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
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 predict(x, alphas):
D = len(x)
f = 0.
for i in range(len(alphas)):
np.random.seed(seed_offset + i)
omega, u = sample_basis(D=D, m=1, gamma=gamma)
phi_x = feature_map(x, omega, u)
f += alphas[i] * phi_x
return f
def sigma_objective(log2_sigma, lmbda):
sigma = 2**log2_sigma
folds = np.zeros(num_repetitions)
for i in range(num_repetitions):
gamma = 0.5 * (sigma**2)
omega, u = sample_basis(D, m, gamma)
folds[i] = np.mean(
xvalidate(Z, lmbda, omega, u, num_folds, num_repetitions=1))
result = np.mean(folds)
logger.info("xvalidation, sigma: %.2f, lambda: %.2f, J=%.3f" % \
(sigma, lmbda, result))
return result
def lmbda_objective(log2_lmbda, sigma):
lmbda = 2**log2_lmbda
gamma = 0.5 * (sigma**2)
omega, u = sample_basis(D, m, gamma)
folds = xvalidate(Z,
lmbda,
omega,
u,
num_folds,
num_repetitions=num_repetitions)
result = np.mean(folds)
logger.info("xvalidation, sigma: %.2f, lambda: %.2f, J=%.3f" % \
(sigma, lmbda, result))
return result
def fun(sigma_lmbda, m=100, num_repetitions=3):
log2_sigma = sigma_lmbda[0]
log2_lmbda = sigma_lmbda[1]
sigma = 2**log2_sigma
gamma = 0.5 * (sigma**2)
lmbda = 2**log2_lmbda
omega, u = sample_basis(D, m, gamma)
folds = [xvalidate(Z, lmbda, omega, u) for _ in range(num_repetitions)]
J = np.mean(folds)
J_std = np.std(folds)
print("fun: log2_sigma=%.2f, log_lmbda=%.2f, J(a)=%.2f" %
(log2_sigma, log2_lmbda, J))
return J, J_std
def multicore_fun(log2_sigma, log2_lmbda, num_repetitions, num_folds, Z, m):
D = Z.shape[1]
lmbda = 2**log2_lmbda
sigma = 2**log2_sigma
gamma = 0.5 * (sigma**2)
folds = np.zeros(num_repetitions)
for j in range(num_repetitions):
logger.debug("xvalidation repetition %d/%d" % (j + 1, num_repetitions))
omega, u = sample_basis(D, m, gamma)
folds[j] = np.mean(
xvalidate(Z, lmbda, omega, u, num_folds, num_repetitions=1))
result = np.mean(folds)
logger.info("cma particle, sigma: %.2f, lambda: %.6f, J=%.4f" % \
(sigma, lmbda, result))
return result
def _f(log2_sigma):
sigma = 2**log2_sigma
folds = np.zeros(num_repetitions)
for i in range(num_repetitions):
gamma = 0.5 * (sigma**2)
omega, u = sample_basis(D, m, gamma)
folds[i] = np.mean(
xvalidate(Z, lmbda, omega, u, num_folds, num_repetitions=1))
result = np.mean(folds)
print("xvalidation, sigma: %.2f, lambda: %.6f, J=%.3f" % \
(sigma, lmbda, result))
