.. _sphx_glr_auto_examples_feature_selection_plot_f_test_vs_mi.py:


===========================================
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 features 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 marks x_3 as irrelevant.



.. image:: /auto_examples/feature_selection/images/sphx_glr_plot_f_test_vs_mi_001.png
    :align: center





.. code-block:: python

    print(__doc__)

    import numpy as np
    import matplotlib.pyplot as plt
    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)
        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 0.221 seconds)



.. container:: sphx-glr-download

    **Download Python source code:** :download:`plot_f_test_vs_mi.py <plot_f_test_vs_mi.py>`


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_f_test_vs_mi.ipynb <plot_f_test_vs_mi.ipynb>`