def test_incomplete_cholesky_asymmetric(): kernel = lambda X, Y=None: gaussian_kernel(X, Y, sigma=1.) X = np.random.randn(1000, 10) Y = np.random.randn(100, 10) low_rank_dim = int(len(X) * 0.8) temp = incomplete_cholesky(X, kernel, eta=low_rank_dim) R, I, nu = (temp["R"], temp["I"], temp["nu"]) # construct train-train kernel matrix approximation using one by one calls R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu) assert_allclose(kernel(X, Y), R.T.dot(R_test), atol=10e-1)
def test_incomplete_cholesky_new_points_euqals_new_point(): kernel = lambda X, Y=None: gaussian_kernel(X, Y, sigma=200.) X = np.random.randn(1000, 10) low_rank_dim = 15 temp = incomplete_cholesky(X, kernel, eta=low_rank_dim) R, I, nu = (temp["R"], temp["I"], temp["nu"]) R_test_full = incomplete_cholesky_new_points(X, X, kernel, I, R, nu) # construct train-train kernel matrix approximation using one by one calls R_test = np.zeros(R.shape) for i in range(low_rank_dim): R_test[:, i] = incomplete_cholesky_new_point(X, X[i], kernel, I, R, nu) assert_allclose(R_test[:, i], R_test_full[:, i])
def test_compute_b_low_rank_matches_full(): sigma = 1. X = np.random.randn(100, 2) Y = np.random.randn(50, 2) low_rank_dim = int(len(X) * 0.9) kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma) K_XY = kernel(X, Y) temp = incomplete_cholesky(X, kernel, eta=low_rank_dim) I, R, nu = (temp["I"], temp["R"], temp["nu"]) R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu) x = _compute_b(X, Y, K_XY, sigma) y = _compute_b_low_rank(X, Y, R.T, R_test.T, sigma) assert_allclose(x, y, atol=5e-1)
def test_score_matching_low_rank_matches_sym(): sigma = 1. lmbda = 1. Z = np.random.randn(100, 2) low_rank_dim = int(len(Z) * .9) kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma) temp = incomplete_cholesky(Z, kernel, eta=low_rank_dim) I, R, nu = (temp["I"], temp["R"], temp["nu"]) R_test = incomplete_cholesky_new_points(Z, Z, kernel, I, R, nu) a_sym = score_matching_low_rank(Z, Z, sigma, lmbda, R.T, R_test.T) a = score_matching_sym_low_rank(Z, sigma, lmbda, R.T) assert_allclose(a, a_sym)
def apply_C_low_rank_matches_sym(): sigma = 1. N_X = 100 X = np.random.randn(N_X, 2) kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma) temp = incomplete_cholesky(X, kernel, eta=0.1) I, R, nu = (temp["I"], temp["R"], temp["nu"]) R_test = incomplete_cholesky_new_points(X, X, kernel, I, R, nu) v = np.random.randn(N_X.shape[0]) lmbda = 1. x = _apply_left_C_low_rank(v, X, X, R.T, R_test.T, lmbda) y = _apply_left_C_sym_low_rank(v, X, R.T, lmbda) assert_allclose(x, y)
def test_objective_low_rank_matches_sym(): sigma = 1. lmbda = 1. Z = np.random.randn(100, 2) kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma) alpha = np.random.randn(len(Z)) temp = incomplete_cholesky(Z, kernel, eta=0.1) I, R, nu = (temp["I"], temp["R"], temp["nu"]) R_test = incomplete_cholesky_new_points(Z, Z, kernel, I, R, nu) b = _compute_b_low_rank(Z, Z, R.T, R_test.T, sigma) J_sym = _objective_sym_low_rank(Z, sigma, lmbda, alpha, R.T, b) J = _objective_low_rank(Z, Z, sigma, lmbda, alpha, R.T, R_test.T, b) assert_close(J, J_sym)
def test_apply_C_left_low_rank_matches_full(): sigma = 1. N = 100 X = np.random.randn(N, 2) Y = np.random.randn(20, 2) low_rank_dim = int(len(X) * .9) kernel = lambda X, Y=None: gaussian_kernel(X, Y, sigma=sigma) K_XY = kernel(X, Y) K = kernel(X) temp = incomplete_cholesky(X, kernel, eta=low_rank_dim) I, R, nu = (temp["I"], temp["R"], temp["nu"]) R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu) v = np.random.randn(X.shape[0]) lmbda = 1. x = (_compute_C(X, Y, K_XY, sigma) + (K + np.eye(len(X))) * lmbda).dot(v) y = _apply_left_C_low_rank(v, X, Y, R.T, R_test.T, lmbda) assert_allclose(x, y, atol=1e-1)
def test_objective_low_rank_matches_full(): sigma = 1. lmbda = 1. X = np.random.randn(100, 2) Y = np.random.randn(10, 2) low_rank_dim = int(len(X) * 0.9) kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma) alpha = np.random.randn(len(X)) K_XY = kernel(X, Y) C = _compute_C(X, Y, K_XY, sigma) b = _compute_b(X, Y, K_XY, sigma) J_full = _objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY, b=b, C=C) temp = incomplete_cholesky(X, kernel, eta=low_rank_dim) I, R, nu = (temp["I"], temp["R"], temp["nu"]) R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu) b = _compute_b_low_rank(X, Y, R.T, R_test.T, sigma) J = _objective_low_rank(X, Y, sigma, lmbda, alpha, R.T, R_test.T, b) assert_close(J, J_full, decimal=1)