306 lines
12 KiB
Python
306 lines
12 KiB
Python
# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
|
|
# Gael Varoquaux <gael.varoquaux@normalesup.org>
|
|
# Virgile Fritsch <virgile.fritsch@inria.fr>
|
|
#
|
|
# License: BSD 3 clause
|
|
|
|
import numpy as np
|
|
import pytest
|
|
|
|
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_warns
|
|
|
|
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(return_X_y=True)
|
|
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)
|
|
with pytest.raises(NotImplementedError):
|
|
cov.error_norm(emp_cov, norm='foo')
|
|
# Mahalanobis distances computation test
|
|
mahal_dist = cov.mahalanobis(X)
|
|
assert 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)
|