def callback_sigma_lmbda(model, bounds, info, x, index, ftrue):
global D
fig = pl.figure(1)
fig.clf()
sigma = 2**info[-1]['xbest'][0]
lmbda = 2**info[-1]['xbest'][1]
pl.title("sigma=%.2f, lmbda=%.6f" % (sigma, lmbda))
gamma = 0.5 * (sigma**2)
omega, u = sample_basis(D, m, gamma)
theta = score_matching_sym(Z, lmbda, omega, u)
logq_est = lambda x: np.dot(theta, feature_map_single(x, omega, u))
dlogq_est = lambda x: np.dot(theta, feature_map_grad_single(x, omega, u))
Xs = np.linspace(-3, 3)
Ys = np.linspace(-3, 3)
Q = evaluate_density_grid(Xs, Ys, logq_est)
plot_array(Xs, Ys, Q, pl.gca(), plot_contour=True)
pl.plot(Z[:, 0], Z[:, 1], 'bx')
for ax in fig.axes: # remove tick labels
ax.set_xticklabels([])
ax.set_yticklabels([])
pl.draw()
pl.show(block=False)
def test_feature_map():
x = 3.
u = 2.
omega = 2.
phi = feature_map_single(x, omega, u)
phi_manual = np.cos(omega * x + u) * np.sqrt(2.)
assert_close(phi, phi_manual)
def update_plot(val=None):
global omega, u
print("Updating plot")
lmbda = 2**s_lmbda.val
sigma = 2**s_sigma.val
b = compute_b(Z, omega, u)
C = compute_C(Z, omega, u)
theta = score_matching_sym(Z, lmbda, omega, u, b, C)
J = objective(Z, theta, lmbda, omega, u, b, C)
J_xval = np.mean(
xvalidate(Z, lmbda, omega, u, n_folds=5, num_repetitions=3))
logq_est = lambda x: np.dot(theta, feature_map_single(x, omega, u))
dlogq_est = lambda x: np.dot(theta, feature_map_grad_single(x, omega, u))
description = "N=%d, sigma: %.2f, lambda: %.2f, m=%.d, J=%.2f, J_xval=%.2f" % \
(N, sigma, lmbda, m, 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()
def test_feature_map_single_equals_feature_map():
N = 10
D = 20
m = 3
X = np.random.randn(N, D)
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
phis = feature_map(X, omega, u)
for i, x in enumerate(X):
phi = feature_map_single(x, omega, u)
assert_allclose(phis[i], phi)
m = N
# cma_opts = {'tolfun':0.3, 'maxiter':10, 'verb_disp':1}
# sigma, lmbda = select_sigma_lambda_cma(Z, m,
# sigma0=sigma, lmbda0=lmbda,
# cma_opts=cma_opts)
# cma_opts = {'tolfun':0.3, 'maxiter':10, 'verb_disp':1}
# sigma, lmbda = select_sigma_lambda_cma(Z, m,
# sigma0=sigma, lmbda0=lmbda,
# cma_opts=cma_opts)
# print sigma,lmbda
gamma = 0.5 * (sigma ** 2)
omega, u = sample_basis(D, m, gamma)
theta = score_matching_sym(Z, lmbda, omega, u)
logq_est = lambda x: log_pdf_estimate(feature_map_single(x, omega, u), theta)
dlogq_est = lambda x: log_pdf_estimate_grad(feature_map_grad_single(x, omega, u),
theta)
# plot density estimate
plt.figure(figsize=(4, 8))
Xs = np.linspace(-15, 15)
Ys = np.linspace(-7, 3)
Xs_grad = np.linspace(-40, 40, 40)
Ys_grad = np.linspace(-15, 25, 40)
G = evaluate_density_grid(Xs, Ys, logq_est)
G_norm, quiver_U, quiver_V, _, _ = evaluate_gradient_grid(Xs_grad, Ys_grad, dlogq_est)
plt.subplot(211)
plt.plot(Z[:, 0], Z[:, 1], 'bx')
plot_array(Xs, Ys, np.exp(G), plot_contour=True)
plt.subplot(212)
def callback_lmbda(model, bounds, info, x, index, ftrue):
global D
"""
Plot the current posterior, the index, and the value of the current
recommendation.
