scikit-learn/sklearn/feature_selection/tests/test_feature_select.py

"""
Todo: cross-check the F-value with stats model
"""
from __future__ import division
import itertools
import warnings
import numpy as np
from scipy import stats, sparse

from sklearn.utils.testing import assert_equal
from sklearn.utils.testing import assert_almost_equal
from sklearn.utils.testing import assert_raises
from sklearn.utils.testing import assert_true
from sklearn.utils.testing import assert_array_equal
from sklearn.utils.testing import assert_array_almost_equal
from sklearn.utils.testing import assert_not_in
from sklearn.utils.testing import assert_less
from sklearn.utils.testing import assert_warns
from sklearn.utils.testing import ignore_warnings
from sklearn.utils.testing import assert_warns_message
from sklearn.utils.testing import assert_greater
from sklearn.utils.testing import assert_greater_equal
from sklearn.utils import safe_mask

from sklearn.datasets.samples_generator import (make_classification,
                                                make_regression)
from sklearn.feature_selection import (chi2, f_classif, f_oneway, f_regression,
                                       SelectPercentile, SelectKBest,
                                       SelectFpr, SelectFdr, SelectFwe,
                                       GenericUnivariateSelect)


##############################################################################
# Test the score functions

def test_f_oneway_vs_scipy_stats():
    # Test that our f_oneway gives the same result as scipy.stats
    rng = np.random.RandomState(0)
    X1 = rng.randn(10, 3)
    X2 = 1 + rng.randn(10, 3)
    f, pv = stats.f_oneway(X1, X2)
    f2, pv2 = f_oneway(X1, X2)
    assert_true(np.allclose(f, f2))
    assert_true(np.allclose(pv, pv2))


def test_f_oneway_ints():
    # Smoke test f_oneway on integers: that it does raise casting errors
    # with recent numpys
    rng = np.random.RandomState(0)
    X = rng.randint(10, size=(10, 10))
    y = np.arange(10)
    fint, pint = f_oneway(X, y)

    # test that is gives the same result as with float
    f, p = f_oneway(X.astype(np.float), y)
    assert_array_almost_equal(f, fint, decimal=4)
    assert_array_almost_equal(p, pint, decimal=4)


def test_f_classif():
    # Test whether the F test yields meaningful results
    # on a simple simulated classification problem
    X, y = make_classification(n_samples=200, n_features=20,
                               n_informative=3, n_redundant=2,
                               n_repeated=0, n_classes=8,
                               n_clusters_per_class=1, flip_y=0.0,
                               class_sep=10, shuffle=False, random_state=0)

    F, pv = f_classif(X, y)
    F_sparse, pv_sparse = f_classif(sparse.csr_matrix(X), y)
    assert_true((F > 0).all())
    assert_true((pv > 0).all())
    assert_true((pv < 1).all())
    assert_true((pv[:5] < 0.05).all())
    assert_true((pv[5:] > 1.e-4).all())
    assert_array_almost_equal(F_sparse, F)
    assert_array_almost_equal(pv_sparse, pv)


def test_f_regression():
    # Test whether the F test yields meaningful results
    # on a simple simulated regression problem
    X, y = make_regression(n_samples=200, n_features=20, n_informative=5,
                           shuffle=False, random_state=0)

    F, pv = f_regression(X, y)
    assert_true((F > 0).all())
    assert_true((pv > 0).all())
    assert_true((pv < 1).all())
    assert_true((pv[:5] < 0.05).all())
    assert_true((pv[5:] > 1.e-4).all())

    # again without centering, compare with sparse
    F, pv = f_regression(X, y, center=False)
    F_sparse, pv_sparse = f_regression(sparse.csr_matrix(X), y, center=False)
    assert_array_almost_equal(F_sparse, F)
    assert_array_almost_equal(pv_sparse, pv)


def test_f_regression_input_dtype():
    # Test whether f_regression returns the same value
    # for any numeric data_type
    rng = np.random.RandomState(0)
    X = rng.rand(10, 20)
    y = np.arange(10).astype(np.int)

    F1, pv1 = f_regression(X, y)
    F2, pv2 = f_regression(X, y.astype(np.float))
    assert_array_almost_equal(F1, F2, 5)
    assert_array_almost_equal(pv1, pv2, 5)


def test_f_regression_center():
    # Test whether f_regression preserves dof according to 'center' argument
    # We use two centered variates so we have a simple relationship between
    # F-score with variates centering and F-score without variates centering.
    # Create toy example
    X = np.arange(-5, 6).reshape(-1, 1)  # X has zero mean
    n_samples = X.size
    Y = np.ones(n_samples)
    Y[::2] *= -1.
    Y[0] = 0.  # have Y mean being null

