.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/model_selection/plot_permutation_tests_for_classification.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here `
to download the full example code or to run this example in your browser via Binder
.. rst-class:: sphx-glr-example-title
.. _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
# 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.
.. GENERATED FROM PYTHON SOURCE LINES 22-29
.. 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.
.. GENERATED FROM PYTHON SOURCE LINES 60-76
.. code-block:: default
from sklearn.svm import SVC
from sklearn.model_selection import StratifiedKFold
from sklearn.model_selection import permutation_test_score
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
)
.. GENERATED FROM PYTHON SOURCE LINES 77-88
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 88-100
.. 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")
.. 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
.. GENERATED FROM PYTHON SOURCE LINES 101-110
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 110-122
.. 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")
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 123-139
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
`_. The
Journal of Machine Learning Research (2010) vol. 11
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 8.658 seconds)
.. _sphx_glr_download_auto_examples_model_selection_plot_permutation_tests_for_classification.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/1.1.X?urlpath=lab/tree/notebooks/auto_examples/model_selection/plot_permutation_tests_for_classification.ipynb
:alt: Launch binder
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_permutation_tests_for_classification.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_permutation_tests_for_classification.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_