# transform to log space to make GP work.
# since unbounded, add constant
# also pybo maximises so invert sign
result = -np.log(result + 100)
return result
def set_up(self):
if self.learn_parameters or self.force_relearn_parameters:
self.sigma, self.lmbda = self.determine_sigma_lmbda()
logger.info("Using sigma=%.2f, lmbda=%.6f" % (self.sigma, self.lmbda))
gamma = 0.5 * (self.sigma**2)
logger.info("Sampling random basis")
omega, u = sample_basis(self.D, self.m, gamma)
logger.info("Estimating density in RKHS, N=%d, m=%d, D=%d" %
(len(self.Z), self.m, self.D))
theta = score_matching_sym(self.Z, self.lmbda, omega, u)
# replace target by kernel estimator to simulate trajectories on
# but keep original target for computing acceptance probability
self.orig_target = self.target
self.target = RandomFeatsEstimator(theta, omega, u)
HMCJob.set_up(self)
# plot density estimate
if self.plot:
import matplotlib.pyplot as plt
from scripts.tools.plotting import evaluate_density_grid, evaluate_gradient_grid, plot_array
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, self.target.log_pdf)
G_norm, quiver_U, quiver_V, _, _ = evaluate_gradient_grid(
Xs_grad, Ys_grad, self.target.grad)
plt.subplot(211)
plt.plot(self.Z[:, 0], self.Z[:, 1], 'bx')
plot_array(Xs, Ys, np.exp(G), plot_contour=True)
plt.subplot(212)
plot_array(Xs_grad, Ys_grad, G_norm, plot_contour=True)
plt.quiver(Xs_grad, Ys_grad, quiver_U, quiver_V, color='m')
plt.ioff()
plt.show()
def select_sigma_grid(Z,
m,
num_folds=5,
num_repetitions=3,
log2_sigma_min=-3,
log2_sigma_max=10,
resolution_sigma=25,
lmbda=0.0001,
plot_surface=False):
D = Z.shape[1]
sigmas = 2**np.linspace(log2_sigma_min, log2_sigma_max, resolution_sigma)
Js = np.zeros(len(sigmas))
for i, sigma in enumerate(sigmas):
gamma = 0.5 * (sigma**2)
folds = np.zeros(num_repetitions)
for j in range(num_repetitions):
# re-sample basis every repetition
omega, u = sample_basis(D, m, gamma)
folds[j] = xvalidate(Z,
lmbda,
omega,
u,
n_folds=num_folds,
num_repetitions=1)
Js[i] = np.mean(folds)
logger.info("fold %d/%d, sigma: %.2f, lambda: %.2f, J=%.3f" % \
(i + 1, len(sigmas), sigma, lmbda, Js[i]))
# if plot_surface:
# plt.figure()
# plt.plot(np.log2(sigmas), Js)
return sigmas[Js.argmin()]
N = 20
D = 2
Z = np.random.randn(N, D)
m = N
# print np.sum(Z) * np.std(Z) * np.sum(Z**2) * np.std(Z**2)
num_folds = 5
num_repetitions = 3
cma_opts = {'tolfun': 0.1, 'maxiter': 1, 'verb_disp': 1}
num_threads = 2
# D = 2
sigma0 = 0.51
lmbda0 = 0.0000081
sigma, lmbda, es = select_sigma_lambda_cma(Z,
m,
num_threads,
num_folds,
num_repetitions,
sigma0,
lmbda0,
cma_opts,
return_cma=True)
gamma = 0.5 * (sigma**2)
omega, u = sample_basis(D, m, gamma)
print(sigma, lmbda,
np.mean(xvalidate(Z, lmbda, omega, u, n_folds=5, num_repetitions=3)))
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)
np.random.seed(seed_offset + i)
omega, u = sample_basis(D=D, m=1, gamma=gamma)
phi_x = feature_map(x, omega, u)
f += alphas[i] * phi_x
return f
alphas = np.zeros(num_iterations)
for i in range(num_iterations):
logger.info("Iteration %d" % i)
x = X[i]
# sample random feature
np.random.seed(seed_offset + i)
omega, u = sample_basis(D=D, m=1, gamma=gamma)
phi_x = feature_map(x, omega, u)
# sample data point and predict
f = predict(x, alphas[:i]) * phi_x
# gradient of f at x
f_grad = feature_map_grad_single(x, omega, u) * f
# gradient
grad = 0
for d in range(D):
phi_derivative_d = feature_map_derivative_d(x, omega, u, d)
phi_derivative2_d = feature_map_derivative2_d(x, omega, u, d)
grad += phi_derivative_d * f_grad[d] + phi_derivative2_d