    F1, _ = f_regression(X, Y, center=True)
    F2, _ = f_regression(X, Y, center=False)
    assert_array_almost_equal(F1 * (n_samples - 1.) / (n_samples - 2.), F2)
    assert_almost_equal(F2[0], 0.232558139)  # value from statsmodels OLS


def test_f_classif_multi_class():
    # Test whether the F test yields meaningful results
    # on a simple simulated classification problem
    X, y = make_classification(n_samples=200, n_features=20,
                               n_informative=3, n_redundant=2,
                               n_repeated=0, n_classes=8,
                               n_clusters_per_class=1, flip_y=0.0,
                               class_sep=10, shuffle=False, random_state=0)

    F, pv = f_classif(X, y)
    assert_true((F > 0).all())
    assert_true((pv > 0).all())
    assert_true((pv < 1).all())
    assert_true((pv[:5] < 0.05).all())
    assert_true((pv[5:] > 1.e-4).all())


def test_select_percentile_classif():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple classification problem
    # with the percentile heuristic
    X, y = make_classification(n_samples=200, n_features=20,
                               n_informative=3, n_redundant=2,
                               n_repeated=0, n_classes=8,
                               n_clusters_per_class=1, flip_y=0.0,
                               class_sep=10, shuffle=False, random_state=0)

    univariate_filter = SelectPercentile(f_classif, percentile=25)
    X_r = univariate_filter.fit(X, y).transform(X)
    X_r2 = GenericUnivariateSelect(f_classif, mode='percentile',
                                   param=25).fit(X, y).transform(X)
    assert_array_equal(X_r, X_r2)
    support = univariate_filter.get_support()
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    assert_array_equal(support, gtruth)


def test_select_percentile_classif_sparse():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple classification problem
    # with the percentile heuristic
    X, y = make_classification(n_samples=200, n_features=20,
                               n_informative=3, n_redundant=2,
                               n_repeated=0, n_classes=8,
                               n_clusters_per_class=1, flip_y=0.0,
                               class_sep=10, shuffle=False, random_state=0)
    X = sparse.csr_matrix(X)
    univariate_filter = SelectPercentile(f_classif, percentile=25)
    X_r = univariate_filter.fit(X, y).transform(X)
    X_r2 = GenericUnivariateSelect(f_classif, mode='percentile',
                                   param=25).fit(X, y).transform(X)
    assert_array_equal(X_r.toarray(), X_r2.toarray())
    support = univariate_filter.get_support()
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    assert_array_equal(support, gtruth)

    X_r2inv = univariate_filter.inverse_transform(X_r2)
    assert_true(sparse.issparse(X_r2inv))
    support_mask = safe_mask(X_r2inv, support)
    assert_equal(X_r2inv.shape, X.shape)
    assert_array_equal(X_r2inv[:, support_mask].toarray(), X_r.toarray())
    # Check other columns are empty
    assert_equal(X_r2inv.getnnz(), X_r.getnnz())


##############################################################################
# Test univariate selection in classification settings

def test_select_kbest_classif():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple classification problem
    # with the k best heuristic
    X, y = make_classification(n_samples=200, n_features=20,
                               n_informative=3, n_redundant=2,
                               n_repeated=0, n_classes=8,
                               n_clusters_per_class=1, flip_y=0.0,
                               class_sep=10, shuffle=False, random_state=0)

    univariate_filter = SelectKBest(f_classif, k=5)
    X_r = univariate_filter.fit(X, y).transform(X)
    X_r2 = GenericUnivariateSelect(
        f_classif, mode='k_best', param=5).fit(X, y).transform(X)
    assert_array_equal(X_r, X_r2)
    support = univariate_filter.get_support()
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    assert_array_equal(support, gtruth)


def test_select_kbest_all():
    # Test whether k="all" correctly returns all features.
    X, y = make_classification(n_samples=20, n_features=10,
                               shuffle=False, random_state=0)

    univariate_filter = SelectKBest(f_classif, k='all')
    X_r = univariate_filter.fit(X, y).transform(X)
    assert_array_equal(X, X_r)


