def main(_):
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(FLAGS.N)
# MODEL
pi = Dirichlet(concentration=tf.ones(FLAGS.K))
mu = Normal(0.0, 1.0, sample_shape=[FLAGS.K, FLAGS.D])
sigma = InverseGamma(concentration=1.0, rate=1.0,
sample_shape=[FLAGS.K, FLAGS.D])
c = Categorical(logits=tf.log(pi) - tf.log(1.0 - pi), sample_shape=FLAGS.N)
x = Normal(loc=tf.gather(mu, c), scale=tf.gather(sigma, c))
# INFERENCE
qpi = Empirical(params=tf.get_variable(
"qpi/params",
[FLAGS.T, FLAGS.K],
initializer=tf.constant_initializer(1.0 / FLAGS.K)))
qmu = Empirical(params=tf.get_variable("qmu/params",
[FLAGS.T, FLAGS.K, FLAGS.D],
initializer=tf.zeros_initializer()))
qsigma = Empirical(params=tf.get_variable("qsigma/params",
[FLAGS.T, FLAGS.K, FLAGS.D],
initializer=tf.ones_initializer()))
qc = Empirical(params=tf.get_variable("qc/params",
[FLAGS.T, FLAGS.N],
initializer=tf.zeros_initializer(),
dtype=tf.int32))
gpi = Dirichlet(concentration=tf.constant([1.4, 1.6]))
gmu = Normal(loc=tf.constant([[1.0, 1.0], [-1.0, -1.0]]),
scale=tf.constant([[0.5, 0.5], [0.5, 0.5]]))
gsigma = InverseGamma(concentration=tf.constant([[1.1, 1.1], [1.1, 1.1]]),
rate=tf.constant([[1.0, 1.0], [1.0, 1.0]]))
gc = Categorical(logits=tf.zeros([FLAGS.N, FLAGS.K]))
inference = ed.MetropolisHastings(
latent_vars={pi: qpi, mu: qmu, sigma: qsigma, c: qc},
proposal_vars={pi: gpi, mu: gmu, sigma: gsigma, c: gc},
data={x: x_data})
inference.initialize()
sess = ed.get_session()
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
t = info_dict['t']
if t == 1 or t % inference.n_print == 0:
qpi_mean, qmu_mean = sess.run([qpi.mean(), qmu.mean()])
print("")
print("Inferred membership probabilities:")
print(qpi_mean)
print("Inferred cluster means:")
print(qmu_mean)
def _test_linear_regression(self, default, dtype):
def build_toy_dataset(N, w, noise_std=0.1):
D = len(w)
x = np.random.randn(N, D)
y = np.dot(x, w) + np.random.normal(0, noise_std, size=N)
return x, y
with self.test_session() as sess:
N = 40 # number of data points
D = 10 # number of features
w_true = np.random.randn(D)
X_train, y_train = build_toy_dataset(N, w_true)
X_test, y_test = build_toy_dataset(N, w_true)
X = tf.placeholder(dtype, [N, D])
w = Normal(loc=tf.zeros(D, dtype=dtype),
scale=tf.ones(D, dtype=dtype))
b = Normal(loc=tf.zeros(1, dtype=dtype),
scale=tf.ones(1, dtype=dtype))
y = Normal(loc=ed.dot(X, w) + b,
scale=0.1 * tf.ones(N, dtype=dtype))
n_samples = 2000
if not default:
qw = Empirical(
tf.Variable(tf.zeros([n_samples, D], dtype=dtype)))
qb = Empirical(
tf.Variable(tf.zeros([n_samples, 1], dtype=dtype)))
inference = ed.SGLD({
w: qw,
b: qb
},
data={
X: X_train,
y: y_train
})
else:
