def _check_elbo(x_mean, x_std):
# check their elbo
def log_joint(observed):
norm = Normal(mean=x_mean, std=x_std)
return norm.log_prob(observed['x'])
lower_bound = elbo(log_joint,
observed={},
latent={'x': [qx_samples, log_qx]},
axis=0)
analytic_lower_bound = -_kl_normal_normal(0., 1., x_mean, x_std)
with self.test_session(use_gpu=True) as sess:
a = sess.run(lower_bound)
b = sess.run(analytic_lower_bound)
# print(a, b)
self.assertNear(a, b, 1e-2)
def _check_monotonous_elbo(x_mean, x_std):
# check their elbo
def log_joint(observed):
norm = Normal(mean=x_mean, std=x_std)
return norm.log_prob(observed['x'])
lower_bound = importance_weighted_objective(
log_joint,
observed={},
latent={'x': [qx_samples_n3, log_qx_n3]},
axis=0)
lower_bound = tf.reduce_mean(lower_bound)
analytic_lower_bound = -_kl_normal_normal(0., 1., x_mean, x_std)
with self.session(use_gpu=True) as sess:
a = sess.run(lower_bound)
b = sess.run(analytic_lower_bound)
self.assertTrue(a > b - 1e-6)
def _check_importance(x_mean, x_std, threshold):
def log_joint(observed):
p = Normal(mean=x_mean, std=x_std)
return p.log_prob(observed['x'])
klpq_obj = klpq(log_joint,
observed={},
latent={'x': [qx_samples, log_qx]},
axis=0)
cost = klpq_obj.importance()
importance_grads = tf.gradients(cost, [mu, sigma])
true_cost = _kl_normal_normal(x_mean, x_std, mu, sigma)
true_grads = tf.gradients(true_cost, [mu, sigma])
with self.session(use_gpu=True) as sess:
g1 = sess.run(importance_grads)
g2 = sess.run(true_grads)
# print('importance_grads:', g1)
# print('true_grads:', g2)
self.assertAllClose(g1, g2, threshold, threshold)
def _check_sgvb(x_mean, x_std, threshold):
def log_joint(observed):
norm = Normal(mean=x_mean, std=x_std)
return norm.log_prob(observed['x'])
lower_bound = elbo(log_joint,
observed={},
latent={'x': [qx_samples, log_qx]},
axis=0)
sgvb_cost = lower_bound.sgvb()
sgvb_grads = tf.gradients(sgvb_cost, [mu, sigma])
true_cost = _kl_normal_normal(mu, sigma, x_mean, x_std)
true_grads = tf.gradients(true_cost, [mu, sigma])
with self.test_session(use_gpu=True) as sess:
g1 = sess.run(sgvb_grads)
g2 = sess.run(true_grads)
# print('sgvb_grads:', g1)
# print('true_grads:', g2)
self.assertAllClose(g1, g2, threshold, threshold)
def _check_reinforce(x_mean, x_std, threshold):
def log_joint(observed):
norm = Normal(mean=x_mean, std=x_std)
return norm.log_prob(observed['x'])
lower_bound = elbo(log_joint,
observed={},
latent={'x': [qx_samples, log_qx]},
axis=0)
# TODO: Check grads when use variance reduction and baseline
reinforce_cost = lower_bound.reinforce(variance_reduction=False)
reinforce_grads = tf.gradients(reinforce_cost, [mu, sigma])
true_cost = _kl_normal_normal(mu, sigma, x_mean, x_std)
true_grads = tf.gradients(true_cost, [mu, sigma])
with self.test_session(use_gpu=True) as sess:
sess.run(tf.global_variables_initializer())
g1 = sess.run(reinforce_grads)
g2 = sess.run(true_grads)
# print('reinforce_grads:', g1)
# print('true_grads:', g2)
self.assertAllClose(g1, g2, threshold, threshold)