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.. _sphx_glr_auto_examples_model_selection_plot_permutation_tests_for_classification.py:


=================================================================
Test with permutations the significance of a classification score
=================================================================

This example demonstrates the use of
:func:`~sklearn.model_selection.permutation_test_score` to evaluate the
significance of a cross-validated score using permutations.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: default


    # Authors:  Alexandre Gramfort <alexandre.gramfort@inria.fr>
    #           Lucy Liu
    # License: BSD 3 clause








.. GENERATED FROM PYTHON SOURCE LINES 17-22

Dataset
-------

We will use the :ref:`iris_dataset`, which consists of measurements taken
from 3 types of irises.

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.. code-block:: default


    from sklearn.datasets import load_iris

    iris = load_iris()
    X = iris.data
    y = iris.target








.. GENERATED FROM PYTHON SOURCE LINES 30-32

We will also generate some random feature data (i.e., 20 features),
uncorrelated with the class labels in the iris dataset.

.. GENERATED FROM PYTHON SOURCE LINES 32-40

.. code-block:: default


    import numpy as np

    n_uncorrelated_features = 20
    rng = np.random.RandomState(seed=0)
    # Use same number of samples as in iris and 20 features
    X_rand = rng.normal(size=(X.shape[0], n_uncorrelated_features))








.. GENERATED FROM PYTHON SOURCE LINES 41-60

Permutation test score
----------------------

Next, we calculate the
:func:`~sklearn.model_selection.permutation_test_score` using the original
iris dataset, which strongly predict the labels and
the randomly generated features and iris labels, which should have
no dependency between features and labels. We use the
:class:`~sklearn.svm.SVC` classifier and :ref:`accuracy_score` to evaluate
the model at each round.

:func:`~sklearn.model_selection.permutation_test_score` generates a null
distribution by calculating the accuracy of the classifier
on 1000 different permutations of the dataset, where features
remain the same but labels undergo different permutations. This is the
distribution for the null hypothesis which states there is no dependency
between the features and labels. An empirical p-value is then calculated as
the percentage of permutations for which the score obtained is greater
that the score obtained using the original data.

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.. code-block:: default


    from sklearn.model_selection import StratifiedKFold, permutation_test_score
    from sklearn.svm import SVC

    clf = SVC(kernel="linear", random_state=7)
    cv = StratifiedKFold(2, shuffle=True, random_state=0)

    score_iris, perm_scores_iris, pvalue_iris = permutation_test_score(
        clf, X, y, scoring="accuracy", cv=cv, n_permutations=1000
    )

    score_rand, perm_scores_rand, pvalue_rand = permutation_test_score(
        clf, X_rand, y, scoring="accuracy", cv=cv, n_permutations=1000
    )








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Original data
^^^^^^^^^^^^^

Below we plot a histogram of the permutation scores (the null
distribution). The red line indicates the score obtained by the classifier
on the original data. The score is much better than those obtained by
using permuted data and the p-value is thus very low. This indicates that
there is a low likelihood that this good score would be obtained by chance
alone. It provides evidence that the iris dataset contains real dependency
between features and labels and the classifier was able to utilize this
to obtain good results.

.. GENERATED FROM PYTHON SOURCE LINES 87-99

.. code-block:: default


    import matplotlib.pyplot as plt

    fig, ax = plt.subplots()

    ax.hist(perm_scores_iris, bins=20, density=True)
    ax.axvline(score_iris, ls="--", color="r")
    score_label = f"Score on original\ndata: {score_iris:.2f}\n(p-value: {pvalue_iris:.3f})"
    ax.text(0.7, 10, score_label, fontsize=12)
    ax.set_xlabel("Accuracy score")
    _ = ax.set_ylabel("Probability density")




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_permutation_tests_for_classification_001.png
   :alt: plot permutation tests for classification
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_permutation_tests_for_classification_001.png
   :class: sphx-glr-single-img





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Random data
^^^^^^^^^^^

Below we plot the null distribution for the randomized data. The permutation
scores are similar to those obtained using the original iris dataset
because the permutation always destroys any feature label dependency present.
The score obtained on the original randomized data in this case though, is
very poor. This results in a large p-value, confirming that there was no
feature label dependency in the original data.

.. GENERATED FROM PYTHON SOURCE LINES 109-121

.. code-block:: default


    fig, ax = plt.subplots()

    ax.hist(perm_scores_rand, bins=20, density=True)
    ax.set_xlim(0.13)
    ax.axvline(score_rand, ls="--", color="r")
    score_label = f"Score on original\ndata: {score_rand:.2f}\n(p-value: {pvalue_rand:.3f})"
    ax.text(0.14, 7.5, score_label, fontsize=12)
    ax.set_xlabel("Accuracy score")
    ax.set_ylabel("Probability density")
    plt.show()




.. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_permutation_tests_for_classification_002.png
   :alt: plot permutation tests for classification
   :srcset: /auto_examples/model_selection/images/sphx_glr_plot_permutation_tests_for_classification_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 122-138

Another possible reason for obtaining a high p-value is that the classifier
was not able to use the structure in the data. In this case, the p-value
would only be low for classifiers that are able to utilize the dependency
present. In our case above, where the data is random, all classifiers would
have a high p-value as there is no structure present in the data.

Finally, note that this test has been shown to produce low p-values even
if there is only weak structure in the data [1]_.

.. topic:: References:

  .. [1] Ojala and Garriga. `Permutation Tests for Studying Classifier
         Performance
         <http://www.jmlr.org/papers/volume11/ojala10a/ojala10a.pdf>`_. The
         Journal of Machine Learning Research (2010) vol. 11



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