Massively Parallel Reweighted Wake-Sleep
Thomas Heap Gavin Leech Laurence Aitchison
Reweighted wake-sleep (RWS) is a machine learning method for performing
Bayesian inference in a very general class of models. RWS draws $K$ samples
from an underlying approximate posterior, then uses importance weighting to
provide a better estimate of the true posterior. RWS then updates its
approximate posterior towards the importance-weighted estimate of the true
posterior. However, recent work [Chattergee and Diaconis, 2018] indicates that
the number of samples required for effective importance weighting is
exponential in the number of latent variables. Attaining such a large number of
importance samples is intractable in all but the smallest models. Here, we
develop massively parallel RWS, which circumvents this issue by drawing $K$
samples of all $n$ latent variables, and individually reasoning about all $K^n$
possible combinations of samples. While reasoning about $K^n$ combinations
might seem intractable, the required computations can be performed in
polynomial time by exploiting conditional independencies in the generative
model. We show considerable improvements over standard "global" RWS, which
draws $K$ samples from the full joint.