View source on GitHub
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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
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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.
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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.
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sampling_dist_q
|
The sampling distribution.
tfp.distributions.Distribution.
float64 dtype recommended.
log_p and q should be supported on the same set.
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z
|
Tensor of samples from q, produced by q.sample for some n.
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n
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Integer Tensor. Number of samples to generate if z is not provided.
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seed
|
Python integer to seed the random number generator. |
name
|
A name to give this Op.
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Returns | |
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Logarithm of the importance sampling estimate. Tensor with shape equal
to batch shape of q, and dtype = q.dtype.
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