def test_compute_b_matches_sym():
sigma = 1.
Z = np.random.randn(10, 2)
K = gaussian_kernel(Z, sigma=sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma=sigma)
b_sym = gaussian.compute_b(Z, Z, K, sigma=sigma)
assert_allclose(b, b_sym)
def test_compute_b_matches_sym():
sigma = 1.
Z = np.random.randn(10, 2)
K = gaussian_kernel(Z, sigma=sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma=sigma)
b_sym = gaussian.compute_b(Z, Z, K, sigma=sigma)
assert_allclose(b, b_sym)
def test_compute_b_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 = gaussian.compute_b(X, Y, K_XY, sigma)
y = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
assert_allclose(x, y, atol=5e-1)
def test_compute_b_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 = gaussian.compute_b(X, Y, K_XY, sigma)
y = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
assert_allclose(x, y, atol=5e-1)
def test_objective_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 = gaussian.compute_C(X, Y, K_XY, sigma)
b = gaussian.compute_b(X, Y, K_XY, sigma)
J_full = gaussian.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 = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
J = gaussian_low_rank.objective(X, Y, sigma, lmbda, alpha, R.T, R_test.T, b)
assert_close(J, J_full, decimal=1)
def test_objective_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 = gaussian.compute_C(X, Y, K_XY, sigma)
b = gaussian.compute_b(X, Y, K_XY, sigma)
J_full = gaussian.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 = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
J = gaussian_low_rank.objective(X, Y, sigma, lmbda, alpha, R.T, R_test.T,
b)
assert_close(J, J_full, decimal=1)