# 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'
)


See the guide: BayesFlow Monte Carlo (contrib) > Ops

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.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.