def update_density_estimate(self):
# load or learn parameters
if self.learn_parameters:
sigma, lmbda = self.determine_sigma_lmbda()
else:
sigma = self.sigma0
lmbda = self.lmbda0
logger.info("Using sigma: %.2f, lmbda=%.6f" % (sigma, lmbda))
D = self.Z.shape[1]
gamma = 0.5 / (sigma**2)
omega, u = sample_basis(D, self.m, gamma)
logger.info("Estimate density in RKHS, N=%d, m=%d" % (self.N, self.m))
theta = score_matching_sym(self.Z, lmbda, omega, u)
# logger.info("Computing objective function")
# J = _objective_sym(Z, sigma, lmbda, a, K, b, C)
# J_xval = np.mean(xvalidate(Z, 5, sigma, self.lmbda, K))
# logger.info("N=%d, sigma: %.2f, lambda: %.2f, J(a)=%.2f, XJ(a)=%.2f" % \
# (self.N, sigma, self.lmbda, J, J_xval))
dlogq_est = lambda x: log_pdf_estimate_grad(
feature_map_grad_single(x, omega, u), theta)
return dlogq_est
lmbda = 1.
sigma = select_sigma_grid(Z, lmbda=lmbda)
K = gaussian_kernel(Z, sigma=sigma)
b = _compute_b_sym(Z, K, sigma)
C = _compute_C_sym(Z, K, sigma)
a = score_matching_sym(Z, sigma, lmbda, K, b, C)
J = _objective_sym(Z, sigma, lmbda, a, K, b, C)
J_xval = np.mean(xvalidate(Z, 5, sigma, lmbda, K))
print("N=%d, sigma: %.2f, lambda: %.2f, J(a)=%.2f, XJ(a)=%.2f" % \
(N, sigma, lmbda, J, J_xval))
kernel = lambda X, Y=None: gaussian_kernel(X, Y, sigma=sigma)
kernel_grad = lambda x, X=None: gaussian_kernel_grad(x, X, sigma)
logq_est = lambda x: log_pdf_estimate(x, a, Z, kernel)
dlogq_est = lambda x: log_pdf_estimate_grad(x, a, Z, kernel_grad)
# momentum
Sigma_p = np.eye(D) * .1
L_p = np.linalg.cholesky(Sigma_p)
logp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=False, is_cholesky=True)
dlogp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=True, is_cholesky=True)
p_sample = lambda: sample_gaussian(
N=1, mu=np.zeros(D), Sigma=L_p, is_cholesky=True)[0]
# starting state
p0 = p_sample()
q0 = np.zeros(D)
q0[:2] = np.array([0, -3])
# estimate density in rkhs
N = 800
mu = np.zeros(D)
Z = np.random.standard_t(df=nu, size=(N, D))
lmbda = 0.0001
sigma = 0.5
gamma = 0.5 * (sigma**2)
m = N
omega = gamma * np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
logger.info("Estimating density")
theta = score_matching_sym(Z, lmbda, omega, u)
logq_est = lambda x: log_pdf_estimate(feature_map(x, omega, u), theta)
dlogq_est = lambda x: log_pdf_estimate_grad(
feature_map_grad_single(x, omega, u), theta)
# momentum
Sigma_p = np.eye(D)
L_p = np.linalg.cholesky(Sigma_p)
logp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=False, is_cholesky=True)
dlogp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=True, is_cholesky=True)
p_sample = lambda: sample_gaussian(
N=1, mu=np.zeros(D), Sigma=L_p, is_cholesky=True)[0]
# starting state
p0 = p_sample()
q0 = np.zeros(D)
q0[:2] = np.array([-1, -1])
