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 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()