def update_plot(val=None):
sigma = 2**s_sigma.val
lmbda = 2**s_lmbda.val
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, num_repetitions=3))
print(a[:5])
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)
description = "N=%d, sigma: %.2f, lambda: %.2f, J(a)=%.2f, XJ(a)=%.2f" % \
(N, sigma, lmbda, J, J_xval)
if plot_pdf:
D = evaluate_density_grid(Xs, Ys, logq_est)
description = "log-pdf: " + description
else:
D = evaluate_density_grad_grid(Xs, Ys, dlogq_est)
description = "norm-grad-log-pdf: " + description
ax.clear()
ax.plot(Z[:, 0], Z[:, 1], 'bx')
plot_array(Xs, Ys, D, ax, plot_contour=True)
ax.set_title(description)
fig.canvas.draw_idle()
mu = np.zeros(D)
Z = sample_banana(N, D)
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()
def compute_trajectory(self, random_start_state=None):
logger.debug("Entering")
if random_start_state is not None:
np.random.set_state(random_start_state)
else:
random_start_state = np.random.get_state()
# momentum
L_p = np.linalg.cholesky(np.eye(self.D) * self.sigma_p)
self.logp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=False, is_cholesky=True)
self.dlogp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=True, is_cholesky=True)
self.p_sample = lambda: sample_gaussian(
N=1, mu=np.zeros(self.D), Sigma=L_p, is_cholesky=True)[0]
self.p_sample = lambda: sample_gaussian(
N=1, mu=np.zeros(self.D), Sigma=L_p, is_cholesky=True)[0]
# set up target and momentum densities and gradients
self.set_up()
logger.info("Learning kernel bandwidth")
sigma = select_sigma_grid(self.Z, lmbda=self.lmbda, log2_sigma_max=15)
logger.info("Using lmbda=%.2f, sigma: %.2f" % (self.lmbda, sigma))
logger.info("Computing kernel matrix")
K = gaussian_kernel(self.Z, sigma=sigma)
logger.info("Estimate density in RKHS")
b = _compute_b_sym(self.Z, K, sigma)
C = _compute_C_sym(self.Z, K, sigma)
a = score_matching_sym(self.Z, sigma, self.lmbda, K, b, C)
# logger.info("Computing objective function")
# J = _objective_sym(Z, sigma, self.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))
kernel_grad = lambda x, X=None: gaussian_kernel_grad(x, X, sigma)
dlogq_est = lambda x: log_pdf_estimate_grad(x, a, self.Z, kernel_grad)
logger.info("Simulating trajectory for L=%d steps of size %.2f" % \
(self.num_steps, self.step_size))
# starting state
p0 = self.p_sample()
q0 = self.q_sample()
Qs, Ps = leapfrog(q0, self.dlogq, p0, self.dlogp, self.step_size,
self.num_steps, self.max_steps)
# run second integrator for same amount of steps
steps_taken = len(Qs)
logger.info("%d steps taken" % steps_taken)
Qs_est, Ps_est = leapfrog(q0, dlogq_est, p0, self.dlogp,
self.step_size, steps_taken)
logger.info("Computing average acceptance probabilities")
log_acc = compute_log_accept_pr(q0, p0, Qs, Ps, self.logq, self.logp)
log_acc_est = compute_log_accept_pr(q0, p0, Qs_est, Ps_est, self.logq,
self.logp)
acc_mean = np.mean(np.exp(log_acc))
acc_est_mean = np.mean(np.exp(log_acc_est))
logger.info("Computing average volumes")
log_det = compute_log_det_trajectory(Qs, Ps)
log_det_est = compute_log_det_trajectory(Qs_est, Ps_est)
logger.info("Average acceptance prob: %.2f, %.2f" %
(acc_mean, acc_est_mean))
logger.info("Log-determinant: %.2f, %.2f" % (log_det, log_det_est))
logger.debug("Leaving")
return acc_mean, acc_est_mean, log_det, log_det_est, steps_taken, random_start_state
def grad(self, x):
k = gaussian_kernel_grad(x, self.Z, sigma=self.sigma)
return self.alpha.dot(k)