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