def test_meta_gradient_with_langevin():
num_samples = 4
num_langevin_steps = 3
D = 2
init_mean = npr.randn(D) * 0.01
init_log_stddevs = np.log(1*np.ones(D)) + npr.randn(D) * 0.01
init_log_stepsizes = np.log(0.01*np.ones(num_langevin_steps)) + npr.randn(num_langevin_steps) * 0.01
init_log_noise_sizes = np.log(.001*np.ones(num_langevin_steps)) + npr.randn(num_langevin_steps) * 0.01
init_log_gradient_scales = np.log(1*np.ones(D))
init_gradient_power = 0.9
sample_and_run_langevin, parser = build_langevin_sampler(logprob_two_moons, D, num_langevin_steps, approx=False)
sampler_params = np.zeros(len(parser))
parser.put(sampler_params, 'mean', init_mean)
parser.put(sampler_params, 'log_stddev', init_log_stddevs)
parser.put(sampler_params, 'log_stepsizes', init_log_stepsizes)
parser.put(sampler_params, 'log_noise_sizes', init_log_noise_sizes)
parser.put(sampler_params, 'log_gradient_scales', init_log_gradient_scales)
parser.put(sampler_params, 'invsig_gradient_power', inv_sigmoid(init_gradient_power))
def get_batch_marginal_likelihood_estimate(sampler_params):
rs = np.random.npr.RandomState(0)
samples, loglik_estimates, entropy_estimates = sample_and_run_langevin(sampler_params, rs, num_samples)
marginal_likelihood_estimates = loglik_estimates + entropy_estimates
return np.mean(marginal_likelihood_estimates)
check_grads(get_batch_marginal_likelihood_estimate, sampler_params)
init_mean = np.zeros(D)
init_stddevs = np.log(init_init_stddev_scale * np.ones((1,D)))
init_log_stepsizes = np.log(init_langevin_stepsize * np.ones(num_steps))
init_log_noise_sizes = np.log(init_langevin_noise_size * np.ones(num_steps))
init_log_gradient_scales = np.log(np.ones((1,D)))
logprob_mvn = build_logprob_mvn(mean=np.array([0.2,0.4]), cov=np.array([[1.0,0.9], [0.9,1.0]]))
sample, parser = build_langevin_sampler(logprob_two_moons, D, num_steps, approx=False)
sampler_params = np.zeros(len(parser))
parser.put(sampler_params, 'mean', init_mean)
parser.put(sampler_params, 'log_stddev', init_stddevs)
parser.put(sampler_params, 'log_stepsizes', init_log_stepsizes)
parser.put(sampler_params, 'log_noise_sizes', init_log_noise_sizes)
parser.put(sampler_params, 'log_gradient_scales', init_log_gradient_scales)
parser.put(sampler_params, 'invsig_gradient_power', inv_sigmoid(init_gradient_power))
def get_batch_marginal_likelihood_estimate(sampler_params):
samples, likelihood_estimates, entropy_estimates = sample(sampler_params, rs, num_samples)
print "Mean loglik:", np.mean(likelihood_estimates.value),\
"Mean entropy:", np.mean(entropy_estimates.value)
plot_density(samples.value, "approximating_dist.png")
return np.mean(likelihood_estimates + entropy_estimates)
ml_and_grad = value_and_grad(get_batch_marginal_likelihood_estimate)
# Optimize Langevin parameters.
for i in xrange(num_sampler_optimization_steps):
ml, dml = ml_and_grad(sampler_params)
print "Iter:", i, "log marginal likelihood:", ml, "avg gradient size: ", np.mean(np.abs(dml))
print "Gradient power:", sigmoid(parser.get(sampler_params, 'invsig_gradient_power'))
np.ones(num_langevin_steps))
init_log_noise_sizes = np.log(init_langevin_noise_size *
np.ones(num_langevin_steps))
init_log_gradient_scales = np.log(np.ones((1, D)))
sample_and_run_langevin, parser = build_langevin_sampler(
prior_func, D, num_langevin_steps, approx=True)
sampler_params = np.zeros(len(parser))
parser.put(sampler_params, 'mean', init_mean)
parser.put(sampler_params, 'log_stddev', init_stddevs)
parser.put(sampler_params, 'log_stepsizes', init_log_stepsizes)
parser.put(sampler_params, 'log_noise_sizes', init_log_noise_sizes)
parser.put(sampler_params, 'log_gradient_scales', init_log_gradient_scales)
parser.put(sampler_params, 'invsig_gradient_power',
inv_sigmoid(init_gradient_power))
rs = np.random.npr.RandomState(0)
def batch_marginal_likelihood_estimate(sampler_params):
samples, likelihood_estimates, entropy_estimates = sample_and_run_langevin(
sampler_params, rs, num_samples)
print "Mean loglik:", np.mean(
likelihood_estimates.value), "Mean entropy:", np.mean(
entropy_estimates.value)
fig = plt.figure(1)
fig.clf()
ax = fig.add_subplot(111)
plot_images(samples.value, ax, ims_per_row=images_per_row)
plt.savefig('samples.png')