inference = ed.SGLD([w, b], data={X: X_train, y: y_train})
qw = inference.latent_vars[w]
qb = inference.latent_vars[b]
inference.run(step_size=0.001)
self.assertAllClose(qw.mean().eval(), w_true, rtol=5e-1, atol=5e-1)
self.assertAllClose(qb.mean().eval(), [0.0], rtol=5e-1, atol=5e-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_linear_regression(self, default, dtype):
def build_toy_dataset(N, w, noise_std=0.1):
D = len(w)
x = np.random.randn(N, D)
y = np.dot(x, w) + np.random.normal(0, noise_std, size=N)
return x, y
with self.test_session() as sess:
N = 40 # number of data points
D = 10 # number of features
w_true = np.random.randn(D)
X_train, y_train = build_toy_dataset(N, w_true)
X_test, y_test = build_toy_dataset(N, w_true)
X = tf.placeholder(dtype, [N, D])
w = Normal(loc=tf.zeros(D, dtype=dtype), scale=tf.ones(D, dtype=dtype))
b = Normal(loc=tf.zeros(1, dtype=dtype), scale=tf.ones(1, dtype=dtype))
y = Normal(loc=ed.dot(X, w) + b, scale=0.1 * tf.ones(N, dtype=dtype))
proposal_w = Normal(loc=w, scale=0.5 * tf.ones(D, dtype=dtype))
proposal_b = Normal(loc=b, scale=0.5 * tf.ones(1, dtype=dtype))
n_samples = 2000
if not default:
qw = Empirical(tf.Variable(tf.zeros([n_samples, D], dtype=dtype)))
qb = Empirical(tf.Variable(tf.zeros([n_samples, 1], dtype=dtype)))
inference = ed.ReplicaExchangeMC(
{w: qw, b: qb}, {w: proposal_w, b: proposal_b},
data={X: X_train, y: y_train})
else:
inference = ed.ReplicaExchangeMC(
[w, b], {w: proposal_w, b: proposal_b},
data={X: X_train, y: y_train})
qw = inference.latent_vars[w]
qb = inference.latent_vars[b]
inference.run()
self.assertAllClose(qw.mean().eval(), w_true, rtol=5e-1, atol=5e-1)
self.assertAllClose(qb.mean().eval(), [0.0], rtol=5e-1, atol=5e-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 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 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 _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_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 _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 main(_):
# DATA
trait_true = np.random.normal(size=[FLAGS.nsubj, 1])
thresh_true = np.random.normal(size=[1, FLAGS.nitem])
X_data = np.random.binomial(1, expit(trait_true - thresh_true))
# MODEL
trait = Normal(loc=0.0, scale=1.0, sample_shape=[FLAGS.nsubj, 1])
thresh = Normal(loc=0.0, scale=1.0, sample_shape=[1, FLAGS.nitem])
X = Bernoulli(logits=trait - thresh)
# INFERENCE
q_trait = Empirical(params=tf.get_variable("q_trait/params",
[FLAGS.T, FLAGS.nsubj, 1]))
q_thresh = Empirical(params=tf.get_variable("q_thresh/params",
[FLAGS.T, 1, FLAGS.nitem]))
inference = ed.HMC({trait: q_trait, thresh: q_thresh}, data={X: X_data})
inference.run(step_size=0.1)
