tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler_logspace

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

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'
)

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.