def test_select_kbest_zero():
    # Test whether k=0 correctly returns no features.
    X, y = make_classification(n_samples=20, n_features=10,
                               shuffle=False, random_state=0)

    univariate_filter = SelectKBest(f_classif, k=0)
    univariate_filter.fit(X, y)
    support = univariate_filter.get_support()
    gtruth = np.zeros(10, dtype=bool)
    assert_array_equal(support, gtruth)
    X_selected = assert_warns_message(UserWarning, 'No features were selected',
                                      univariate_filter.transform, X)
    assert_equal(X_selected.shape, (20, 0))


def test_select_heuristics_classif():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple classification problem
    # with the fdr, fwe and fpr heuristics
    X, y = make_classification(n_samples=200, n_features=20,
                               n_informative=3, n_redundant=2,
                               n_repeated=0, n_classes=8,
                               n_clusters_per_class=1, flip_y=0.0,
                               class_sep=10, shuffle=False, random_state=0)

    univariate_filter = SelectFwe(f_classif, alpha=0.01)
    X_r = univariate_filter.fit(X, y).transform(X)
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    for mode in ['fdr', 'fpr', 'fwe']:
        X_r2 = GenericUnivariateSelect(
            f_classif, mode=mode, param=0.01).fit(X, y).transform(X)
        assert_array_equal(X_r, X_r2)
        support = univariate_filter.get_support()
        assert_array_almost_equal(support, gtruth)


##############################################################################
# Test univariate selection in regression settings


def assert_best_scores_kept(score_filter):
    scores = score_filter.scores_
    support = score_filter.get_support()
    assert_array_equal(np.sort(scores[support]),
                       np.sort(scores)[-support.sum():])


def test_select_percentile_regression():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple regression problem
    # with the percentile heuristic
    X, y = make_regression(n_samples=200, n_features=20,
                           n_informative=5, shuffle=False, random_state=0)

    univariate_filter = SelectPercentile(f_regression, percentile=25)
    X_r = univariate_filter.fit(X, y).transform(X)
    assert_best_scores_kept(univariate_filter)
    X_r2 = GenericUnivariateSelect(
        f_regression, mode='percentile', param=25).fit(X, y).transform(X)
    assert_array_equal(X_r, X_r2)
    support = univariate_filter.get_support()
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    assert_array_equal(support, gtruth)
    X_2 = X.copy()
    X_2[:, np.logical_not(support)] = 0
    assert_array_equal(X_2, univariate_filter.inverse_transform(X_r))
    # Check inverse_transform respects dtype
    assert_array_equal(X_2.astype(bool),
                       univariate_filter.inverse_transform(X_r.astype(bool)))


def test_select_percentile_regression_full():
    # Test whether the relative univariate feature selection
    # selects all features when '100%' is asked.
    X, y = make_regression(n_samples=200, n_features=20,
                           n_informative=5, shuffle=False, random_state=0)

    univariate_filter = SelectPercentile(f_regression, percentile=100)
    X_r = univariate_filter.fit(X, y).transform(X)
    assert_best_scores_kept(univariate_filter)
    X_r2 = GenericUnivariateSelect(
        f_regression, mode='percentile', param=100).fit(X, y).transform(X)
    assert_array_equal(X_r, X_r2)
    support = univariate_filter.get_support()
    gtruth = np.ones(20)
    assert_array_equal(support, gtruth)


def test_invalid_percentile():
    X, y = make_regression(n_samples=10, n_features=20,
                           n_informative=2, shuffle=False, random_state=0)

    assert_raises(ValueError, SelectPercentile(percentile=-1).fit, X, y)
    assert_raises(ValueError, SelectPercentile(percentile=101).fit, X, y)
    assert_raises(ValueError, GenericUnivariateSelect(mode='percentile',
                                                      param=-1).fit, X, y)
    assert_raises(ValueError, GenericUnivariateSelect(mode='percentile',
                                                      param=101).fit, X, y)


def test_select_kbest_regression():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple regression problem
    # with the k best heuristic
    X, y = make_regression(n_samples=200, n_features=20, n_informative=5,
                           shuffle=False, random_state=0, noise=10)

    univariate_filter = SelectKBest(f_regression, k=5)
    X_r = univariate_filter.fit(X, y).transform(X)
    assert_best_scores_kept(univariate_filter)
    X_r2 = GenericUnivariateSelect(
        f_regression, mode='k_best', param=5).fit(X, y).transform(X)
    assert_array_equal(X_r, X_r2)
    support = univariate_filter.get_support()
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    assert_array_equal(support, gtruth)