# Alternatively, use variational inference.
# q_trait = Normal(
# loc=tf.get_variable("q_trait/loc", [FLAGS.nsubj, 1]),
# scale=tf.nn.softplus(
# tf.get_variable("q_trait/scale", [FLAGS.nsubj, 1])))
# q_thresh = Normal(
# loc=tf.get_variable("q_thresh/loc", [1, FLAGS.nitem]),
# scale=tf.nn.softplus(
# tf.get_variable("q_thresh/scale", [1, FLAGS.nitem])))
# inference = ed.KLqp({trait: q_trait, thresh: q_thresh}, data={X: X_data})
# inference.run(n_iter=2500, n_samples=10)
# CRITICISM
# Check that the inferred posterior mean captures the true traits.
plt.scatter(trait_true, q_trait.mean().eval())
plt.show()
print("MSE between true traits and inferred posterior mean:")
print(np.mean(np.square(trait_true - q_trait.mean().eval())))
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 test_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(mu=0.0, sigma=1.0)
x = Normal(mu=tf.ones(50) * mu, sigma=1.0)
qmu = Empirical(params=tf.Variable(tf.ones(5000)))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.SGLD({mu: qmu}, data={x: x_data})
inference.run(step_size=0.2)
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.std().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=0.0, scale=1.0)
x = Normal(loc=mu, scale=1.0, sample_shape=50)
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_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)
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_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()
def main(_):
# Data generation (known mean)
xn_data = np.random.normal(FLAGS.loc, FLAGS.scale, FLAGS.N)
print("scale: {}".format(FLAGS.scale))
# Prior definition
alpha = 0.5
beta = 0.7
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha, beta)
xn = Normal(FLAGS.loc, tf.sqrt(ig), sample_shape=FLAGS.N)
# Inference
qig = Empirical(params=tf.get_variable(
"qig/params", [1000], initializer=tf.constant_initializer(0.5)))
proposal_ig = InverseGamma(2.0, 2.0)
inference = ed.MetropolisHastings({ig: qig}, {ig: proposal_ig},
data={xn: xn_data})
inference.run()
sess = ed.get_session()
print("Inferred scale: {}".format(sess.run(tf.sqrt(qig.mean()))))
def main(_):
# Data generation (known mean)
xn_data = np.random.normal(FLAGS.loc, FLAGS.scale, FLAGS.N)
print("scale: {}".format(FLAGS.scale))
# Prior definition
alpha = 0.5
beta = 0.7
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha, beta)
xn = Normal(FLAGS.loc, tf.sqrt(ig), sample_shape=FLAGS.N)
# Inference
qig = Empirical(params=tf.get_variable(
"qig/params", [1000], initializer=tf.constant_initializer(0.5)))
proposal_ig = InverseGamma(2.0, 2.0)
inference = ed.MetropolisHastings({ig: qig},
{ig: proposal_ig}, data={xn: xn_data})
inference.run()
sess = ed.get_session()
print("Inferred scale: {}".format(sess.run(tf.sqrt(qig.mean()))))
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()
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)
def main(_):
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(FLAGS.N)
# MODEL
pi = Dirichlet(concentration=tf.ones(FLAGS.K))
mu = Normal(0.0, 1.0, sample_shape=[FLAGS.K, FLAGS.D])
sigma = InverseGamma(concentration=1.0,
rate=1.0,
sample_shape=[FLAGS.K, FLAGS.D])
c = Categorical(logits=tf.log(pi) - tf.log(1.0 - pi), sample_shape=FLAGS.N)
x = Normal(loc=tf.gather(mu, c), scale=tf.gather(sigma, c))
# INFERENCE
qpi = Empirical(
params=tf.get_variable("qpi/params", [FLAGS.T, FLAGS.K],
initializer=tf.constant_initializer(1.0 /
FLAGS.K)))
qmu = Empirical(
params=tf.get_variable("qmu/params", [FLAGS.T, FLAGS.K, FLAGS.D],
initializer=tf.zeros_initializer()))
qsigma = Empirical(
params=tf.get_variable("qsigma/params", [FLAGS.T, FLAGS.K, FLAGS.D],
initializer=tf.ones_initializer()))
qc = Empirical(params=tf.get_variable("qc/params", [FLAGS.T, FLAGS.N],
initializer=tf.zeros_initializer(),
dtype=tf.int32))
gpi = Dirichlet(concentration=tf.constant([1.4, 1.6]))
gmu = Normal(loc=tf.constant([[1.0, 1.0], [-1.0, -1.0]]),
scale=tf.constant([[0.5, 0.5], [0.5, 0.5]]))
gsigma = InverseGamma(concentration=tf.constant([[1.1, 1.1], [1.1, 1.1]]),
rate=tf.constant([[1.0, 1.0], [1.0, 1.0]]))
gc = Categorical(logits=tf.zeros([FLAGS.N, FLAGS.K]))
inference = ed.MetropolisHastings(latent_vars={
pi: qpi,
mu: qmu,
sigma: qsigma,
c: qc
},
proposal_vars={
pi: gpi,
mu: gmu,
sigma: gsigma,
c: gc
},
data={x: x_data})
inference.initialize()
sess = ed.get_session()
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
t = info_dict['t']
if t == 1 or t % inference.n_print == 0:
