tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler

tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler(
    f,
    log_p,
    sampling_dist_q,
    z=None,
    n=None,
    seed=None,
    name='expectation_importance_sampler'
)

Defined in tensorflow/contrib/bayesflow/python/ops/monte_carlo_impl.py.

Monte Carlo estimate of \(E_p[f(Z)] = E_q[f(Z) p(Z) / q(Z)]\).

With \(p(z) := exp^{log_p(z)}\), this Op returns

\(n^{-1} sum_{i=1}^n [ f(z_i) p(z_i) / q(z_i) ], z_i ~ q,\) \(\approx E_q[ f(Z) p(Z) / q(Z) ]\) \(= E_p[f(Z)]\)

This integral is done in log-space with max-subtraction to better handle the often extreme values that f(z) p(z) / q(z) can take on.

If f >= 0, it is up to 2x more efficient to exponentiate the result of expectation_importance_sampler_logspace applied to Log[f].

User supplies either Tensor of samples z, or number of samples to draw n

Args:

  • f: Callable mapping samples from sampling_dist_q to Tensors with shape broadcastable to q.batch_shape. For example, f works "just like" q.log_prob.
  • log_p: Callable mapping samples from sampling_dist_q to Tensors with shape broadcastable to q.batch_shape. For example, log_p works "just like" sampling_dist_q.log_prob.
  • sampling_dist_q: The sampling distribution. tfp.distributions.Distribution. float64 dtype recommended. log_p and q should be supported on the same set.
  • z: Tensor of samples from q, produced by q.sample for some n.
  • n: Integer Tensor. Number of samples to generate if z is not provided.
  • seed: Python integer to seed the random number generator.
  • name: A name to give this Op.

Returns:

The importance sampling estimate. Tensor with shape equal to batch shape of q, and dtype = q.dtype.