Abstract
Training deep generative models with maximum likelihood remains a challenge.
The typical workaround is to use variational inference (VI) and maximize a
lower bound to the log marginal likelihood of the data. Variational
auto-encoders (VAEs) adopt this approach. They further amortize the cost of
inference by using a recognition network to parameterize the variational
family. Amortized VI scales approximate posterior inference in deep generative
models to large datasets. However it introduces an amortization gap and leads
to approximate posteriors of reduced expressivity due to the problem known as
posterior collapse. In this paper, we consider expectation maximization (EM) as
a paradigm for fitting deep generative models. Unlike VI, EM directly maximizes
the log marginal likelihood of the data. We rediscover the importance weighted
auto-encoder (IWAE) as an instance of EM and propose a new EM-based algorithm
for fitting deep generative models called reweighted expectation maximization
(REM). REM learns better generative models than the IWAE by decoupling the
learning dynamics of the generative model and the recognition network using a
separate expressive proposal found by moment matching. We compared REM to the
VAE and the IWAE on several density estimation benchmarks and found it leads to
significantly better performance as measured by log-likelihood.
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