SARlib: Statistical Agnostic Regression Library

This library provides tools for statistical analysis, regression modeling, sample size analysis, and visualization. It includes OLS and SAR models, as well as utilities for data preprocessing and plotting.

A formal description and analysis are included in the following reference:

J. M. Gorriz, J. Ramirez, F. Segovia, C. Jimenez-Mesa, F. J. Martinez-Murcia, y J. Suckling, «Statistical agnostic regression: A machine learning method to validate regression models», Journal of Advanced Research, may 2025, doi: 10.1016/j.jare.2025.04.026.

Features

• Data Preprocessing: Standardize and clean input data, handle missing values.
• Visualization: Scatter plots for exploratory data analysis.
• OLS Regression: Permutation-based p-value, power, R², and coefficient estimation.
• SAR Regression: Support Vector Regression with advanced generalization bounds.
• Sample Size Analysis: Empirical study of how sample size affects model statistics.
• Plotting Utilities: Visualize loss, threshold, power, p-value, and coefficients as functions of sample size.

Installation

SARlib can be installed via PyPI:

pip install sarlib

Alternatively, you can install it manually by downloading the source code. In that case, make sure you have the following dependencies installed:

• numpy
• matplotlib
• statsmodels
• scikit-learn
• scipy

Main Components

Classes:

• SAR: Statistical Analysis Regression with PAC-Bayes, Vapnik, and IGP bounds.

• OLS: Ordinary Least Squares regression with permutation-based significance and power analysis.

• SampleSizeAnalysis: Analyzes the effect of sample size on model performance and statistics.

Functions:

• fix_data(x, y): Standardizes and cleans input data.

• show_scatter(x, y, ...): Visualizes predictors vs. response.

Usage

1. Import packages and prepare your data as numpy arrays:

   from sarlib import SAR, OLS, SampleSizeAnalysis, show_scatter
   import numpy as np
   x = np.random.randn(100, 3)  # predictors
   y = np.random.randn(100)     # response

2. Visualize data:

   show_scatter(x, y)

3. Fit SAR model:

   model_sar = SAR(n_realiz=100, norm='epsins', alpha=0.05)
   stats_sar = model_sar.fit(x, y, verbose=True)

4. Compare with an OLS model:

   model_ols = OLS(n_realiz=100, alpha=0.05)
   stats_ols = model_ols.fit(x, y, verbose=True)

5. Analyze sample size effect:

   analysis = SampleSizeAnalysis(model_sar, x, y, steps=7)
   analysis.plot_loss()
   analysis.plot_pvalue()
   analysis.plot_coef()

Function/Class Documentation

All functions and classes are documented with docstrings. Please refer to the code for parameter details and usage.

Author & License

Author: Sipba Group, UGR, https://sipba.ugr.es/

Please cite: J. M. Gorriz, J. Ramirez, F. Segovia, C. Jimenez-Mesa, F. J. Martinez-Murcia, y J. Suckling, «Statistical agnostic regression: A machine learning method to validate regression models», Journal of Advanced Research, may 2025, doi: 10.1016/j.jare.2025.04.026.

License: GPL Version 3