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# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
# Gael Varoquaux <gael.varoquaux@normalesup.org>
# Virgile Fritsch <virgile.fritsch@inria.fr>
#
# License: BSD Style.
from numpy.testing import assert_almost_equal, assert_array_almost_equal
import numpy as np
from sklearn import datasets
from sklearn.covariance import empirical_covariance, EmpiricalCovariance, \
ShrunkCovariance, shrunk_covariance, LedoitWolf, ledoit_wolf, OAS, oas
X = datasets.load_iris().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)
assert_array_almost_equal(empirical_covariance(X), cov.covariance_, 4)
assert_almost_equal(cov.error_norm(empirical_covariance(X)), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), norm='spectral'), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), norm='frobenius'), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), scaling=False), 0)
assert_almost_equal(
cov.error_norm(empirical_covariance(X), squared=False), 0)
# Mahalanobis distances computation test
mahal_dist = cov.mahalanobis(X)
assert(np.amax(mahal_dist) < 250)
assert(np.amin(mahal_dist) > 50)
# 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 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)
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
lw = LedoitWolf()
lw.fit(X, assume_centered=True)
assert_almost_equal(lw.shrinkage_, 0.00192, 4)
assert_almost_equal(lw.score(X, assume_centered=True), -2.89795, 4)
# compare shrunk covariance obtained from data and from MLE estimate
lw_cov_from_mle, lw_shinkrage_from_mle = ledoit_wolf(X,
assume_centered=True)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shinkrage_from_mle, lw.shrinkage_)
# compare estimates given by LW and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=lw.shrinkage_)
scov.fit(X, assume_centered=True)
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, assume_centered=True)
lw_cov_from_mle, lw_shinkrage_from_mle = ledoit_wolf(X_1d,
assume_centered=True)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shinkrage_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)
lw.fit(X, assume_centered=True)
assert_almost_equal(lw.score(X, assume_centered=True), -2.89795, 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_, 0.007582, 4)
assert_almost_equal(lw.score(X), 2.243483, 4)
# compare shrunk covariance obtained from data and from MLE estimate
lw_cov_from_mle, lw_shinkrage_from_mle = ledoit_wolf(X)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shinkrage_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_shinkrage_from_mle = ledoit_wolf(X_1d)
assert_array_almost_equal(lw_cov_from_mle, lw.covariance_, 4)
assert_almost_equal(lw_shinkrage_from_mle, lw.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), lw.covariance_, 4)
# 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), 2.2434839, 4)
assert(lw.precision_ is None)
def test_oas():
"""Tests OAS module on a simple dataset.
"""
# test shrinkage coeff on a simple data set
oa = OAS()
oa.fit(X, assume_centered=True)
assert_almost_equal(oa.shrinkage_, 0.018740, 4)
assert_almost_equal(oa.score(X, assume_centered=True), -5.03605, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
# compare estimates given by OAS and ShrunkCovariance
scov = ShrunkCovariance(shrinkage=oa.shrinkage_)
scov.fit(X, assume_centered=True)
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, assume_centered=True)
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X_1d, assume_centered=True)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_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)
oa.fit(X, assume_centered=True)
assert_almost_equal(oa.score(X, assume_centered=True), -5.03605, 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_, 0.020236, 4)
assert_almost_equal(oa.score(X), 2.079025, 4)
# compare shrunk covariance obtained from data and from MLE estimate
oa_cov_from_mle, oa_shinkrage_from_mle = oas(X)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_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_shinkrage_from_mle = oas(X_1d)
assert_array_almost_equal(oa_cov_from_mle, oa.covariance_, 4)
assert_almost_equal(oa_shinkrage_from_mle, oa.shrinkage_)
assert_array_almost_equal(empirical_covariance(X_1d), oa.covariance_, 4)
# 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), 2.079025, 4)
assert(oa.precision_ is None)
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