class_docstr: Stochastic gradient Hamiltonian Monte Carlo [@chen2014stochastic].
  
  #### Notes
  
  In conditional inference, we infer $z$ in $p(z, \beta
  \mid x)$ while fixing inference over $\beta$ using another
  distribution $q(\beta)$.
  `SGHMC` substitutes the model's log marginal density
  
  $\log p(x, z) = \log \mathbb{E}_{q(\beta)} [ p(x, z, \beta) ]
                \approx \log p(x, z, \beta^*)$
  
  leveraging a single Monte Carlo sample, where $\beta^* \sim
  q(\beta)$. This is unbiased (and therefore asymptotically exact as a
  pseudo-marginal method) if $q(\beta) = p(\beta \mid x)$.
  
  #### Examples
  
  ```python
  mu = Normal(loc=0.0, scale=1.0)
  x = Normal(loc=mu, scale=1.0, sample_shape=10)
  
  qmu = Empirical(tf.Variable(tf.zeros(500)))
  inference = ed.SGHMC({mu: qmu}, {x: np.zeros(10, dtype=np.float32)})
  ```
docstr: Simulate Hamiltonian dynamics with friction using a discretized
  integrator. Its discretization error goes to zero as the learning
  rate decreases.
  
  Implements the update equations from (15) of @chen2014stochastic.
docstr_tok: ["Simulate","Hamiltonian","dynamics","with","friction","using","a","discretized","integrator",".","Its","discretization","error","goes","to","zero","as","the","learning","rate","decreases",".","Implements","the","update","equations","from","(","15",")","of","@","chen2014stochastic","."]
code: def build_update(self):
      """Simulate Hamiltonian dynamics with friction using a discretized
      integrator. Its discretization error goes to zero as the learning
      rate decreases.
  
      Implements the update equations from (15) of @chen2014stochastic.
      """
      old_sample = {
          z: tf.gather(qz.params, tf.maximum(self.t - 1, 0))
          for z, qz in six.iteritems(self.latent_vars)
      }
      old_v_sample = {z: v for z, v in six.iteritems(self.v)}
  
      # Simulate Hamiltonian dynamics with friction.
      learning_rate = self.step_size * 0.01
      grad_log_joint = tf.gradients(
          self._log_joint(old_sample), list(six.itervalues(old_sample))
      )
  
      # v_sample is so named b/c it represents a velocity rather than momentum.
      sample = {}
      v_sample = {}
      for z, grad_log_p in zip(
          six.iterkeys(old_sample), grad_log_joint
      ):
          qz = self.latent_vars[z]
          event_shape = qz.event_shape
          stddev = tf.sqrt(
              tf.cast(learning_rate * self.friction, qz.dtype)
          )
          normal = tf.random_normal(event_shape, dtype=qz.dtype)
          sample[z] = old_sample[z] + old_v_sample[z]
          v_sample[z] = (
              (1.0 - 0.5 * self.friction) * old_v_sample[z]
              + learning_rate * tf.convert_to_tensor(grad_log_p)
              + stddev * normal
          )
  
      # Update Empirical random variables.
      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, sample[z])
          )
          assign_ops.append(tf.assign(self.v[z], v_sample[z]).op)
  
      # Increment n_accept.
      assign_ops.append(self.n_accept.assign_add(1))
      return tf.group(*assign_ops)
  
file_path: edward/edward/inferences/sghmc.py
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import six
  import tensorflow
  from edward.inferences.monte_carlo import MonteCarlo
  from edward.models import RandomVariable, Empirical
  from edward.util import copy
label_desc: Use image node_id 3 for calling the SGHMC obj's underlying member method code with example usage: obj.build_update() and returns: tf