code: def csiszar_vimco(
      f,
      p_log_prob,
      q,
      num_draws,
      num_batch_draws=1,
      seed=None,
      name=None,
  ):
      """Use VIMCO to lower the variance of gradient[csiszar_function(log(Avg(u))].
  
      This function generalizes VIMCO [(Mnih and Rezende, 2016)][1] to Csiszar
      f-Divergences.
  
      Note: if `q.reparameterization_type = tfd.FULLY_REPARAMETERIZED`,
      consider using `monte_carlo_variational_loss`.
  
      The VIMCO loss is:
  
      ```none
      vimco = f(log(Avg{u[i] : i=0,...,m-1}))
      where,
        logu[i] = log( p(x, h[i]) / q(h[i] | x) )
        h[i] iid~ q(H | x)
      ```
  
      Interestingly, the VIMCO gradient is not the naive gradient of `vimco`.
      Rather, it is characterized by:
  
      ```none
      grad[vimco] - variance_reducing_term
      where,
        variance_reducing_term = Sum{ grad[log q(h[i] | x)] *
                                        (vimco - f(log Avg{h[j;i] : j=0,...,m-1}))
                                     : i=0, ..., m-1 }
        h[j;i] = { u[j]                             j!=i
                 { GeometricAverage{ u[k] : k!=i}   j==i
      ```
  
      (We omitted `stop_gradient` for brevity. See implementation for more details.)
  
      The `Avg{h[j;i] : j}` term is a kind of "swap-out average" where the `i`-th
      element has been replaced by the leave-`i`-out Geometric-average.
  
      This implementation prefers numerical precision over efficiency, i.e.,
      `O(num_draws * num_batch_draws * prod(batch_shape) * prod(event_shape))`.
      (The constant may be fairly large, perhaps around 12.)
  
      Args:
        f: Python `callable` representing a Csiszar-function in log-space.
        p_log_prob: Python `callable` representing the natural-log of the
          probability under distribution `p`. (In variational inference `p` is the
          joint distribution.)
        q: `tf.Distribution`-like instance; must implement: `sample(n, seed)`, and
          `log_prob(x)`. (In variational inference `q` is the approximate posterior
          distribution.)
        num_draws: Integer scalar number of draws used to approximate the
          f-Divergence expectation.
        num_batch_draws: Integer scalar number of draws used to approximate the
          f-Divergence expectation.
        seed: PRNG seed for `q.sample`; see `tfp.random.sanitize_seed` for details.
        name: Python `str` name prefixed to Ops created by this function.
  
      Returns:
        vimco: The Csiszar f-Divergence generalized VIMCO objective.
  
      Raises:
        ValueError: if `num_draws < 2`.
  
      #### References
  
      [1]: Andriy Mnih and Danilo Rezende. Variational Inference for Monte Carlo
           objectives. In _International Conference on Machine Learning_, 2016.
           https://arxiv.org/abs/1602.06725
      """
      with tf.name_scope(name or "csiszar_vimco"):
          if num_draws < 2:
              raise ValueError("Must specify num_draws > 1.")
          stop = tf.stop_gradient  # For readability.
  
          sample_seed, target_seed = samplers.split_seed(seed, 2)
          q_sample = q.sample(
              sample_shape=[num_draws, num_batch_draws],
              seed=sample_seed,
          )
          x = tf.nest.map_structure(stop, q_sample)
          logqx = q.log_prob(x)
          logu = (
              _call_fn_maybe_with_seed(p_log_prob, x, seed=target_seed)
              - logqx
          )
          f_log_sooavg_u, f_log_avg_u = map(
              f, log_soomean_exp(logu, axis=0)
          )
  
          dotprod = tf.reduce_sum(
              logqx * stop(f_log_avg_u - f_log_sooavg_u), axis=0
          )  # Sum over iid samples.
          # We now rewrite f_log_avg_u so that:
          #   `grad[f_log_avg_u] := grad[f_log_avg_u + dotprod]`.
          # To achieve this, we use a trick that
          #   `f(x) - stop(f(x)) == zeros_like(f(x))`
          # but its gradient is grad[f(x)].
          # Note that IEEE754 specifies that `x - x == 0.` and `x + 0. == x`, hence
          # this trick loses no precision. For more discussion regarding the relevant
          # portions of the IEEE754 standard, see the StackOverflow question,
          # "Is there a floating point value of x, for which x-x == 0 is false?"
          # http://stackoverflow.com/q/2686644
          # Following is same as adding zeros_like(dot_prod).
          f_log_avg_u = f_log_avg_u + dotprod - stop(dotprod)
          return tf.reduce_mean(f_log_avg_u, axis=0)
  
imports: import enum
  import functools
  import warnings
  import numpy
  import tensorflow.compat.v2
  from tensorflow_probability.python import monte_carlo
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import nest_util
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal.reparameterization import FULLY_REPARAMETERIZED
  from tensorflow_probability.python.stats.leave_one_out import log_soomean_exp
  from tensorflow.python.util import deprecation
label_desc: Use image node_id 21 for calling a global function with example usage: csiszar_vimco(f, p_log_prob, q, num_draws, num_batch_draws, seed, name) and returns: tf