def test_suffstat_sk_full():
# compare the precision matrix compute from the
# EmpiricalCovariance.covariance fitted on X*sqrt(resp)
# with _sufficient_sk_full, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
# special case 1, assuming data is "centered"
X = rng.rand(n_samples, n_features)
resp = rng.rand(n_samples, 1)
X_resp = np.sqrt(resp) * X
nk = np.array([n_samples])
xk = np.zeros((1, n_features))
precs_pred = _estimate_gaussian_precisions_cholesky_full(
resp, X, nk, xk, 0)
covars_pred = linalg.inv(np.dot(precs_pred[0], precs_pred[0].T))
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred, norm='spectral'), 0)
# special case 2, assuming resp are all ones
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean(axis=0).reshape((1, -1))
precs_pred = _estimate_gaussian_precisions_cholesky_full(
resp, X, nk, xk, 0)
covars_pred = linalg.inv(np.dot(precs_pred[0], precs_pred[0].T))
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred, norm='spectral'), 0)
def test_suffstat_sk_full():
# compare the precision matrix compute from the
# EmpiricalCovariance.covariance fitted on X*sqrt(resp)
# with _sufficient_sk_full, n_components=1
rng = np.random.RandomState(0)
n_samples, n_features = 500, 2
# special case 1, assuming data is "centered"
X = rng.rand(n_samples, n_features)
resp = rng.rand(n_samples, 1)
X_resp = np.sqrt(resp) * X
nk = np.array([n_samples])
xk = np.zeros((1, n_features))
precs_pred = _estimate_gaussian_precisions_cholesky_full(resp, X,
nk, xk, 0)
covars_pred = linalg.inv(np.dot(precs_pred[0], precs_pred[0].T))
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred, norm='spectral'), 0)
# special case 2, assuming resp are all ones
resp = np.ones((n_samples, 1))
nk = np.array([n_samples])
xk = X.mean(axis=0).reshape((1, -1))
precs_pred = _estimate_gaussian_precisions_cholesky_full(resp, X,
nk, xk, 0)
covars_pred = linalg.inv(np.dot(precs_pred[0], precs_pred[0].T))
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred, norm='spectral'), 0)
def test_suffstat_sk_diag():
# test against 'full' case
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 500, 2, 2
resp = rng.rand(n_samples, n_components)
resp = resp / resp.sum(axis=1)[:, np.newaxis]
X = rng.rand(n_samples, n_features)
nk = resp.sum(axis=0)
xk = np.dot(resp.T, X) / nk[:, np.newaxis]
precs_pred_full = _estimate_gaussian_precisions_cholesky_full(
resp, X, nk, xk, 0)
covars_pred_full = [
linalg.inv(np.dot(precision_chol, precision_chol.T))
for precision_chol in precs_pred_full
]
precs_pred_diag = _estimate_gaussian_precisions_cholesky_diag(
resp, X, nk, xk, 0)
covars_pred_diag = np.array([np.diag(1. / d)**2 for d in precs_pred_diag])
ecov = EmpiricalCovariance()
for (cov_full, cov_diag) in zip(covars_pred_full, covars_pred_diag):
ecov.covariance_ = np.diag(np.diag(cov_full))
assert_almost_equal(ecov.error_norm(cov_diag, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(cov_diag, norm='spectral'), 0)
def test_suffstat_sk_tied():
# use equation Nk * Sk / N = S_tied
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 500, 2, 2
resp = rng.rand(n_samples, n_components)
resp = resp / resp.sum(axis=1)[:, np.newaxis]
X = rng.rand(n_samples, n_features)
nk = resp.sum(axis=0)
xk = np.dot(resp.T, X) / nk[:, np.newaxis]
precs_pred_full = _estimate_gaussian_precisions_cholesky_full(
resp, X, nk, xk, 0)
covars_pred_full = [
linalg.inv(np.dot(precision_chol, precision_chol.T))
for precision_chol in precs_pred_full
]
covars_pred_full = np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full,
0) / n_samples
precs_pred_tied = _estimate_gaussian_precisions_cholesky_tied(
resp, X, nk, xk, 0)
covars_pred_tied = linalg.inv(np.dot(precs_pred_tied, precs_pred_tied.T))
ecov = EmpiricalCovariance()
ecov.covariance_ = covars_pred_full
assert_almost_equal(ecov.error_norm(covars_pred_tied, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred_tied, norm='spectral'), 0)
def test_suffstat_sk_diag():
# test against 'full' case
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 500, 2, 2
resp = rng.rand(n_samples, n_components)
resp = resp / resp.sum(axis=1)[:, np.newaxis]
X = rng.rand(n_samples, n_features)
nk = resp.sum(axis=0)
xk = np.dot(resp.T, X) / nk[:, np.newaxis]
precs_pred_full = _estimate_gaussian_precisions_cholesky_full(resp, X,
nk, xk, 0)
covars_pred_full = [linalg.inv(np.dot(precision_chol, precision_chol.T))
for precision_chol in precs_pred_full]
precs_pred_diag = _estimate_gaussian_precisions_cholesky_diag(resp, X,
nk, xk, 0)
covars_pred_diag = np.array([np.diag(1. / d) ** 2
for d in precs_pred_diag])
ecov = EmpiricalCovariance()
for (cov_full, cov_diag) in zip(covars_pred_full, covars_pred_diag):
ecov.covariance_ = np.diag(np.diag(cov_full))
assert_almost_equal(ecov.error_norm(cov_diag, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(cov_diag, norm='spectral'), 0)
def test_suffstat_sk_tied():
# use equation Nk * Sk / N = S_tied
rng = np.random.RandomState(0)
n_samples, n_features, n_components = 500, 2, 2
resp = rng.rand(n_samples, n_components)
resp = resp / resp.sum(axis=1)[:, np.newaxis]
X = rng.rand(n_samples, n_features)
nk = resp.sum(axis=0)
xk = np.dot(resp.T, X) / nk[:, np.newaxis]
precs_pred_full = _estimate_gaussian_precisions_cholesky_full(resp, X,
nk, xk, 0)
covars_pred_full = [linalg.inv(np.dot(precision_chol, precision_chol.T))
for precision_chol in precs_pred_full]
covars_pred_full = np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full,
0) / n_samples
precs_pred_tied = _estimate_gaussian_precisions_cholesky_tied(resp, X,
nk, xk, 0)
covars_pred_tied = linalg.inv(np.dot(precs_pred_tied, precs_pred_tied.T))
ecov = EmpiricalCovariance()
ecov.covariance_ = covars_pred_full
assert_almost_equal(ecov.error_norm(covars_pred_tied, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred_tied, norm='spectral'), 0)
