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)
sampler_learn_rate = 0.01
init_init_stddev_scale = 1.0
init_langevin_stepsize = 0.1
init_langevin_noise_size = 0.001
init_gradient_power = 0.95
D = 2
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)
print "True normalizing constant:", log_normalizing_constant_of_a_guassian(
all_cov)
print "True entropy:", entropy_of_a_gaussian(all_cov)
prior_func = build_logprob_mvn(all_mean, all_cov)
init_mean = all_mean
init_stddevs = np.log(init_init_stddev_scale * np.ones((1, D)))
init_log_stepsizes = np.log(init_langevin_stepsize *
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)
matplotlib.image.imsave("all_mean", (all_mean.reshape((28, 28))))
labels = np.zeros((num_samples, 1))
cond_like = generative_conditional(labels)
D = 784
init_mean = all_mean
# init_stddevs = np.diag(all_cov)+.1
# init_mean = np.zeros((1,D))
init_stddevs = np.log(.0000001 * np.ones((1, D)))
init_log_stepsizes = np.log(0.0001 * np.ones(num_langevin_steps))
init_log_noise_sizes = np.log(.00001 * np.ones(num_langevin_steps))
rs = np.random.npr.RandomState(0)
sample_and_run_langevin, parser = build_langevin_sampler(
simple_conditional, 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)
def get_batch_marginal_likelihood_estimate(sampler_params):
samples, marginal_likelihood_estimates = sample_and_run_langevin(
sampler_params, rs, num_samples)
matplotlib.image.imsave("optimizing", (samples[0, :].reshape(
(28, 28))).value)
return np.mean(marginal_likelihood_estimates)
likelihood = nn_loglik(trained_weights, squashed_images, labels)
return likelihood # prior + likelihood
gen_labels = one_hot(np.array([i % 10 for i in range(num_samples)]), 10)
labeled_likelihood = lambda images: nn_likelihood(images, gen_labels)
#init_mean = all_mean
# init_stddevs = np.diag(all_cov)+.1
init_mean = np.zeros((1, D))
init_stddevs = np.log(init_init_stddev_scale * np.ones((1, D)))
init_log_stepsizes = np.log(init_langevin_stepsize *
np.ones(num_langevin_steps))
init_log_noise_sizes = np.log(init_langevin_noise_size *
np.ones(num_langevin_steps))
sample_and_run_langevin, parser = build_langevin_sampler(
labeled_likelihood, 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)
labels = np.zeros((num_samples,1))
cond_like = generative_conditional(labels)
D = 784
init_mean = all_mean
# init_stddevs = np.diag(all_cov)+.1
# init_mean = np.zeros((1,D))
init_stddevs = np.log(.00001*np.ones((1,D)))
init_log_stepsizes = np.log(0.001*np.ones(num_langevin_steps))
init_log_noise_sizes = np.log(.001*np.ones(num_langevin_steps))
rs = np.random.npr.RandomState(0)
sample_and_run_langevin, parser = build_langevin_sampler(cond_like, 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)
#
# def get_batch_marginal_likelihood_estimate(sampler_params):
# samples = [] # np.zeros((num_samples, D))
# mls = []
# for s in range(num_samples):
# z, marginal_likelihood_estimate = sample_and_run_langevin(sampler_params, rs)
# samples.append(z.value)
# mls.append(marginal_likelihood_estimate)
#