Comparison of F-test and mutual information#

This example illustrates the differences between univariate F-test statistics and mutual information.

We consider 3 features x_1, x_2, x_3 distributed uniformly over [0, 1], the target depends on them as follows:

y = x_1 + sin(6 * pi * x_2) + 0.1 * N(0, 1), that is the third feature is completely irrelevant.

The code below plots the dependency of y against individual x_i and normalized values of univariate F-tests statistics and mutual information.

As F-test captures only linear dependency, it rates x_1 as the most discriminative feature. On the other hand, mutual information can capture any kind of dependency between variables and it rates x_2 as the most discriminative feature, which probably agrees better with our intuitive perception for this example. Both methods correctly mark x_3 as irrelevant.

F-test=1.00, MI=0.36, F-test=0.28, MI=1.00, F-test=0.00, MI=0.00
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

import matplotlib.pyplot as plt
import numpy as np

from sklearn.feature_selection import f_regression, mutual_info_regression

np.random.seed(0)
X = np.random.rand(1000, 3)
y = X[:, 0] + np.sin(6 * np.pi * X[:, 1]) + 0.1 * np.random.randn(1000)

f_test, _ = f_regression(X, y)
f_test /= np.max(f_test)

mi = mutual_info_regression(X, y)
mi /= np.max(mi)

plt.figure(figsize=(15, 5))
for i in range(3):
    plt.subplot(1, 3, i + 1)
    plt.scatter(X[:, i], y, edgecolor="black", s=20)
    plt.xlabel("$x_{}$".format(i + 1), fontsize=14)
    if i == 0:
        plt.ylabel("$y$", fontsize=14)
    plt.title("F-test={:.2f}, MI={:.2f}".format(f_test[i], mi[i]), fontsize=16)
plt.show()

Total running time of the script: (0 minutes 0.235 seconds)

Related examples

Test with permutations the significance of a classification score

Test with permutations the significance of a classification score

Adjustment for chance in clustering performance evaluation

Adjustment for chance in clustering performance evaluation

Univariate Feature Selection

Univariate Feature Selection

Comparison between grid search and successive halving

Comparison between grid search and successive halving

Gallery generated by Sphinx-Gallery