
-
    
-
    
-
    
-
    
-
    Example Use Cases
    
-
    
-	
-		
    Linear Regression
    
-		
    
-			Linear regression is used to model the linear relationship of a scalar dependent variable to one or more explanatory independent variables.
-					
    
-	    
-
    
-
    
-	
-		
    Latent Dirichlet Allocation
    
-		
    
-			Latent Dirichlet Allocation is a topic modeling function used to identify recurring themes in a large document corpus.
-					
    
-	    
-
    
-
    
-	
-		
    Summary
    
-		
    
-			The summary function provides summary statistics for any data table.  These statistics include: number of distinct values, number of missing values, mean, variance, min, max, most frequent values, quantiles, etc.
-					
    
-	    
-
    
-
    
-	
-		
    Logistic Regression
    
-		
    
-			Logistic regression is used to predict a binary outcome of a dependent variable from one or more explanatory independent variables.
-					
    
-	    
-
    
-
    
-	
-		
    Elastic Net Regularization
    
-		
    
-			Elastic Net regularization is a technique that can be applied to either linear or logistic regression to build a more robust model, in the event of large numbers of explanatory independent variables.
-					
    
-	    
-
    
-
    
-	
-		
    Principal Component Analysis
    
-		
    
-			Pricipal Component Analysis is a dimensional reduction technique that can be used to transform a high dimensional space into a lower dimensional space.
-					
    
-	    
-
    
-
    
-	
-		
    Apriori
    
-		
    
-			Apriori is a technique for evaluating frequent item-sets, which allows analysis of what events tend to occur together.  For example, which items do customers frequently purchase together in a single transaction?
-					
    
-	    
-
    
-
    
-	
-		
    k-Means
    
-		
    
-			k-Means is a clustering method used to identify regions of similarity within a dataset.   It can be used for many types of analysis including customer segmentation.
-					
    
-	    
-
    
-
    
-	
-		
    Shortest Path in a Graph
    
-		
    
-			Finds a path from a source vertex to every other vertex in the graph.   Example uses include vehicle routing/navigation, degrees of separation in a social network and minimum delay path in a telecommunications network.
-					
    
-	    
-
    
-
    
-
    			
    
-	
    
-	  
    
-		 	
-		  
    
-		  
    
-	    
    
-	      Copyright ©  The Apache Software Foundation, Licensed under the Apache License, Version 2.0.
-	      
    
-	      Apache, Apache MADlib, the Apache feather and the MADlib logo are trademarks of The Apache Software Foundation
-	    
    
-	  
    
-	
    
-
-
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-
-
-
-  
-  
-  Apache MADlib
-  
-  
-  
-  
-
-
-	
    
-		
    
-			
-			
    
-				
    
-				
    
-			
    
-		
    
-	
    
-	
    
-		
    
-			
    
-				
    Download
    
-			
    
-		
    
-		
    
-			
    
-				
    
-					
    Release Integrity
    
-				
    
-				
    
-                                
    You must verify the integrity of the downloaded files. We provide OpenPGP signatures for every release file. This signature should be matched against the KEYS file which contains the OpenPGP keys of MADlib's Release Managers. We also provide MD5 and SHA-512 checksums for every release file. After you download the file, you should calculate a checksum for your download, and make sure it is the same as ours.
-				
    
-			
    
-		
    
-		
    
-			
    
-				
    
-					
    MADlib 
    Development Code
    
-				
    
-				
    
-					
    The latest development code is available in source from the main source repository.
    
-
-					
    Apache GitHub mirror:
    
-
-					
-				
    
-			
    
-		
    
-		
    
-			
    
-				
    
-					
    Current Release
    
-				
    
-				
    
-					
    v2.1.0
    
-					
    Source Code
    
-
-					
    MADlib® source code is available from the Apache distribution site.
    
-
-					
    Latest stable release:
    
-
-					
-				
    
-			
    
-		
    
-		
    
-			
    
-				
    
-					
    Previous Apache Releases
    
-				
    
-				
    
-
-					
    v2.0.0
    
-					
    Source Code
    
-
-					
    MADlib® source code is available from the Apache distribution site.
    
-
-					
    Latest stable release:
    
-
-					
-
-					
    v1.21.0
    
-					
    Source Code
    
-
-					
    MADlib® source code is available from the Apache distribution site.
    
