def test_normalnormal_float32(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=mu, scale=1.0, sample_shape=50)
n_samples = 2000
qmu = Empirical(params=tf.Variable(tf.ones(n_samples)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu}, {mu: mu},
data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(),
np.sqrt(1 / 51),
rtol=1e-1,
atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(old_t, n_samples)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def main(_):
ed.set_seed(42)
# MODEL
z = MultivariateNormalTriL(
loc=tf.ones(2),
scale_tril=tf.cholesky(tf.constant([[1.0, 0.8], [0.8, 1.0]])))
# INFERENCE
qz = Empirical(params=tf.get_variable("qz/params", [1000, 2]))
inference = ed.HMC({z: qz})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
fig, ax = plt.subplots()
trace = sess.run(qz.params)
ax.scatter(trace[:, 0], trace[:, 1], marker=".")
mvn_plot_contours(z, ax=ax)
plt.show()
def main(_):
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 = Empirical(params=tf.get_variable(
"qp/params", [1000], initializer=tf.constant_initializer(0.5)))
proposal_p = Beta(3.0, 9.0)
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data={x: x_data})
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, stddev = sess.run([qp.mean(), qp.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
x_post = ed.copy(x, {p: qp})
tx_rep, tx = ed.ppc(
lambda xs, zs: tf.reduce_mean(tf.cast(xs[x_post], tf.float32)),
data={x_post: x_data})
ed.ppc_stat_hist_plot(
tx[0], tx_rep, stat_name=r'$T \equiv$mean', bins=10)
plt.show()
def test_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=tf.ones(50) * mu, scale=1.0)
n_samples = 2000
qmu = Empirical(params=tf.Variable(tf.ones(n_samples)))
proposal_mu = Normal(loc=0.0, scale=1.0)
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu},
{mu: proposal_mu},
data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-1, atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(old_t, n_samples)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def _test_normal_normal(self, default, dtype):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=tf.constant(0.0, dtype=dtype),
scale=tf.constant(1.0, dtype=dtype))
x = Normal(loc=mu, scale=tf.constant(1.0, dtype=dtype),
sample_shape=50)
n_samples = 2000
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
if not default:
qmu = Empirical(params=tf.Variable(tf.ones(n_samples, dtype=dtype)))
inference = ed.Gibbs({mu: qmu}, data={x: x_data})
else:
inference = ed.Gibbs([mu], data={x: x_data})
qmu = inference.latent_vars[mu]
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-1, atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
if not default:
self.assertEqual(old_t, n_samples)
else:
self.assertEqual(old_t, 1e4)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def _test_normal_normal(self, default, dtype):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=tf.constant(0.0, dtype=dtype),
scale=tf.constant(1.0, dtype=dtype))
x = Normal(loc=mu, scale=tf.constant(1.0, dtype=dtype),
sample_shape=50)
n_samples = 2000
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
if not default:
qmu = Empirical(params=tf.Variable(tf.ones(n_samples, dtype=dtype)))
inference = ed.HMC({mu: qmu}, data={x: x_data})
else:
inference = ed.HMC([mu], data={x: x_data})
qmu = inference.latent_vars[mu]
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-1, atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
if not default:
self.assertEqual(old_t, n_samples)
else:
self.assertEqual(old_t, 1e4)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def test_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=tf.ones(50) * mu, scale=1.0)
qmu = Empirical(params=tf.Variable(tf.ones(2000)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-2, atol=1e-2)
def test_data_tensor(self):
with self.test_session() as sess:
x_data = tf.zeros(50)
mu = Normal(0.0, 1.0)
x = Normal(mu, 1.0, sample_shape=50)
qmu = Empirical(tf.Variable(tf.ones(1000)))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.Gibbs({mu: qmu}, data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-2, atol=1e-2)
def test_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=tf.ones(50) * mu, scale=1.0)
