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 _estimate_gaussian_correlations_tied(resp,
X,
nk,
means,
reg_covar,
resp_fair=None,
X_fair=None,
nk_fair=None,
means_fair=None):
"""Estimate the tied correlation matrix. Then obtain covariance matrix by scaling
it using component-wise variances.
Parameters
----------
resp : array-like, shape (n_samples, n_components)
X : array-like, shape (n_samples, n_features)
nk : array-like, shape (n_components,)
means : array-like, shape (n_components, n_features)
reg_covar : float
Returns
-------
covariance : array, shape (n_components, n_features, n_features)
The correlation-tied covariance matrix of the components.
"""
# Note: maybe we should require to either provide all or none of the fair parameters
if resp_fair is None:
resp_fair = resp
if X_fair is None:
X_fair = X
if nk_fair is None:
nk_fair = nk
if means_fair is None:
means_fair = means
tied_covariance = _estimate_gaussian_covariances_tied(
resp_fair, X_fair, nk_fair, means_fair, reg_covar)
tied_inv_scaler = 1.0 / np.sqrt(np.diag(tied_covariance))
tied_correlation = np.outer(tied_inv_scaler,
tied_inv_scaler) * tied_covariance
comp_variances = _estimate_gaussian_covariances_diag(
resp, X, nk, means, reg_covar)
comp_scaler = [np.outer(c, c) for c in np.sqrt(comp_variances)]
comp_covariance = [tied_correlation * s for s in comp_scaler]
return np.array(comp_covariance)