-
-					
    Latest stable release:
    
-
-					
-
-
-					
    v1.20.0
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code is available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.19.0
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code is available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.18.0
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.17.0
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.16
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.15.1
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.15
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.14
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.13
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.12
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-
-					
    v1.11 (incubating)
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
      
-						
    • Source code tar.gz
      • 
-						
    • Linux — CentOS / Red Hat 5 and higher (64 bit).  For all supported platforms.
      • 
-			            
    • Mac OS X — OS 10.6 and higher.  PostgreSQL 9.5 and 9.6.
      • 
-					
    
-
-					
    v1.10 (incubating)
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
      
-						
    • Source code tar.gz
      • 
-						
    • Linux — CentOS / Red Hat 5 and higher (64 bit).  For all supported platforms.
      • 
-			            
    • Mac OS X — OS 10.6 and higher.  PostgreSQL 9.5 and 9.6.
      • 
-					
    
-
-					
    v1.9.1 (incubating)
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
      
-						
    • Source code tar.gz
      • 
-						
    • Linux — CentOS / Red Hat 5 and higher (64 bit).  For all supported platforms.
      • 
-			            
    • Mac OS X — OS 10.6 and higher.  PostgreSQL 9.4 and 9.5.
      • 
-					
    
-
-					
    v1.9 (incubating)
    
-					
    Source Code and Convenience Binaries
    
-
-					
    MADlib® source code and convenience binaries are available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
      
-						
    • Source code tar.gz
      • 
-						
    • Linux — CentOS / Red Hat 5 and higher (64 bit).  For all supported platforms.
      • 
-			            
    • Mac OS X — OS 10.6 and higher.  PostgreSQL 9.4.
      • 
-					
    
-
-				
    
-			
    
-			
    
-				
    
-				
    
-				
    
-					
    v1.9 alpha  (incubating)
    
-					
    Source Code
    
-
-					
    This is a source code only release.  MADlib® source code is available from the Apache distribution site.
    
-
-					
    Release artifacts:
    
-
-					
-				
    
-			
    
-		
    
-		
    
-			
    
-				
    
-					
    Pre-Apache Releases
    
-				
    
-				
    
-
-					
    All pre-Apache releases of MADlib are available from the original repo.
    
-
-					
    Original MADlib GitHub repo:
    
-
-					
-
-				
    
-			
    
-			
    
-				
    
-				
    
-				
    
-					
    
-					
    v1.8
    
-					
    Binary packages
    
-					
    Pre-built binary packages are available for a number of different operating systems and server platforms.
    
-
-					
    Postgres and Greenplum Community Edition
    
-
-					
      
-						
    • Linux — CentOS / Red Hat 5 and higher (64 bit)
      • 
-					  
    • Mac OS X — OS 10.6 and higher
      • 
-					
    
-
-					
    Source Code
    
-					
    MADlib® source code is available from the original repository on GitHub.
    
-
-					
-
-				
    
-			
    
-			
    
-				
    
-				
    
-				
    
-					
    
-					
    v1.0.0 - v1.7.1
    
-					
    Older versions are available in .zip, tar.gz, .rpm, and .dmg formats via GitHub:
    
-
-
-					
    v1.7.1
    
-					
    v1.7.0
    
-					
    v1.6.0
    
-					
    v1.5.0
    
-					
    v1.4.0
    
-					
    v1.3.0
    
-					
    v1.2.0
    
-					
    v1.1.0
    
-					
    v1.0.0
    
-
-				
    
-			
    
-		
    
-		
    
-			
    
-				
    
-					
      
-						
    • 
-							
      Future Releases
      
-							
      Official releases are created when the community feels that the product has progressed sufficiently and is at a stable state.  Watch the user mailing list for latest release announcements and the developer mailing list for ongoing discussions related to the current release status. As always we welcome new members to the community.
      
-							
-						
      • 
-						
    • 
-							
      Backward Compatibility of Releases
      
-							
      The MADlib project uses Semantic Versioning.  All versions, starting with MADlib v1.0, will be API compliant and we will supply mechanisms for upgrading from prior versions to the current active version until the release of MADlib v2.0 which may have different API.  In many cases this may mean that a particular function may become deprecated, yet still remain callable, until a later major version is released.
      