qmu = Empirical(params=tf.Variable(tf.ones(2000)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-2, atol=1e-2)
def main(_):
ed.set_seed(42)
# MODEL
z = MultivariateNormalTriL(
loc=tf.ones(2),
scale_tril=tf.cholesky(tf.constant([[1.0, 0.8], [0.8, 1.0]])))
# INFERENCE
qz = Empirical(params=tf.get_variable("qz/params", [2000, 2]))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
def main(_):
ed.set_seed(42)
# MODEL
z = MultivariateNormalTriL(loc=tf.ones(2),
scale_tril=tf.cholesky(
tf.constant([[1.0, 0.8], [0.8, 1.0]])))
# INFERENCE
qz = Empirical(params=tf.get_variable("qz/params", [2000, 2]))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
def test_normalnormal_float64(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float64)
mu = Normal(loc=tf.constant(0.0, dtype=tf.float64),
scale=tf.constant(1.0, dtype=tf.float64))
x = Normal(loc=mu,
scale=tf.constant(1.0, dtype=tf.float64),
sample_shape=50)
qmu = Empirical(
params=tf.Variable(tf.ones(5000, dtype=tf.float64)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.SGHMC({mu: qmu}, data={x: x_data})
inference.run(step_size=0.025)
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1.5e-2)
self.assertAllClose(qmu.stddev().eval(),
np.sqrt(1 / 51),
rtol=5e-2,
atol=5e-2)
def test_normalnormal_float32(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=tf.constant(0.0, dtype=tf.float64),
scale=tf.constant(1.0, dtype=tf.float64))
x = Normal(loc=mu,
scale=tf.constant(1.0, dtype=tf.float64),
sample_shape=50)
n_samples = 2000
qmu = Empirical(params=tf.Variable(tf.ones(n_samples, dtype=tf.float64)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu},
{mu: mu},
data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-1, atol=1e-1)
def main(_):
ed.set_seed(42)
# DATA
x_data = np.array([0.0] * 50)
# MODEL: Normal-Normal with known variance
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=mu, scale=1.0, sample_shape=50)
# INFERENCE
qmu = Empirical(params=tf.get_variable("qmu/params", [1000],
initializer=tf.zeros_initializer()))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qmu.mean(), qmu.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
# Check convergence with visual diagnostics.
samples = sess.run(qmu.params)
# Plot histogram.
plt.hist(samples, bins='auto')
plt.show()
# Trace plot.
plt.plot(samples)
plt.show()
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Beta, Empirical
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(tf.ones(10) * p)
# INFERENCE
qp = Empirical(params=tf.Variable(tf.zeros([1000]) + 0.5))
proposal_p = Beta(3.0, 9.0)
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data={x: x_data})
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, stddev = sess.run([qp.mean(), qp.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Beta, Empirical
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 = Empirical(params=tf.Variable(tf.zeros([1000]) + 0.5))
proposal_p = Beta(3.0, 9.0)
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data={x: x_data})
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, stddev = sess.run([qp.mean(), qp.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
x = Normal(loc=tf.ones(50) * mu, scale=1.0)
# INFERENCE
qmu = Empirical(params=tf.Variable(tf.zeros([1000])))
proposal_mu = Normal(loc=0.0, scale=tf.sqrt(1.0 / 51.0))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu}, {mu: proposal_mu},
data={x: x_data})
inference.run()
# CRITICISM
# Check convergence with visual diagnostics.
sess = ed.get_session()
mean, stddev = sess.run([qmu.mean(), qmu.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
# Check convergence with visual diagnostics.
samples = sess.run(qmu.params)
# Plot histogram.
plt.hist(samples, bins='auto')
plt.show()
# Trace plot.
plt.plot(samples)
plt.show()
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import edward as ed
import tensorflow as tf
from edward.models import Empirical, MultivariateNormalTriL
ed.set_seed(42)
# MODEL
z = MultivariateNormalTriL(
loc=tf.ones(2),
scale_tril=tf.cholesky(tf.constant([[1.0, 0.8], [0.8, 1.0]])))
# INFERENCE
qz = Empirical(params=tf.Variable(tf.random_normal([2000, 2])))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
