tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler_logspace

Importance sampling with a positive function, in log-space.

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

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

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.

In contrast to expectation_importance_sampler, this Op returns values in log-space.

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

Args
log_f Callable mapping samples from sampling_dist_q to Tensors with shape broadcastable to q.batch_shape. For example, log_f works "just like" sampling_dist_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" 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
Logarithm of the importance sampling estimate. Tensor with shape equal to batch shape of q, and dtype = q.dtype.

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Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/versions/r1.15/api_docs/python/tf/contrib/bayesflow/monte_carlo/expectation_importance_sampler_logspace