-						
      • 
-					
    
-				
    
-			
    
-		
    
-	
    
-	
    
-	  
    
-		 	
-		  
    
-		  
    
-	    
    
-	      Copyright ©  The Apache Software Foundation, Licensed under the Apache License, Version 2.0.
-	      
    
-	      Apache, Apache MADlib, the Apache feather and the MADlib logo are trademarks of The Apache Software Foundation
-	    
    
-	  
    
-	
    
-
-
diff --git a/index.html b/index.html
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+++ /dev/null
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-
-
-
-  
-  
-  Apache MADlib
-  
-  
-  
-  
-
-
-	
    
-		
    
-			
-			
    
-				
    
-				
    
-			
    
-		
    
-	
    
-	
    
-	
    
-	
    
-	
    Apache MADlib: Big Data Machine Learning in SQL
    
-	
      
-		
    • Open source, commercially friendly Apache license
      • 
-		
    • For PostgreSQL and Greenplum Database®
      • 
-		
    • Powerful machine learning, graph, statistics and analytics for data scientists
      • 
-	
    
-	
    Read More
    
-
-	
    
-	
    
-	
    
-	
    
-	
    
-	
    
-	
    
-
-	
    
-		
    
-			
    Getting Started with Apache MADlib using Jupyter Notebooks
    
-			We have created a library of Jupyter Notebooks to help you get started quickly with MADlib.  It
-			includes many commonly used algorithms by data scientists.
-	
    
-     			
    
-	
    
-
-	
    
-		
    
-			
    MADlib 2.1.0 Release
    
-			On September 8, 2023, MADlib completed its thirteenth release as an Apache Software Foundation Top Level Project.
-	
    
-    
    Improvements:
    
-    
      
-    
    • Build: Fix PG 15 support
      
-    
    • Assoc_rules: Fix SERIAL cache issue
      
-    
    • DL: Remove SERIAL from load_keras_model
      
-    
    • Build: Add ubuntu flag for PyXB installation
      
-    
    • Build: Add the actual path of $libdir to dynamic_library_path
      
-    
    • Build: Remove PyXB as a packaged dependency and replace it with external pyxb-x dependency.
      
-    
    • Build: Use PG15 in Jenkins CI
      
-    
    • CRF: Fix anyarray -> anycompatiblearray change for PG14
      
-    
    
-	
    You are invited to download the 2.1.0 release and review the release notes. Also please refer to the list of supported databases and OS.
    
-	 			
    
-	
    
-
-  
    
-    
    
-      
    MADlib 2.0.0 Release
    
-      On June 20, 2023, MADlib completed its second major release.
-  
    
-    
    New features include:
    
-    
      
-    
    • Build: Add support for python3
      
-    
    • Build: Add support for GP7 Beta, GP6 python3 extension, Postgres 13/14/15
      
-    
    
-    
    Improvements:
    
-    
      
-    
    • XGBoost: Add support for version 1.7.5
      
-    
    • DL: Add support for tensorflow 2.10.1 and keras 2.10.0
      
-    
    • DBScan: Add support for rtree 1.0.1
      
-    
    
-  
    You are invited to download the 2.0.0 release and review the release notes. Also please refer to the list of supported databases and OS.
    
-         
    
-  
    
-
-	
    
-		
    
-			
    MADlib 1.21.0 Release
    
-			On March 1, 2023, MADlib completed its eleventh release as an Apache Software Foundation Top Level Project.
-	
    
-    
    New features include:
    
-    
      
-    
    • Graph: Add warm start for weakly connected components.
      
-    
    • Graph: Add multicolumn identifier support for SSSP and APSP.
      
-    
    • Build: Add support for Photon3 OS.
      
-    
    
-    
    Improvements:
    
-    
      
-    
    • XGBoost: Add support for bigint and varchar columns.
      
-    
    • XGBoost: Enable eval_metrics parameter.
      
-    
    
-	
    You are invited to download the 1.21.0 release and review the release notes. Also please refer to the list of supported databases and OS.
    
-	 			
    
-	
    
-
-	
    
-		
    
-			
    MADlib 1.20.0 Release
    
-			On August 3, 2022, MADlib completed its tenth release as an Apache Software Foundation Top Level Project.
-	
    
-    
    New features include:
    
-    
      
-    
    • XGBoost: Python based XGBoost with single and grid search executions.
      
-    
    • Graph: Add multicolumn support for WCC and Pagerank.
      
-    
    
-    
    Improvements:
    
-    
      
-    
    • Utilities: Reuse update plan in GroupIterationController.
      
-    
    • Documentation: Update online examples for various modules.
      
-    
    • Elastic Net - GLM - SVM: Adjust ORCA to reduce planning time.
      
-    
    
-	
    You are invited to download the 1.20.0 release and review the release notes. Also please refer to the list of supported databases and OS.
    
-	 			
    
-	
    
-
-	
    
-		
    
-			
    MADlib 1.19.0 Release
    
-			On March 8, 2022, MADlib completed its ninth release as an Apache Software Foundation Top Level Project.
-	
    
-    
    New features include:
    
-    
      
-    
    • DBSCAN: Fast parallel-optimized DBSCAN.
      
