Source code for pyro.infer.reparam.conjugate

# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0

import pyro
import pyro.distributions as dist

from .reparam import Reparam

[docs]class ConjugateReparam(Reparam): """ EXPERIMENTAL Reparameterize to a conjugate updated distribution. This updates a prior distribution ``fn`` using the :meth:`~pyro.distributions.Distribution.conjugate_update` method. The guide may be either a distribution object or a callable inputting model ``*args,**kwargs`` and returning a distribution object. The guide may be approximate or learned. For example consider the model and naive variational guide:: total = torch.tensor(10.) count = torch.tensor(2.) def model(): prob = pyro.sample("prob", dist.Beta(0.5, 1.5)) pyro.sample("count", dist.Binomial(total, prob), obs=count) guide = AutoDiagonalNormal(model) # learns the posterior over prob Instead of using this learned guide, we can hand-compute the conjugate posterior distribution over "prob", and then use a simpler guide during inference, in this case an empty guide:: reparam_model = poutine.reparam(model, { "prob": ConjugateReparam(dist.Beta(1 + count, 1 + total - count)) }) def reparam_guide(): pass # nothing remains to be modeled! :param guide: A likelihood distribution or a callable returning a guide distribution. Only a few distributions are supported, depending on the prior distribution's :meth:`~pyro.distributions.Distribution.conjugate_update` implementation. :type guide: ~pyro.distributions.Distribution or callable """ def __init__(self, guide): = guide
[docs] def __call__(self, name, fn, obs): assert obs is None, "PosteriorReparam does not support observe statements" # Compute a guide distribution, either static or dependent. guide_dist = if not isinstance(guide_dist, dist.Distribution): args, kwargs = self.args_kwargs guide_dist = guide_dist(*args, **kwargs) assert isinstance(guide_dist, dist.Distribution) # Draw a sample from the updated distribution. fn, log_normalizer = fn.conjugate_update(guide_dist) assert isinstance(guide_dist, dist.Distribution) if not fn.has_rsample: # Note supporting non-reparameterized sites would require more delicate # handling of traced sites than the crude _do_not_trace flag below. raise NotImplementedError("ConjugateReparam inference supports only reparameterized " "distributions, but got {}".format(type(fn))) value = pyro.sample("{}_updated".format(name), fn, infer={"is_auxiliary": True, "_do_not_trace": True}) # Compute importance weight. Let p(z) be the original fn, q(z|x) be # the guide, and u(z) be the conjugate_updated distribution. Then # normalizer = p(z) q(z|x) / u(z). # Since we've sampled from u(z) instead of p(z), we # need an importance weight # p(z) / u(z) = normalizer / q(z|x) (Eqn 1) # Note that q(z|x) is often approximate; in the exact case # q(z|x) = p(x|z) / integral p(x|z) dz # so this site and the downstream likelihood site will have combined density # (p(z) / u(z)) p(x|z) = (normalizer / q(z|x)) p(x|z) # = normalizer integral p(x|z) dz # Hence in the exact case, downstream probability does not depend on the sampled z, # permitting this reparameterizer to be used in HMC. log_density = log_normalizer - guide_dist.log_prob(value) # By Eqn 1. # Return an importance-weighted point estimate. new_fn = dist.Delta(value, log_density=log_density, event_dim=fn.event_dim) return new_fn, value