"""
xmin, xmax = bounds[0]
xx_ = np.linspace(xmin, xmax, 500) # define grid
xx = xx_[:, None]
# ff = ftrue(xx) # compute true function
acq = index(xx) # compute acquisition
mu, s2 = model.posterior(xx) # compute posterior and
lo = mu - 2 * np.sqrt(s2) # quantiles
hi = mu + 2 * np.sqrt(s2)
# ymin, ymax = ff.min(), ff.max() # get plotting ranges
# ymin -= 0.2 * (ymax - ymin)
# ymax += 0.2 * (ymax - ymin)
kwplot = {'lw': 2, 'alpha': 0.5} # common plotting kwargs
fig = pl.figure(1)
fig.clf()
pl.subplot(221)
# pl.plot(xx, ff, 'k:', **kwplot) # plot true function
pl.plot(xx, mu, 'b-', **kwplot) # plot the posterior and
pl.fill_between(xx_, lo, hi, color='b', alpha=0.1) # uncertainty bands
pl.scatter(
info['x'],
info['y'], # plot data
marker='o',
facecolor='none',
zorder=3)
pl.axvline(x, color='r', **kwplot) # latest selection
pl.axvline(info[-1]['xbest'], color='g',
**kwplot) # current recommendation
# pl.axis((xmin, xmax, ymin, ymax))
pl.ylabel('posterior')
pl.subplot(223)
pl.fill_between(
xx_,
acq.min(),
acq, # plot acquisition
color='r',
alpha=0.1)
pl.axis('tight')
pl.axvline(x, color='r', **kwplot) # plot latest selection
pl.xlabel('input')
pl.ylabel('acquisition')
pl.subplot(224)
pl.plot(info['x'], 'g')
pl.subplot(222)
lmbda = 2**info[-1]['xbest']
gamma = 0.5 * (sigma**2)
omega, u = sample_basis(D, m, gamma)
theta = score_matching_sym(Z, lmbda, omega, u)
logq_est = lambda x: np.dot(theta, feature_map_single(x, omega, u))
dlogq_est = lambda x: np.dot(theta, feature_map_grad_single(x, omega, u))
Xs = np.linspace(-3, 3)
Ys = np.linspace(-3, 3)
Q = evaluate_density_grid(Xs, Ys, logq_est)
plot_array(Xs, Ys, Q, pl.gca(), plot_contour=True)
pl.plot(Z[:, 0], Z[:, 1], 'bx')
for ax in fig.axes: # remove tick labels
ax.set_xticklabels([])
ax.set_yticklabels([])
pl.draw()
pl.show(block=False)
def log_pdf(self, x):
phi = feature_map_single(x, self.omega, self.u)
return np.dot(phi, self.theta)
D = 2
Z = np.random.randn(N, D)
m = 200
omega = gamma * np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
theta = score_matching_sym(Z, lmbda, omega, u)
# compute log-density and true log density
Xs = np.linspace(-3, 3)
Ys = np.linspace(-3, 3)
D = np.zeros((len(Xs), len(Ys)))
G = np.zeros(D.shape)
for i in range(len(Xs)):
for j in range(len(Ys)):
x = np.array([Xs[i], Ys[j]])
phi = feature_map_single(x, omega, u)
D[j, i] = theta.dot(phi)
G[j, i] = -np.linalg.norm(x) ** 2
plt.figure(figsize=(16,4))
plt.subplot(131)
plt.imshow(G)
plt.colorbar()
plt.title("Truth")
plt.subplot(132)
plt.imshow(D)
plt.title("Random features")
plt.colorbar()
plt.subplot(133)
plt.plot(theta)
plt.title("theta")