-    
    • MLP: Add rmsprop and Adam optimization techniques.
      
-    
    
-    
    Improvements:
    
-    
      
-    
    • Graph: Improve WCC subtx count and catalog entry frequency.
      
-    
    • MLP: Set lambda value for minibatch.
      
-    
    • GLM-multinom: Use non-temp tables in GroupIterationController.
      
-    
    • Jenkins: Add new dockerfile for PG11.
      
-    
    • Build: Use dynamic_library_path for module pathname.
      
-    
    
-	
    You are invited to download the 1.19.0 release and review the release notes. Also please refer to the list of supported databases and OS.
    
-	 			
    
-	
    
-
-    
    
-		
    
-			
    MADlib 1.18.0 Release
    
-			On April 5, 2021, MADlib completed its eighth release as an Apache Software Foundation Top Level Project.
-	
    
-    
    New features include:
    
-    
      
-    
    • Deep learning - New grid and random search methods.
      
-    
    • Deep learning - AutoML methods Hyperband and Hyperopt.
      
-    
    • Deep learning - Custom loss functions and custom metrics.
      
-    
    • Deep learning - TensorBoard support.
      
-    
    • Deep learning - Multi-input and output support for fit and evaluate.
      
-    
    • DBSCAN - Density based clustering (phase 1).
      
-    
    
-    
    Improvements:
    
-    
      
-    
    • Deep learning - Implement cache logic to speed performance.
      
-    
    • Deep learning - Reduce GPU idle time when moving model state between workers.
      
-    
    • Deep learning - Use Keras version from TensorFlow.
      
-    
    • Deep learning - Add top n to evaluate.
      
-    
    • Graph - Support BIGINT for all graph methods.
      
-    
    • Infra - Switch to CloudBees (was Jenkins).
      
-    
    
-	
    You are invited to download the 1.18.0 release and review the release notes. Also please refer to the list of supported databases and OS.
    
-	 			
    
-	
    
-
-	
    
-		
    
-			
    MADlib 1.17.0 Release
    
-			On April 9, 2020, MADlib completed its seventh release as an Apache Software Foundation Top Level Project.
-	
    
-    
    New features include:
    
-    
      
-    
    • Deep learning - Model selection framework for 
-    Keras with Tensorflow
-    backend with GPU acceleration, for model architecture search and
-    hyperparameter optimization.
      
-    
    • Deep learning - Support for heterogeneous clusters
-    where GPUs are attached to only certain segment hosts.
      
-    
    • Deep learning - Support inference for imported
-    models not trained in MADlib ("bring your own model").
      
-    
    • Deep learning - Support transfer learning
-    for multiple model fit function.
      
-    
    • Deep learning - Generate model selection
-    table for grid search or random search.
      
-    
    • Deep learning - Helper function to
-    get GPU type and configuration in a database cluster.
      
-    
    • k-Means clustering - Select optimal number of centroids
-    using elbow or silhouette methods.
      
-    
    • PostgreSQL 12 support.
      
-    
    
-    
    Improvements:
    
-    
      
-    
    • Association rules - Add option to set number 
-    of posterior rules.
      
-    
    • Correlation and covariance - Improve memory
-    usage with large number of groups.
      
-    
    • Deep learning - Improve performance of
-    mini-batch preprocessor and fit functions.
      
-    
    • Docs - Inprove installation guide on wiki.
      
-    
    • Graph - SSSP should not show vertices in output 
-    table that are unreachable.
      
-    
    • LDA - Add stopping criteria on perplexity.
      
-    
    
-	
    You are invited to download the 1.17.0 release and review the release notes.
-	For more details about the new deep learning feature, please refer to the
-	Apache MADlib deep learning notes and
-	the Jupyter notebook examples.
    
-	 			
    
-	
    
-
-	
    
-	
    
-
-        
    
-	
-	
    
-
-        
    
-	  
-	
    
-
-	
    
-	
    
-	
    
-	  
    
-		 	
-		  
    
-		  
    
-	    
    
-	      Copyright ©  The Apache Software Foundation, Licensed under the Apache License, Version 2.0.
-	      
    
-	      Apache, Apache MADlib, the Apache feather and the MADlib logo are trademarks of The Apache Software Foundation
-	    
    
-	  
    
-	
    
-
-
diff --git a/jquery-1.10.2.min.js b/jquery-1.10.2.min.js
deleted file mode 100644
index da417064..00000000
--- a/jquery-1.10.2.min.js
+++ /dev/null
@@ -1,6 +0,0 @@
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