tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler_logspace()

tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler_logspace(log_f, log_p, sampling_dist_q, z=None, n=None, seed=None, name='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. tf.contrib.distributions.BaseDistribution. float64 dtype recommended. log_p and q should be supported on the same set.
• z: Tensor of samples from q, produced by q.sample_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.