View source on GitHub |
Monte Carlo estimate of \(E_p[f(Z)] = E_q[f(Z) p(Z) / q(Z)]\).
tf.contrib.bayesflow.monte_carlo.expectation_importance_sampler(
f, log_p, sampling_dist_q, z=None, n=None, seed=None,
name='expectation_importance_sampler'
)
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 .
|