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]
covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
covars_pred_full = np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full,
0) / n_samples
covars_pred_tied = _estimate_gaussian_covariances_tied(resp, X, nk, xk, 0)
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)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_tied, 'tied')
precs_pred = np.dot(precs_chol_pred, precs_chol_pred.T)
precs_est = linalg.inv(covars_pred_tied)
assert_array_almost_equal(precs_est, precs_pred)
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]
covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
covars_pred_full = np.sum(nk[:, np.newaxis, np.newaxis] * covars_pred_full,
0) / n_samples
covars_pred_tied = _estimate_gaussian_covariances_tied(resp, X, nk, xk, 0)
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)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_tied, 'tied')
precs_pred = np.dot(precs_chol_pred, precs_chol_pred.T)
precs_est = linalg.inv(covars_pred_tied)
assert_array_almost_equal(precs_est, precs_pred)
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))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
# 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))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
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))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=True)
ecov.fit(X_resp)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
# 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))
covars_pred = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance(assume_centered=False)
ecov.fit(X)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(covars_pred[0], norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred, 'full')
precs_pred = np.array([np.dot(prec, prec.T) for prec in precs_chol_pred])
precs_est = np.array([linalg.inv(cov) for cov in covars_pred])
assert_array_almost_equal(precs_est, precs_pred)
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]
covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
covars_pred_diag = _estimate_gaussian_covariances_diag(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance()
for (cov_full, cov_diag) in zip(covars_pred_full, covars_pred_diag):
ecov.covariance_ = np.diag(np.diag(cov_full))
cov_diag = np.diag(cov_diag)
assert_almost_equal(ecov.error_norm(cov_diag, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(cov_diag, norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_diag, 'diag')
assert_almost_equal(covars_pred_diag, 1. / precs_chol_pred**2)
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]
covars_pred_full = _estimate_gaussian_covariances_full(resp, X, nk, xk, 0)
covars_pred_diag = _estimate_gaussian_covariances_diag(resp, X, nk, xk, 0)
ecov = EmpiricalCovariance()
for (cov_full, cov_diag) in zip(covars_pred_full, covars_pred_diag):
ecov.covariance_ = np.diag(np.diag(cov_full))
cov_diag = np.diag(cov_diag)
assert_almost_equal(ecov.error_norm(cov_diag, norm='frobenius'), 0)
assert_almost_equal(ecov.error_norm(cov_diag, norm='spectral'), 0)
# check the precision computation
precs_chol_pred = _compute_precision_cholesky(covars_pred_diag, 'diag')
assert_almost_equal(covars_pred_diag, 1. / precs_chol_pred ** 2)