qpi_mean, qmu_mean = sess.run([qpi.mean(), qmu.mean()])
print("")
print("Inferred membership probabilities:")
print(qpi_mean)
print("Inferred cluster means:")
print(qmu_mean)
def bayes_mult_cmd(table_file, metadata_file, formula, output_file):
#metadata = _type_cast_to_float(metadata.copy())
metadata = pd.read_table(metadata_file, index_col=0)
G_data = dmatrix(formula, metadata, return_type='dataframe')
table = load_table(table_file)
# basic filtering parameters
soil_filter = lambda val, id_, md: id_ in metadata.index
read_filter = lambda val, id_, md: np.sum(val) > 10
#sparse_filter = lambda val, id_, md: np.mean(val > 0) > 0.1
sample_filter = lambda val, id_, md: np.sum(val) > 1000
table = table.filter(soil_filter, axis='sample')
table = table.filter(sample_filter, axis='sample')
table = table.filter(read_filter, axis='observation')
#table = table.filter(sparse_filter, axis='observation')
print(table.shape)
y_data = pd.DataFrame(np.array(table.matrix_data.todense()).T,
index=table.ids(axis='sample'),
columns=table.ids(axis='observation'))
y_data, G_data = y_data.align(G_data, axis=0, join='inner')
psi = _gram_schmidt_basis(y_data.shape[1])
G_data = G_data.values
y_data = y_data.values
N, D = y_data.shape
p = G_data.shape[1] # number of covariates
r = G_data.shape[1] # rank of covariance matrix
psi = tf.convert_to_tensor(psi, dtype=tf.float32)
n = tf.convert_to_tensor(y_data.sum(axis=1), dtype=tf.float32)
# hack to get multinomial working
def _sample_n(self, n=1, seed=None):
# define Python function which returns samples as a Numpy array
def np_sample(p, n):
return multinomial.rvs(p=p, n=n, random_state=seed).astype(np.float32)
# wrap python function as tensorflow op
val = tf.py_func(np_sample, [self.probs, n], [tf.float32])[0]
# set shape from unknown shape
batch_event_shape = self.batch_shape.concatenate(self.event_shape)
shape = tf.concat(
[tf.expand_dims(n, 0), tf.convert_to_tensor(batch_event_shape)], 0)
val = tf.reshape(val, shape)
return val
Multinomial._sample_n = _sample_n
# dummy variable for gradient
G = tf.placeholder(tf.float32, [N, p])
b = Exponential(rate=1.0)
B = Normal(loc=tf.zeros([p, D-1]),
scale=tf.ones([p, D-1]) )
# Factorization of covariance matrix
# http://edwardlib.org/tutorials/klqp
l = Exponential(rate=1.0)
L = Normal(loc=tf.zeros([p, D-1]),
scale=tf.ones([p, D-1]) )
z = Normal(loc=tf.zeros([N, p]),
scale=tf.ones([N, p]))
# Cholesky trick to get multivariate normal
v = tf.matmul(G, B) + tf.matmul(z, L)
# get clr transformed values
eta = tf.matmul(v, psi)
Y = Multinomial(total_count=n, logits=eta)
T = 100000 # the number of mixin samples from MCMC sampling
qb = PointMass(params=tf.Variable(tf.random_normal([])))
qB = PointMass(params=tf.Variable(tf.random_normal([p, D-1])))
qz = Empirical(params=tf.Variable(tf.random_normal([T, N, p])))
ql = PointMass(params=tf.Variable(tf.random_normal([])))
qL = PointMass(params=tf.Variable(tf.random_normal([p, D-1])))
# Imputation
inference_z = ed.SGLD(
{z: qz},
data={G: G_data, Y: y_data, B: qB, L: qL}
)
# Maximization
inference_BL = ed.MAP(
{B: qB, L: qL, b: qb, l: ql},
data={G: G_data, Y: y_data, z: qz}
)
inference_z.initialize(step_size=1e-10)
inference_BL.initialize(n_iter=1000)
sess = ed.get_session()
saver = tf.train.Saver()
tf.global_variables_initializer().run()
for i in range(inference_BL.n_iter):
inference_z.update() # e-step
# will need to compute the expectation of z
info_dict = inference_BL.update() # m-step
inference_BL.print_progress(info_dict)
save_path = saver.save(sess, output_file)
print("Model saved in file: %s" % save_path)
pickle.dump({'qB': sess.run(qB.mean()),
'qL': sess.run(qL.mean()),
'qz': sess.run(qz.mean())},
open(output_file + '.params.pickle', 'wb')
)
from edward.models import Bernoulli, Normal, Empirical
from scipy.special import expit
# DATA
nsubj = 200
nitem = 25
trait_true = np.random.normal(size=[nsubj, 1])
thresh_true = np.random.normal(size=[1, nitem])
X_data = np.random.binomial(1, expit(trait_true - thresh_true))
# MODEL
trait = Normal(loc=tf.zeros([nsubj, 1]), scale=tf.ones([nsubj, 1]))
thresh = Normal(loc=tf.zeros([1, nitem]), scale=tf.ones([1, nitem]))
X = Bernoulli(logits=trait - thresh)
# INFERENCE
T = 5000 # number of posterior samples
q_trait = Empirical(params=tf.Variable(tf.zeros([T, nsubj, 1])))
q_thresh = Empirical(params=tf.Variable(tf.zeros([T, 1, nitem])))
inference = ed.HMC({trait: q_trait, thresh: q_thresh}, data={X: X_data})
inference.run(step_size=0.1)
