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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 .
|