Nonlinear regression simulations for existing split criteria

[morgsmss7]

Reference Issues/PRs

Fixes Issue 16370 in scikit-learn. Also see Issue 2 in tealeaf.

What does this implement/fix? Explain your changes.

This PR adds simulations and plots that show how split criteria compare on several nonlinear regression simulations including sinusoidal, logarithmic, multiplicative, and independence. There is not much information on scikit-learn's documentation about how to go about choosing which to use (mse, mae, or friedman mse) for the criterion parameter. This example demonstrates how to go about finding differences and shows that it may not always matter which criterion is chosen.

Any other comments?

This PR in sklearn will include these files:

sklearn/datasets/tests/test_samples_generator.py 
sklearn/datasets/samples_generator.py
sklearn/datasets/__init__.py
examples/ensemble/plot_random_forest_regression_criteria_comparison.py
examples/datasets/plot_nonlinear_regression_datasets.py 
doc/modules/classes.rst 
doc/datasets/index.rst

The other files that were changed for Vivek's PR will not be changed in sklearn.

[morgsmss7]

Split Criteria Comparison Experiment and Results

For each simulation type (Logarithmic, Sine, Square, Multiplicative, Independence)
And For each split criterion (mse, mae, friedman mse)

1. Generate 30 noisy training sets (10 dimensions, 50 samples)
2. Generate 1 noisy test set (10 dimensions, 1000 samples)
3. Train and evaluate using mse for all 30 training sets with random forests (500 trees) varying number of samples ( np.arange(5, 51, 3) )

[eigenvivek]

Overall, it looks great! I made some minor comments asking for stylistic changes to the comments.

[j1c]

This looks great. I think you wanted to make a PR to real sklearn right? My only concern is that the current NDD master has bunch of changes from other people that would be merged in as well. For this, I think the best course of action is to make a new branch, fetch the latest sklearn, add in these two examples along with the data generation code. Then make the PR from that branch.

These changes have been made in both the real sklearn version and the NDD version