Gibbs Sampling

edward/__init__.py

@@ -13,7 +13,7 @@
     KLpq, KLqp, ReparameterizationKLqp, ReparameterizationKLKLqp, \
     ReparameterizationEntropyKLqp, ScoreKLqp, ScoreKLKLqp, ScoreEntropyKLqp, \
     GANInference, WGANInference, ImplicitKLqp, MAP, Laplace, \
-    complete_conditional
+    complete_conditional, Gibbs
 from edward.models import RandomVariable
 from edward.util import check_data, check_latent_vars, copy, dot, \
     get_ancestors, get_blanket, get_children, get_control_variate_coef, \

edward/inferences/__init__.py

@@ -4,6 +4,7 @@
 
 from edward.inferences.conjugacy import complete_conditional
 from edward.inferences.gan_inference import *
+from edward.inferences.gibbs import *
 from edward.inferences.hmc import *
 from edward.inferences.implicit_klqp import *
 from edward.inferences.inference import *

edward/inferences/conjugacy/conjugacy.py

@@ -11,7 +11,7 @@
 from edward.inferences.conjugacy.simplify \
     import symbolic_suff_stat, full_simplify, expr_contains, reconstruct_expr
 from edward.models import random_variables as rvs
-from edward.util import copy, random_variables
+from edward.util import copy, get_blanket
 
 
 def normal_from_natural_params(p1, p2):
@@ -94,7 +94,7 @@ def complete_conditional(rv, cond_set=None):
   result in unpredictable behavior.
   """
   if cond_set is None:
-    cond_set = random_variables()
+    cond_set = get_blanket(rv) + [rv]
   with tf.name_scope('complete_conditional_%s' % rv.name) as scope:
     # log_joint holds all the information we need to get a conditional.
     cond_set = set([rv] + list(cond_set))

edward/inferences/gibbs.py

@@ -0,0 +1,146 @@
+from __future__ import absolute_import
+from __future__ import division
+from __future__ import print_function
+
+import random
+import six
+import tensorflow as tf
+
+from collections import OrderedDict
+from edward.inferences.conjugacy import complete_conditional
+from edward.inferences.monte_carlo import MonteCarlo
+from edward.models import RandomVariable
+from edward.util import check_latent_vars, get_session
+
+
+class Gibbs(MonteCarlo):
+  """Gibbs sampling (Geman and Geman, 1984).
+  """
+  def __init__(self, latent_vars, proposal_vars=None, data=None):
+    """
+    Parameters
+    ----------
+    proposal_vars : dict of RandomVariable to RandomVariable, optional
+      Collection of random variables to perform inference on; each is
+      binded to its complete conditionals which Gibbs cycles draws on.
+      If not specified, default is to use ``ed.complete_conditional``.
+
+    Examples
+    --------
+    >>> x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
+    >>>
+    >>> p = Beta(1.0, 1.0)
+    >>> x = Bernoulli(p=p, sample_shape=10)
+    >>>
+    >>> qp = Empirical(tf.Variable(tf.zeros(500)))
+    >>> inference = ed.Gibbs({p: qp}, data={x: x_data})
+    """
+    if proposal_vars is None:
+      proposal_vars = {z: complete_conditional(z)
+                       for z in six.iterkeys(latent_vars)}
+    else:
+      check_latent_vars(proposal_vars)
+
+    self.proposal_vars = proposal_vars
+    super(Gibbs, self).__init__(latent_vars, data)
+
+  def initialize(self, scan_order='random', *args, **kwargs):
+    """
+    Parameters
+    ----------
+    scan_order : list or str, optional
+      The scan order for each Gibbs update. If list, it is the
+      deterministic order of latent variables. An element in the list
+      can be a ``RandomVariable`` or itself a list of
+      ``RandomVariable``s (this defines a blocked Gibbs sampler). If
+      'random', will use a random order at each update.
+    """
+    self.scan_order = scan_order
+    self.feed_dict = {}
+    return super(Gibbs, self).initialize(*args, **kwargs)
+
+  def update(self, feed_dict=None):
+    """Run one iteration of Gibbs sampling.
+
+    Parameters
+    ----------
+    feed_dict : dict, optional
+      Feed dictionary for a TensorFlow session run. It is used to feed
+      placeholders that are not fed during initialization.
+
+    Returns
+    -------
+    dict
+      Dictionary of algorithm-specific information. In this case, the
+      acceptance rate of samples since (and including) this iteration.
+    """
+    sess = get_session()
+    if not self.feed_dict:
+      # Initialize feed for all conditionals to be the draws at step 0.
+      samples = OrderedDict(self.latent_vars)
+      inits = sess.run([qz.params[0] for qz in six.itervalues(samples)])
+      for z, init in zip(six.iterkeys(samples), inits):
+        self.feed_dict[z] = init
+
+      for key, value in six.iteritems(self.data):
+        if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
+          self.feed_dict[key] = value
+        elif isinstance(key, RandomVariable) and isinstance(value, tf.Variable):
+          self.feed_dict[key] = sess.run(value)
+
+    if feed_dict is None:
+      feed_dict = {}
+
+    feed_dict.update(self.feed_dict)
+
+    # Determine scan order.
+    if self.scan_order == 'random':
+      scan_order = list(six.iterkeys(self.latent_vars))
+      random.shuffle(scan_order)
+    else:  # list
+      scan_order = self.scan_order
+
+    # Fetch samples by iterating over complete conditional draws.
+    for z in scan_order:
+      if isinstance(z, RandomVariable):
+        draw = sess.run(self.proposal_vars[z], feed_dict)
+        feed_dict[z] = draw
+        self.feed_dict[z] = draw
+      else:  # list
+        draws = sess.run([self.proposal_vars[zz] for zz in z], feed_dict)
+        for zz, draw in zip(z, draws):
+          feed_dict[zz] = draw
+          self.feed_dict[zz] = draw
+
+    # Assign the samples to the Empirical random variables.
+    _, accept_rate = sess.run([self.train, self.n_accept_over_t], feed_dict)
+    t = sess.run(self.increment_t)
+
+    if self.debug:
+      sess.run(self.op_check)
+
+    if self.logging and self.n_print != 0:
+      if t == 1 or t % self.n_print == 0:
+        summary = sess.run(self.summarize, feed_dict)
+        self.train_writer.add_summary(summary, t)
+
+    return {'t': t, 'accept_rate': accept_rate}
+
+  def build_update(self):
+    """
+    Notes
+    -----
+    The updates assume each Empirical random variable is directly
+    parameterized by ``tf.Variable``s.
+    """
+    # Update Empirical random variables according to the complete
+    # conditionals. We will feed the conditionals when calling ``update()``.
+    assign_ops = []
+    for z, qz in six.iteritems(self.latent_vars):
+      variable = qz.get_variables()[0]
+      assign_ops.append(
+          tf.scatter_update(variable, self.t, self.proposal_vars[z]))
+
+    # Increment n_accept (if accepted).
+    assign_ops.append(self.n_accept.assign_add(1))
+    return tf.group(*assign_ops)

tests/test-inferences/test_gibbs.py

@@ -0,0 +1,52 @@
+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, Empirical, Normal
+
+
+class test_gibbs_class(tf.test.TestCase):
+
+  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(a=1.0, b=1.0)
+      x = Bernoulli(p=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(a=3.0, b=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 test_normal_normal(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=mu, sigma=1.0, sample_shape=50)
+
+      qmu = Empirical(params=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.std().eval(), np.sqrt(1 / 51),
+                          rtol=1e-2, atol=1e-2)
+
+if __name__ == '__main__':
+  ed.set_seed(127832)
+  tf.test.main()