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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 fromsampling_dist_q
toTensors
with shape broadcastable toq.batch_shape
. For example,f
works "just like"q.log_prob
.log_p
: Callable mapping samples fromsampling_dist_q
toTensors
with shape broadcastable toq.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
andq
should be supported on the same set.z
:Tensor
of samples fromq
, produced byq.sample
for somen
.n
: IntegerTensor
. Number of samples to generate ifz
is not provided.seed
: Python integer to seed the random number generator.name
: A name to give thisOp
.
Returns:
The importance sampling estimate. Tensor
with shape
equal
to batch shape of q
, and dtype
= q.dtype
.