def test_klqp_betabernoulli(self):
with self.test_session() as sess:
# model
z = Beta(1., 1., name="z")
xs = Bernoulli(probs=z, sample_shape=10)
x_obs = np.asarray([0, 0, 1, 1, 0, 0, 0, 0, 0, 1], dtype=np.int32)
# inference
qz_mean = tf.get_variable("qz_mean",
initializer=tf.random_normal(()))
qz_std = tf.nn.softplus(
tf.get_variable(name="qz_prestd",
initializer=tf.random_normal(())))
qz_unconstrained = ed.models.Normal(loc=qz_mean,
scale=qz_std,
name="z_posterior")
inference_klqp = ed.inferences.KLqp({z: qz_unconstrained},
data={xs: x_obs})
inference_klqp.run(n_iter=500, auto_transform=True)
z_unconstrained = inference_klqp.transformations[z]
qz_constrained = z_unconstrained.bijector.inverse(
qz_unconstrained.sample(1000))
qz_mean, qz_var = sess.run(tf.nn.moments(qz_constrained, 0))
true_posterior = Beta(np.sum(x_obs) + 1., np.sum(1 - x_obs) + 1.)
pz_mean, pz_var = sess.run(
(true_posterior.mean(), true_posterior.variance()))
self.assertAllClose(qz_mean, pz_mean, rtol=5e-2, atol=5e-2)
self.assertAllClose(qz_var, pz_var, rtol=1e-2, atol=1e-2)
def test_hmc_betabernoulli(self):
"""Do we correctly handle dependencies of transformed variables?"""
with self.test_session() as sess:
# model
z = Beta(1., 1., name="z")
xs = Bernoulli(probs=z, sample_shape=10)
x_obs = np.asarray([0, 0, 1, 1, 0, 0, 0, 0, 0, 1], dtype=np.int32)
# inference
qz_samples = tf.Variable(tf.random_uniform(shape=(1000, )))
qz = ed.models.Empirical(params=qz_samples, name="z_posterior")
inference_hmc = ed.inferences.HMC({z: qz}, data={xs: x_obs})
inference_hmc.run(step_size=1.0, n_steps=5, auto_transform=True)
# check that inferred posterior mean/variance is close to
# that of the exact Beta posterior
z_unconstrained = inference_hmc.transformations[z]
qz_constrained = z_unconstrained.bijector.inverse(qz_samples)
qz_mean, qz_var = sess.run(tf.nn.moments(qz_constrained, 0))
true_posterior = Beta(1. + np.sum(x_obs), 1. + np.sum(1 - x_obs))
pz_mean, pz_var = sess.run(
(true_posterior.mean(), true_posterior.variance()))
self.assertAllClose(qz_mean, pz_mean, rtol=5e-2, atol=5e-2)
self.assertAllClose(qz_var, pz_var, rtol=1e-2, atol=1e-2)
def test_klqp_betabernoulli(self):
with self.test_session() as sess:
# model
z = Beta(1., 1., name="z")
xs = Bernoulli(probs=z, sample_shape=10)
x_obs = np.asarray([0, 0, 1, 1, 0, 0, 0, 0, 0, 1], dtype=np.int32)
# inference
qz_mean = tf.get_variable("qz_mean",
initializer=tf.random_normal(()))
qz_std = tf.nn.softplus(tf.get_variable(name="qz_prestd",
initializer=tf.random_normal(())))
qz_unconstrained = ed.models.Normal(
loc=qz_mean, scale=qz_std, name="z_posterior")
inference_klqp = ed.inferences.KLqp(
{z: qz_unconstrained}, data={xs: x_obs})
inference_klqp.run(n_iter=500, auto_transform=True)
z_unconstrained = inference_klqp.transformations[z]
qz_constrained = z_unconstrained.bijector.inverse(
qz_unconstrained.sample(1000))
qz_mean, qz_var = sess.run(tf.nn.moments(qz_constrained, 0))
true_posterior = Beta(np.sum(x_obs) + 1., np.sum(1 - x_obs) + 1.)
pz_mean, pz_var = sess.run((true_posterior.mean(),
true_posterior.variance()))
self.assertAllClose(qz_mean, pz_mean, rtol=5e-2, atol=5e-2)
self.assertAllClose(qz_var, pz_var, rtol=1e-2, atol=1e-2)
def test_hmc_betabernoulli(self):
"""Do we correctly handle dependencies of transformed variables?"""
with self.test_session() as sess:
# model
z = Beta(1., 1., name="z")
xs = Bernoulli(probs=z, sample_shape=10)
x_obs = np.asarray([0, 0, 1, 1, 0, 0, 0, 0, 0, 1], dtype=np.int32)
# inference
qz_samples = tf.Variable(tf.random_uniform(shape=(1000,)))
qz = ed.models.Empirical(params=qz_samples, name="z_posterior")
inference_hmc = ed.inferences.HMC({z: qz}, data={xs: x_obs})
inference_hmc.run(step_size=1.0, n_steps=5, auto_transform=True)
# check that inferred posterior mean/variance is close to
# that of the exact Beta posterior
z_unconstrained = inference_hmc.transformations[z]
qz_constrained = z_unconstrained.bijector.inverse(qz_samples)
qz_mean, qz_var = sess.run(tf.nn.moments(qz_constrained, 0))
true_posterior = Beta(1. + np.sum(x_obs), 1. + np.sum(1 - x_obs))
pz_mean, pz_var = sess.run((true_posterior.mean(),
true_posterior.variance()))
self.assertAllClose(qz_mean, pz_mean, rtol=5e-2, atol=5e-2)
self.assertAllClose(qz_var, pz_var, rtol=1e-2, atol=1e-2)
def test_beta_bernoulli(self):
with self.test_session() as sess:
x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
p = Beta(1.0, 1.0)
x = Bernoulli(probs=p, sample_shape=10)
qp = Empirical(tf.Variable(tf.zeros(1000)))
inference = ed.Gibbs({p: qp}, data={x: x_data})
inference.run()
true_posterior = Beta(3.0, 9.0)
val_est, val_true = sess.run([qp.mean(), true_posterior.mean()])
self.assertAllClose(val_est, val_true, rtol=1e-2, atol=1e-2)
val_est, val_true = sess.run([qp.variance(), true_posterior.variance()])
self.assertAllClose(val_est, val_true, rtol=1e-2, atol=1e-2)
"""A simple coin flipping example. Inspired by Stan's toy example.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import edward as ed
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Beta
ed.set_seed(42)
# DATA
x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
# MODEL
p = Beta(1.0, 1.0)
x = Bernoulli(probs=p, sample_shape=10)
# INFERENCE
qp_a = tf.nn.softplus(tf.Variable(tf.random_normal([])))
qp_b = tf.nn.softplus(tf.Variable(tf.random_normal([])))
qp = Beta(qp_a, qp_b)
inference = ed.KLqp({p: qp}, data={x: x_data})
inference.run(n_iter=500)
print("Posterior mean of probability: {}".format(qp.mean().eval()))
