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()
Z = sample_gaussian(N, mu, Sigma=L, is_cholesky=True)
lmbda = 1.
sigma = select_sigma_grid(Z, lmbda=lmbda, plot_surface=False)
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)
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])
# parameters