# Author: Alexandre Gramfort # Gael Varoquaux # Virgile Fritsch # # License: BSD 3 clause import numpy as np from sklearn.utils.testing import assert_almost_equal from sklearn.utils.testing import assert_array_almost_equal from sklearn.utils.testing import assert_array_equal from sklearn.utils.testing import assert_raises from sklearn.utils.testing import assert_warns from sklearn.utils.testing import assert_greater from sklearn import datasets from sklearn.covariance import empirical_covariance, EmpiricalCovariance, \ ShrunkCovariance, shrunk_covariance, \ LedoitWolf, ledoit_wolf, ledoit_wolf_shrinkage, OAS, oas X = datasets.load_diabetes().data X_1d = X[:, 0] n_samples, n_features = X.shape def test_covariance(): # Tests Covariance module on a simple dataset. # test covariance fit from data cov = EmpiricalCovariance() cov.fit(X) emp_cov = empirical_covariance(X) assert_array_almost_equal(emp_cov, cov.covariance_, 4) assert_almost_equal(cov.error_norm(emp_cov), 0) assert_almost_equal( cov.error_norm(emp_cov, norm='spectral'), 0) assert_almost_equal( cov.error_norm(emp_cov, norm='frobenius'), 0) assert_almost_equal( cov.error_norm(emp_cov, scaling=False), 0) assert_almost_equal( cov.error_norm(emp_cov, squared=False), 0) assert_raises(NotImplementedError, cov.error_norm, emp_cov, norm='foo') # Mahalanobis distances computation test mahal_dist = cov.mahalanobis(X) assert_greater(np.amin(mahal_dist), 0) # test with n_features = 1 X_1d = X[:, 0].reshape((-1, 1)) cov = EmpiricalCovariance() cov.fit(X_1d) assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4) assert_almost_equal(cov.error_norm(empirical_covariance(X_1d)), 0) assert_almost_equal( cov.error_norm(empirical_covariance(X_1d), norm='spectral'), 0) # test with one sample # Create X with 1 sample and 5 features X_1sample = np.arange(5).reshape(1, 5) cov = EmpiricalCovariance() assert_warns(UserWarning, cov.fit, X_1sample) assert_array_almost_equal(cov.covariance_, np.zeros(shape=(5, 5), dtype=np.float64)) # test integer type X_integer = np.asarray([[0, 1], [1, 0]]) result = np.asarray([[0.25, -0.25], [-0.25, 0.25]]) assert_array_almost_equal(empirical_covariance(X_integer), result) # test centered case cov = EmpiricalCovariance(assume_centered=True) cov.fit(X) assert_array_equal(cov.location_, np.zeros(X.shape[1])) def test_shrunk_covariance(): # Tests ShrunkCovariance module on a simple dataset. # compare shrunk covariance obtained from data and from MLE estimate cov = ShrunkCovariance(shrinkage=0.5) cov.fit(X) assert_array_almost_equal( shrunk_covariance(empirical_covariance(X), shrinkage=0.5), cov.covariance_, 4) # same test with shrinkage not provided cov = ShrunkCovariance() cov.fit(X) assert_array_almost_equal( shrunk_covariance(empirical_covariance(X)), cov.covariance_, 4) # same test with shrinkage = 0 (<==> empirical_covariance) cov = ShrunkCovariance(shrinkage=0.) cov.fit(X) assert_array_almost_equal(empirical_covariance(X), cov.covariance_, 4) # test with n_features = 1 X_1d = X[:, 0].reshape((-1, 1)) cov = ShrunkCovariance(shrinkage=0.3) cov.fit(X_1d) assert_array_almost_equal(empirical_covariance(X_1d), cov.covariance_, 4) # test shrinkage coeff on a simple data set (without saving precision) cov = ShrunkCovariance(shrinkage=0.5, store_precision=False) cov.fit(X) assert(cov.precision_ is None) def test_ledoit_wolf(): # Tests LedoitWolf module on a simple dataset. # test shrinkage coeff on a simple data set X_centered = X - X.mean(axis=0) lw = LedoitWolf(assume_centered=True) lw.fit(X_centered) shrinkage_ = lw.shrinkage_ score_ = lw.score(X_centered) assert_almost_equal(ledoit_wolf_shrinkage(X_centered, assume_centered=True), shrinkage_) assert_almost_equal(ledoit_wolf_shrinkage(X_centered, assume_centered=True, block_size=6), shrinkage_) # compare shrunk covariance obtained from data and from MLE estimate lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X_centered, assume_centered=True) assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4) assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_) # compare estimates given by LW and ShrunkCovariance scov = ShrunkCovariance(shrinkage=lw.shrinkage_, assume_centered=True) scov.fit(X_centered) assert_array_almost_equal(scov.covariance_, lw.covariance_, 4) # test with n_features = 1 X_1d = X[:, 0].reshape((-1, 1)) lw = LedoitWolf(assume_centered=True) lw.fit(X_1d) lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X_1d, assume_centered=True) assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4) assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_) assert_array_almost_equal((X_1d ** 2).sum() / n_samples, lw.covariance_, 4) # test shrinkage coeff on a simple data set (without saving precision) lw = LedoitWolf(store_precision=False, assume_centered=True) lw.fit(X_centered) assert_almost_equal(lw.score(X_centered), score_, 4) assert(lw.precision_ is None) # Same tests without assuming centered data # test shrinkage coeff on a simple data set lw = LedoitWolf() lw.fit(X) assert_almost_equal(lw.shrinkage_, shrinkage_, 4) assert_almost_equal(lw.shrinkage_, ledoit_wolf_shrinkage(X)) assert_almost_equal(lw.shrinkage_, ledoit_wolf(X)[1]) assert_almost_equal(lw.score(X), score_, 4) # compare shrunk covariance obtained from data and from MLE estimate lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X) assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4) assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_) # compare estimates given by LW and ShrunkCovariance scov = ShrunkCovariance(shrinkage=lw.shrinkage_) scov.fit(X) assert_array_almost_equal(scov.covariance_, lw.covariance_, 4) # test with n_features = 1 X_1d = X[:, 0].reshape((-1, 1)) lw = LedoitWolf() lw.fit(X_1d) lw_cov_from_mle, lw_shrinkage_from_mle = ledoit_wolf(X_1d) assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4) assert_almost_equal(lw_shrinkage_from_mle, lw.shrinkage_) assert_array_almost_equal(empirical_covariance(X_1d), lw.covariance_, 4) # test with one sample # warning should be raised when using only 1 sample X_1sample = np.arange(5).reshape(1, 5) lw = LedoitWolf() assert_warns(UserWarning, lw.fit, X_1sample) assert_array_almost_equal(lw.covariance_, np.zeros(shape=(5, 5), dtype=np.float64)) # test shrinkage coeff on a simple data set (without saving precision) lw = LedoitWolf(store_precision=False) lw.fit(X) assert_almost_equal(lw.score(X), score_, 4) assert(lw.precision_ is None) def _naive_ledoit_wolf_shrinkage(X): # A simple implementation of the formulas from Ledoit & Wolf # The computation below achieves the following computations of the # "O. Ledoit and M. Wolf, A Well-Conditioned Estimator for # Large-Dimensional Covariance Matrices" # beta and delta are given in the beginning of section 3.2 n_samples, n_features = X.shape emp_cov = empirical_covariance(X, assume_centered=False) mu = np.trace(emp_cov) / n_features delta_ = emp_cov.copy() delta_.flat[::n_features + 1] -= mu delta = (delta_ ** 2).sum() / n_features X2 = X ** 2 beta_ = 1. / (n_features * n_samples) \ * np.sum(np.dot(X2.T, X2) / n_samples - emp_cov ** 2) beta = min(beta_, delta) shrinkage = beta / delta return shrinkage def test_ledoit_wolf_small(): # Compare our blocked implementation to the naive implementation X_small = X[:, :4] lw = LedoitWolf() lw.fit(X_small) shrinkage_ = lw.shrinkage_ assert_almost_equal(shrinkage_, _naive_ledoit_wolf_shrinkage(X_small)) def test_ledoit_wolf_large(): # test that ledoit_wolf doesn't error on data that is wider than block_size rng = np.random.RandomState(0) # use a number of features that is larger than the block-size X = rng.normal(size=(10, 20)) lw = LedoitWolf(block_size=10).fit(X) # check that covariance is about diagonal (random normal noise) assert_almost_equal(lw.covariance_, np.eye(20), 0) cov = lw.covariance_ # check that the result is consistent with not splitting data into blocks. lw = LedoitWolf(block_size=25).fit(X) assert_almost_equal(lw.covariance_, cov) def test_oas(): # Tests OAS module on a simple dataset. # test shrinkage coeff on a simple data set X_centered = X - X.mean(axis=0) oa = OAS(assume_centered=True) oa.fit(X_centered) shrinkage_ = oa.shrinkage_ score_ = oa.score(X_centered) # compare shrunk covariance obtained from data and from MLE estimate oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_centered, assume_centered=True) assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4) assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_) # compare estimates given by OAS and ShrunkCovariance scov = ShrunkCovariance(shrinkage=oa.shrinkage_, assume_centered=True) scov.fit(X_centered) assert_array_almost_equal(scov.covariance_, oa.covariance_, 4) # test with n_features = 1 X_1d = X[:, 0:1] oa = OAS(assume_centered=True) oa.fit(X_1d) oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d, assume_centered=True) assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4) assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_) assert_array_almost_equal((X_1d ** 2).sum() / n_samples, oa.covariance_, 4) # test shrinkage coeff on a simple data set (without saving precision) oa = OAS(store_precision=False, assume_centered=True) oa.fit(X_centered) assert_almost_equal(oa.score(X_centered), score_, 4) assert(oa.precision_ is None) # Same tests without assuming centered data-------------------------------- # test shrinkage coeff on a simple data set oa = OAS() oa.fit(X) assert_almost_equal(oa.shrinkage_, shrinkage_, 4) assert_almost_equal(oa.score(X), score_, 4) # compare shrunk covariance obtained from data and from MLE estimate oa_cov_from_mle, oa_shrinkage_from_mle = oas(X) assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4) assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_) # compare estimates given by OAS and ShrunkCovariance scov = ShrunkCovariance(shrinkage=oa.shrinkage_) scov.fit(X) assert_array_almost_equal(scov.covariance_, oa.covariance_, 4) # test with n_features = 1 X_1d = X[:, 0].reshape((-1, 1)) oa = OAS() oa.fit(X_1d) oa_cov_from_mle, oa_shrinkage_from_mle = oas(X_1d) assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4) assert_almost_equal(oa_shrinkage_from_mle, oa.shrinkage_) assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4) # test with one sample # warning should be raised when using only 1 sample X_1sample = np.arange(5).reshape(1, 5) oa = OAS() assert_warns(UserWarning, oa.fit, X_1sample) assert_array_almost_equal(oa.covariance_, np.zeros(shape=(5, 5), dtype=np.float64)) # test shrinkage coeff on a simple data set (without saving precision) oa = OAS(store_precision=False) oa.fit(X) assert_almost_equal(oa.score(X), score_, 4) assert(oa.precision_ is None)