def test_primal_dual_relationship():
y = y_diabetes.reshape(-1, 1)
coef = _solve_cholesky(X_diabetes, y, alpha=[1e-2])
K = np.dot(X_diabetes, X_diabetes.T)
dual_coef = _solve_cholesky_kernel(K, y, alpha=[1e-2])
coef2 = np.dot(X_diabetes.T, dual_coef).T
assert_array_almost_equal(coef, coef2)
def test_ridge_sample_weights_in_feature_space():
"""Check that Cholesky solver in feature space applies sample_weights
correctly.
"""
rng = np.random.RandomState(42)
n_samples_list = [5, 6, 7] * 2
n_features_list = [7, 6, 5] * 2
n_targets_list = [1, 1, 1, 2, 2, 2]
noise = 1.
alpha = 2.
alpha = np.atleast_1d(alpha)
for n_samples, n_features, n_targets in zip(n_samples_list,
n_features_list,
n_targets_list):
X = rng.randn(n_samples, n_features)
beta = rng.randn(n_features, n_targets)
Y = X.dot(beta)
Y_noisy = Y + rng.randn(*Y.shape) * np.sqrt((Y**2).sum(0)) * noise
K = X.dot(X.T)
sample_weights = 1. + (rng.randn(n_samples)**2) * 10
coef_sample_space = _solve_cholesky_kernel(
K, Y_noisy, alpha, sample_weight=sample_weights)
coef_feature_space = _solve_cholesky(X,
Y_noisy,
alpha,
sample_weight=sample_weights)
assert_array_almost_equal(X.T.dot(coef_sample_space),
coef_feature_space.T)
def test_primal_dual_relationship():
y = y_diabetes.reshape(-1, 1)
coef = _solve_cholesky(X_diabetes, y, alpha=[1e-2])
K = np.dot(X_diabetes, X_diabetes.T)
dual_coef = _solve_cholesky_kernel(K, y, alpha=[1e-2])
coef2 = np.dot(X_diabetes.T, dual_coef).T
assert_array_almost_equal(coef, coef2)
def test_ridge_sample_weights_in_feature_space():
"""Check that Cholesky solver in feature space applies sample_weights
correctly.
"""
rng = np.random.RandomState(42)
n_samples_list = [5, 6, 7] * 2
n_features_list = [7, 6, 5] * 2
n_targets_list = [1, 1, 1, 2, 2, 2]
noise = 1.
alpha = 2.
alpha = np.atleast_1d(alpha)
for n_samples, n_features, n_targets in zip(n_samples_list,
n_features_list,
n_targets_list):
X = rng.randn(n_samples, n_features)
beta = rng.randn(n_features, n_targets)
Y = X.dot(beta)
Y_noisy = Y + rng.randn(*Y.shape) * np.sqrt((Y ** 2).sum(0)) * noise
K = X.dot(X.T)
sample_weights = 1. + (rng.randn(n_samples) ** 2) * 10
coef_sample_space = _solve_cholesky_kernel(K, Y_noisy, alpha,
sample_weight=sample_weights)
coef_feature_space = _solve_cholesky(X, Y_noisy, alpha,
sample_weight=sample_weights)
assert_array_almost_equal(X.T.dot(coef_sample_space),
coef_feature_space.T)