# CRITICISM
# Check that the inferred posterior mean captures the true traits.
plt.scatter(trait_true, q_trait.mean().eval())
plt.show()
print("MSE between true traits and inferred posterior mean:")
print(np.mean(np.square(trait_true - q_trait.mean().eval())))
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 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(a=1.0, b=1.0)
x = Bernoulli(p=tf.ones(10) * p)
# INFERENCE
qp = Empirical(params=tf.Variable(tf.zeros([1000]) + 0.5))
proposal_p = Beta(a=3.0, b=9.0)
data = {x: x_data}
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data)
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, std = sess.run([qp.mean(), qp.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
import tensorflow as tf
from edward.models import InverseGamma, Normal, Empirical
N = 1000
# Data generation (known mean)
mu = 7.0
sigma = 0.7
xn_data = np.random.normal(mu, sigma, N)
print('sigma={}'.format(sigma))
# Prior definition
alpha = tf.Variable(0.5, dtype=tf.float32, trainable=False)
beta = tf.Variable(0.7, dtype=tf.float32, trainable=False)
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha=alpha, beta=beta)
xn = Normal(mu=mu, sigma=tf.ones([N]) * tf.sqrt(ig))
# Inference
qig = Empirical(params=tf.Variable(tf.zeros(1000) + 0.5))
proposal_ig = InverseGamma(alpha=2.0, beta=2.0)
inference = ed.MetropolisHastings({ig: qig}, {ig: proposal_ig},
data={xn: xn_data})
inference.run()
sess = ed.get_session()
print('Inferred sigma={}'.format(sess.run(tf.sqrt(qig.mean()))))
"""
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, MultivariateNormalFull
ed.set_seed(42)
# MODEL
z = MultivariateNormalFull(
mu=tf.ones(2),
sigma=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, std = sess.run([qz.mean(), qz.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
pi: qpi,
mu: qmu,
sigma: qsigma,
c: qc
},
proposal_vars={
pi: gpi,
mu: gmu,
sigma: gsigma,
c: gc
},
data={x: x_data})
inference.initialize()
sess = ed.get_session()
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
t = info_dict['t']
if t == 1 or t % inference.n_print == 0:
qpi_mean, qmu_mean = sess.run([qpi.mean(), qmu.mean()])
print("")
print("Inferred membership probabilities:")
print(qpi_mean)
print("Inferred cluster means:")
print(qmu_mean)
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Empirical, Normal
from scipy.special import expit
ed.set_seed(123)
N = 5810 # number of data points
D = 54 # number of features
# DATA
w_true = np.random.randn(D)
X_data = np.random.randn(N, D)
p = expit(np.dot(X_data, w_true))
y_data = np.array([np.random.binomial(1, i) for i in p])
# MODEL
X = tf.Variable(X_data.astype(np.float32), trainable=False)
w = Normal(mu=tf.zeros(D), sigma=tf.ones(D))
y = Bernoulli(logits=ed.dot(X, w))
# INFERENCE
T = 5000
qw = Empirical(params=tf.Variable(tf.zeros([T, D])))
inference = ed.HMC({w: qw}, data={y: y_data})
inference.run(step_size=0.05)
# CRITICISM
print("Mean squared error in true values to inferred posterior mean:")
print(tf.reduce_mean(tf.square(w_true - qw.mean())).eval())
import tensorflow as tf
from edward.models import InverseGamma, Normal, Empirical
N = 1000
# Data generation (known mean)
loc = 7.0
scale = 0.7
xn_data = np.random.normal(loc, scale, N)
print('sigma={}'.format(sigma))
# Prior definition
alpha = tf.Variable(0.5, trainable=False)
beta = tf.Variable(0.7, trainable=False)
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha, beta)
xn = Normal(loc, tf.ones([N]) * tf.sqrt(ig))
