def test_score_matching_sym_low_rank_time():
sigma = 1.
lmbda = 1.
N = 20000
Z = np.random.randn(N, 2)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
score_matching_sym_low_rank(Z, sigma, lmbda, L=R.T, cg_tol=1e-1)
def test_compute_b_low_rank_matches_sym():
sigma = 1.
X = np.random.randn(10, 2)
R = incomplete_cholesky_gaussian(X, sigma, eta=0.1)["R"]
x = _compute_b_low_rank(X, X, R.T, R.T, sigma)
y = _compute_b_low_rank_sym(X, R.T, sigma)
assert_allclose(x, y)
def test_score_matching_sym_low_rank_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
a = score_matching_sym(Z, sigma, lmbda)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
a_cholesky_cg = score_matching_sym_low_rank(Z, sigma, lmbda, L=R.T)
assert_allclose(a, a_cholesky_cg, atol=3)
def test_compute_b_sym_low_rank_matches_full():
sigma = 1.
Z = np.random.randn(100, 2)
low_rank_dim = int(len(Z) * .9)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=low_rank_dim)["R"]
x = _compute_b_sym(Z, K, sigma)
y = _compute_b_low_rank_sym(Z, R.T, sigma)
assert_allclose(x, y, atol=5e-1)
def test_apply_C_left_sym_low_rank_matches_full():
sigma = 1.
N = 10
Z = np.random.randn(N, 2)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
v = np.random.randn(Z.shape[0])
lmbda = 1.
x = (_compute_C_sym(Z, K, sigma) + lmbda * (K + np.eye(len(K)))).dot(v)
y = _apply_left_C_sym_low_rank(v, Z, R.T, lmbda)
assert_allclose(x, y, atol=1e-1)
def test_objective_sym_low_rank_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a_opt = score_matching_sym(Z, sigma, lmbda, K)
J_opt = _objective_sym(Z, sigma, lmbda, a_opt, K)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.01)["R"].T
a_opt_chol = score_matching_sym_low_rank(Z, sigma, lmbda, L)
J_opt_chol = _objective_sym_low_rank(Z, sigma, lmbda, a_opt_chol, L)
assert_almost_equal(J_opt, J_opt_chol, delta=2.)
def test_objective_sym_low_rank_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"].T
a = score_matching_sym_low_rank(Z, sigma, lmbda, L)
b = _compute_b_low_rank_sym(Z, L, sigma)
J_opt = _objective_sym_low_rank(Z, sigma, lmbda, a, L, b)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = _objective_sym_low_rank(Z, sigma, lmbda, a_random, L)
assert J >= J_opt
from kmc.score_matching.kernel.incomplete_cholesky import incomplete_cholesky_gaussian
from kmc.score_matching.kernel.kernels import gaussian_kernel
from kmc.score_matching.lite.gaussian_rkhs import score_matching_sym,\
score_matching_sym_low_rank
import matplotlib.pyplot as plt
import numpy as np
if __name__ == "__main__":
sigma = 1.
lmbda = 1.
N = 1000
Z = np.random.randn(N, 2)
a = score_matching_sym(Z, sigma, lmbda)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
print("Low rank dimension: %d/%d" % (R.shape[0], N))
a_chol = score_matching_sym_low_rank(Z, sigma, lmbda, L=R.T)
# compute log-density and true log density
Xs = np.linspace(-4, 4)
Ys = np.linspace(-4, 4)
D = np.zeros((len(Xs), len(Ys)))
D_chol = np.zeros(D.shape)
G = np.zeros(D.shape)
for i in range(len(Xs)):
for j in range(len(Ys)):
x = np.array([[Xs[i], Ys[j]]])
k = gaussian_kernel(Z, x)[:, 0]
D[j, i] = k.dot(a)
D_chol[j, i] = k.dot(a_chol)
G[j, i] = -np.linalg.norm(x)**2