Test with permutations the significance of a classification score

In order to test if a classification score is significative a technique in repeating the classification procedure after randomizing, permuting, the labels. The p-value is then given by the percentage of runs for which the score obtained is greater than the classification score obtained in the first place.

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

print(__doc__)

import numpy as np
import matplotlib.pyplot as plt

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

Loading a dataset

iris = datasets.load_iris()
X = iris.data
y = iris.target
n_classes = np.unique(y).size

# Some noisy data not correlated
random = np.random.RandomState(seed=0)
E = random.normal(size=(len(X), 2200))

# Add noisy data to the informative features for make the task harder
X = np.c_[X, E]

svm = SVC(kernel='linear')
cv = StratifiedKFold(2)

score, permutation_scores, pvalue = permutation_test_score(
    svm, X, y, scoring="accuracy", cv=cv, n_permutations=100, n_jobs=1)

print("Classification score %s (pvalue : %s)" % (score, pvalue))

Out:

Classification score 0.513333333333 (pvalue : 0.00990099009901)

View histogram of permutation scores

plt.hist(permutation_scores, 20, label='Permutation scores')
ylim = plt.ylim()
# BUG: vlines(..., linestyle='--') fails on older versions of matplotlib
#plt.vlines(score, ylim[0], ylim[1], linestyle='--',
#          color='g', linewidth=3, label='Classification Score'
#          ' (pvalue %s)' % pvalue)
#plt.vlines(1.0 / n_classes, ylim[0], ylim[1], linestyle='--',
#          color='k', linewidth=3, label='Luck')
plt.plot(2 * [score], ylim, '--g', linewidth=3,
         label='Classification Score'
         ' (pvalue %s)' % pvalue)
plt.plot(2 * [1. / n_classes], ylim, '--k', linewidth=3, label='Luck')

plt.ylim(ylim)
plt.legend()
plt.xlabel('Score')
plt.show()

Total running time of the script: (0 minutes 6.600 seconds)