# Inference
qig = Empirical(params=tf.Variable(tf.zeros(1000) + 0.5))
proposal_ig = InverseGamma(2.0, 2.0)
inference = ed.MetropolisHastings({ig: qig},
{ig: proposal_ig}, data={xn: xn_data})
inference.run()
sess = ed.get_session()
print('Inferred sigma={}'.format(sess.run(tf.sqrt(qig.mean()))))
x = Normal(mu=tf.ones(50) * mu, sigma=1.0)
# INFERENCE
qmu = Empirical(params=tf.Variable(tf.zeros([1000])))
proposal_mu = Normal(mu=0.0, sigma=tf.sqrt(1.0 / 51.0))
# analytic solution: N(mu=0.0, sigma=\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, std = sess.run([qmu.mean(), qmu.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
# 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 edward.models import Bernoulli, Normal, Empirical
from scipy.special import expit
# DATA
nsubj = 200
nitem = 25
trait_true = np.random.normal(size=[nsubj, 1])
thresh_true = np.random.normal(size=[1, nitem])
X_data = np.random.binomial(1, expit(trait_true - thresh_true))
# MODEL
trait = Normal(mu=tf.zeros([nsubj, 1]), sigma=tf.ones([nsubj, 1]))
thresh = Normal(mu=tf.zeros([1, nitem]), sigma=tf.ones([1, nitem]))
X = Bernoulli(logits=tf.sub(trait, thresh))
# INFERENCE
T = 5000 # number of posterior samples
q_trait = Empirical(params=tf.Variable(tf.zeros([T, nsubj, 1])))
q_thresh = Empirical(params=tf.Variable(tf.zeros([T, 1, nitem])))
inference = ed.HMC({trait: q_trait, thresh: q_thresh}, data={X: X_data})
inference.run(step_size=0.1)
# CRITICISM
# Check that the inferred posterior mean captures the true traits.
plt.scatter(trait_true, q_trait.mean().eval())
plt.show()
print("MSE between true traits and inferred posterior mean:")
print(np.mean(np.square(trait_true - q_trait.mean().eval())))
"""
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, MultivariateNormalFull
ed.set_seed(42)
# MODEL
z = MultivariateNormalFull(
mu=tf.ones(2),
sigma=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, std = sess.run([qz.mean(), qz.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
"""
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)
qw = Empirical(params=tf.Variable(tf.random_normal([T, D])))
qb = Empirical(params=tf.Variable(tf.random_normal([T, 1])))
inference = ed.SGHMC({w: qw, b: qb}, data={X: X_train, y: y_train})
inference.run(step_size=1e-3)
# CRITICISM
# Plot posterior samples.
sns.jointplot(qb.params.eval()[nburn:T:stride],
qw.params.eval()[nburn:T:stride])
plt.show()
# Posterior predictive checks.
y_post = ed.copy(y, {w: qw.mean(), b: qb.mean()})
# This is equivalent to
# y_post = Normal(mu=ed.dot(X, qw.mean()) + qb.mean(), sigma=tf.ones(N))
print("Mean squared error on test data:")
print(ed.evaluate('mean_squared_error', data={X: X_test, y_post: y_test}))
print("Displaying prior predictive samples.")
n_prior_samples = 10
w_prior = w.sample(n_prior_samples).eval()
b_prior = b.sample(n_prior_samples).eval()
plt.scatter(X_train, y_train)
inputs = np.linspace(-1, 10, num=400, dtype=np.float32)
inference = ed.MetropolisHastings(latent_vars={
pi: qpi,
mu: qmu,
sigma: qsigma,
c: qc
},
proposal_vars={
pi: gpi,
mu: gmu,
sigma: gsigma,
c: gc
},
data={x: x_data})
inference.initialize()
sess = ed.get_session()
init = tf.initialize_all_variables()
init.run()
for _ in range(T):
info_dict = inference.update()
t = info_dict['t']
if t == 1 or t % inference.n_print == 0:
accept_rate = info_dict['accept_rate']
print("iter {:d} accept rate {:.2f}".format(t, accept_rate))
print("Inferred membership probabilities:")
print(sess.run(qpi.mean()))
print("Inferred cluster means:")
print(sess.run(qmu.mean()))