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_shinkrage_from_mle = ledoit_wolf(X_centered,
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_, 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_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, assume_centered=True)
lw.fit(X_centered)
assert_almost_equal(lw.score(X_centered), score_, 4)
assert (lw.precision_ is None)
# (too) large data set
X_large = np.ones((20, 200))
assert_raises(MemoryError, ledoit_wolf, X_large, block_size=100)
# 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_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 with one sample
# FIXME I don't know what this test does
X_1sample = np.arange(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 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_shinkrage_from_mle = ledoit_wolf(X_centered,
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_, 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_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, assume_centered=True)
lw.fit(X_centered)
assert_almost_equal(lw.score(X_centered), score_, 4)
assert(lw.precision_ is None)
# (too) large data set
X_large = np.ones((20, 200))
assert_raises(MemoryError, ledoit_wolf, X_large, block_size=100)
# 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_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 with one sample
X_1sample = np.arange(5)
lw = LedoitWolf()
with warnings.catch_warnings(record=True):
lw.fit(X_1sample)
# 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 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)
# Perform Factor analysis
fa = FactorAnalysis(n_components=64, random_state=1000)
fah = FactorAnalysis(n_components=64, random_state=1000)
Xfa = fa.fit_transform(X)
Xfah = fah.fit_transform(Xh)
print('Factor analysis score X: {}'.format(fa.score(X)))
print('Factor analysis score Xh: {}'.format(fah.score(Xh)))
# Perform Lodoit-Wolf shrinkage
ldw = LedoitWolf()
ldwh = LedoitWolf()
ldw.fit(X)
ldwh.fit(Xh)
print('Ledoit-Wolf score X: {}'.format(ldw.score(X)))
print('Ledoit-Wolf score Xh: {}'.format(ldwh.score(Xh)))
# Show the components
fig, ax = plt.subplots(8, 8, figsize=(10, 10))
for i in range(8):
for j in range(8):
ax[i, j].imshow(fah.components_[(i * 8) + j].reshape((28, 28)),
cmap='gray')
ax[i, j].axis('off')
plt.show()
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()
warn_msg = (
"Only one sample available. You may want to reshape your data array")
with pytest.warns(UserWarning, match=warn_msg):
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 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_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)
Xfa = fa.fit_transform(X)
Xfah = fah.fit_transform(Xh)
print('Factor analysis score X: {:.3f}'.
format(fa.score(X)))
print('Factor analysis score Xh: {:.3f}'.
format(fah.score(Xh)))
# Perform Lodoit-Wolf shrinkage
ldw = LedoitWolf()
ldwh = LedoitWolf()
ldw.fit(X)
ldwh.fit(Xh)
print('Ledoit-Wolf score X: {:.3f}'.
format(ldw.score(X)))
print('Ledoit-Wolf score Xh: {:.3f}'.
format(ldwh.score(Xh)))
# Show the components
fig, ax = plt.subplots(8, 8, figsize=(10, 10))
for i in range(8):
for j in range(8):
ax[i, j].imshow(fah.components_[(i * 8) + j].reshape((28, 28)), cmap='gray')
ax[i, j].axis('off')
plt.show()