def test_select_heuristics_regression():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple regression problem
    # with the fpr, fdr or fwe heuristics
    X, y = make_regression(n_samples=200, n_features=20, n_informative=5,
                           shuffle=False, random_state=0, noise=10)

    univariate_filter = SelectFpr(f_regression, alpha=0.01)
    X_r = univariate_filter.fit(X, y).transform(X)
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    for mode in ['fdr', 'fpr', 'fwe']:
        X_r2 = GenericUnivariateSelect(
            f_regression, mode=mode, param=0.01).fit(X, y).transform(X)
        assert_array_equal(X_r, X_r2)
        support = univariate_filter.get_support()
        assert_array_equal(support[:5], np.ones((5, ), dtype=np.bool))
        assert_less(np.sum(support[5:] == 1), 3)


def test_select_fdr_regression():
    # Test that fdr heuristic actually has low FDR.
    def single_fdr(alpha, n_informative, random_state):
        X, y = make_regression(n_samples=150, n_features=20,
                               n_informative=n_informative, shuffle=False,
                               random_state=random_state, noise=10)

        with warnings.catch_warnings(record=True):
            # Warnings can be raised when no features are selected
            # (low alpha or very noisy data)
            univariate_filter = SelectFdr(f_regression, alpha=alpha)
            X_r = univariate_filter.fit(X, y).transform(X)
            X_r2 = GenericUnivariateSelect(
                f_regression, mode='fdr', param=alpha).fit(X, y).transform(X)

        assert_array_equal(X_r, X_r2)
        support = univariate_filter.get_support()
        num_false_positives = np.sum(support[n_informative:] == 1)
        num_true_positives = np.sum(support[:n_informative] == 1)

        if num_false_positives == 0:
            return 0.
        false_discovery_rate = (num_false_positives /
                                (num_true_positives + num_false_positives))
        return false_discovery_rate

    for alpha in [0.001, 0.01, 0.1]:
        for n_informative in [1, 5, 10]:
            # As per Benjamini-Hochberg, the expected false discovery rate
            # should be lower than alpha:
            # FDR = E(FP / (TP + FP)) <= alpha
            false_discovery_rate = np.mean([single_fdr(alpha, n_informative,
                                                       random_state) for
                                            random_state in range(30)])
            assert_greater_equal(alpha, false_discovery_rate)

            # Make sure that the empirical false discovery rate increases
            # with alpha:
            if false_discovery_rate != 0:
                assert_greater(false_discovery_rate, alpha / 10)


def test_select_fwe_regression():
    # Test whether the relative univariate feature selection
    # gets the correct items in a simple regression problem
    # with the fwe heuristic
    X, y = make_regression(n_samples=200, n_features=20,
                           n_informative=5, shuffle=False, random_state=0)

    univariate_filter = SelectFwe(f_regression, alpha=0.01)
    X_r = univariate_filter.fit(X, y).transform(X)
    X_r2 = GenericUnivariateSelect(
        f_regression, mode='fwe', param=0.01).fit(X, y).transform(X)
    assert_array_equal(X_r, X_r2)
    support = univariate_filter.get_support()
    gtruth = np.zeros(20)
    gtruth[:5] = 1
    assert_array_equal(support[:5], np.ones((5, ), dtype=np.bool))
    assert_less(np.sum(support[5:] == 1), 2)


def test_selectkbest_tiebreaking():
    # Test whether SelectKBest actually selects k features in case of ties.
    # Prior to 0.11, SelectKBest would return more features than requested.
    Xs = [[0, 1, 1], [0, 0, 1], [1, 0, 0], [1, 1, 0]]
    y = [1]
    dummy_score = lambda X, y: (X[0], X[0])
    for X in Xs:
        sel = SelectKBest(dummy_score, k=1)
        X1 = ignore_warnings(sel.fit_transform)([X], y)
        assert_equal(X1.shape[1], 1)
        assert_best_scores_kept(sel)

        sel = SelectKBest(dummy_score, k=2)
        X2 = ignore_warnings(sel.fit_transform)([X], y)
        assert_equal(X2.shape[1], 2)
        assert_best_scores_kept(sel)


