.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/feature_selection/plot_f_test_vs_mi.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_feature_selection_plot_f_test_vs_mi.py>`
        to download the full example code or to run this example in your browser via JupyterLite or Binder

.. rst-class:: sphx-glr-example-title

.. _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 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.

.. GENERATED FROM PYTHON SOURCE LINES 25-50



.. image-sg:: /auto_examples/feature_selection/images/sphx_glr_plot_f_test_vs_mi_001.png
   :alt: F-test=1.00, MI=0.36, F-test=0.28, MI=1.00, F-test=0.00, MI=0.00
   :srcset: /auto_examples/feature_selection/images/sphx_glr_plot_f_test_vs_mi_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    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()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.296 seconds)


.. _sphx_glr_download_auto_examples_feature_selection_plot_f_test_vs_mi.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/feature_selection/plot_f_test_vs_mi.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/feature_selection/plot_f_test_vs_mi.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_f_test_vs_mi.ipynb <plot_f_test_vs_mi.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

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


.. include:: plot_f_test_vs_mi.recommendations


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_