def test_selectpercentile_tiebreaking():
    # Test if SelectPercentile selects the right n_features in case of ties.
    Xs = [[0, 1, 1], [0, 0, 1], [1, 0, 0], [1, 1, 0]]
    y = [1]
    dummy_score = lambda X, y: (X[0], X[0])
    for X in Xs:
        sel = SelectPercentile(dummy_score, percentile=34)
        X1 = ignore_warnings(sel.fit_transform)([X], y)
        assert_equal(X1.shape[1], 1)
        assert_best_scores_kept(sel)

        sel = SelectPercentile(dummy_score, percentile=67)
        X2 = ignore_warnings(sel.fit_transform)([X], y)
        assert_equal(X2.shape[1], 2)
        assert_best_scores_kept(sel)


def test_tied_pvalues():
    # Test whether k-best and percentiles work with tied pvalues from chi2.
    # chi2 will return the same p-values for the following features, but it
    # will return different scores.
    X0 = np.array([[10000, 9999, 9998], [1, 1, 1]])
    y = [0, 1]

    for perm in itertools.permutations((0, 1, 2)):
        X = X0[:, perm]
        Xt = SelectKBest(chi2, k=2).fit_transform(X, y)
        assert_equal(Xt.shape, (2, 2))
        assert_not_in(9998, Xt)

        Xt = SelectPercentile(chi2, percentile=67).fit_transform(X, y)
        assert_equal(Xt.shape, (2, 2))
        assert_not_in(9998, Xt)


def test_tied_scores():
    # Test for stable sorting in k-best with tied scores.
    X_train = np.array([[0, 0, 0], [1, 1, 1]])
    y_train = [0, 1]

    for n_features in [1, 2, 3]:
        sel = SelectKBest(chi2, k=n_features).fit(X_train, y_train)
        X_test = sel.transform([[0, 1, 2]])
        assert_array_equal(X_test[0], np.arange(3)[-n_features:])


def test_nans():
    # Assert that SelectKBest and SelectPercentile can handle NaNs.
    # First feature has zero variance to confuse f_classif (ANOVA) and
    # make it return a NaN.
    X = [[0, 1, 0], [0, -1, -1], [0, .5, .5]]
    y = [1, 0, 1]

    for select in (SelectKBest(f_classif, 2),
                   SelectPercentile(f_classif, percentile=67)):
        ignore_warnings(select.fit)(X, y)
        assert_array_equal(select.get_support(indices=True), np.array([1, 2]))


def test_score_func_error():
    X = [[0, 1, 0], [0, -1, -1], [0, .5, .5]]
    y = [1, 0, 1]

    for SelectFeatures in [SelectKBest, SelectPercentile, SelectFwe,
                           SelectFdr, SelectFpr, GenericUnivariateSelect]:
        assert_raises(TypeError, SelectFeatures(score_func=10).fit, X, y)


def test_invalid_k():
    X = [[0, 1, 0], [0, -1, -1], [0, .5, .5]]
    y = [1, 0, 1]

    assert_raises(ValueError, SelectKBest(k=-1).fit, X, y)
    assert_raises(ValueError, SelectKBest(k=4).fit, X, y)
    assert_raises(ValueError,
                  GenericUnivariateSelect(mode='k_best', param=-1).fit, X, y)
    assert_raises(ValueError,
                  GenericUnivariateSelect(mode='k_best', param=4).fit, X, y)


def test_f_classif_constant_feature():
    # Test that f_classif warns if a feature is constant throughout.

    X, y = make_classification(n_samples=10, n_features=5)
    X[:, 0] = 2.0
    assert_warns(UserWarning, f_classif, X, y)


def test_no_feature_selected():
    rng = np.random.RandomState(0)

    # Generate random uncorrelated data: a strict univariate test should
    # rejects all the features
    X = rng.rand(40, 10)
    y = rng.randint(0, 4, size=40)
    strict_selectors = [
        SelectFwe(alpha=0.01).fit(X, y),
        SelectFdr(alpha=0.01).fit(X, y),
        SelectFpr(alpha=0.01).fit(X, y),
        SelectPercentile(percentile=0).fit(X, y),
        SelectKBest(k=0).fit(X, y),
    ]
    for selector in strict_selectors:
        assert_array_equal(selector.get_support(), np.zeros(10))
        X_selected = assert_warns_message(
            UserWarning, 'No features were selected', selector.transform, X)
        assert_equal(X_selected.shape, (40, 0))