Variational inference for Monte Carlo objectives

TL;DR

This paper introduces a new unbiased gradient estimator for variational inference with Monte Carlo objectives, extending multi-sample methods to discrete variables and improving training of deep generative models.

Contribution

It develops the first unbiased gradient estimator for importance-sampled variational objectives, enhancing training efficiency for models with discrete latent variables.

Findings

The estimator is simpler and more effective than previous methods.

It achieves higher likelihoods in deep generative models.

The approach is competitive with biased estimators.

Abstract

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood, using samples from the variational posterior to compute the required gradients. Recently, Burda et al. (2016) have derived a tighter lower bound using a multi-sample importance sampling estimate of the likelihood and showed that optimizing it yields models that use more of their capacity and achieve higher likelihoods. This development showed the importance of such multi-sample objectives and explained the success of several related approaches. We extend the multi-sample approach to discrete latent variables and analyze the difficulty encountered when estimating the gradients involved. We then develop the first unbiased gradient estimator designed for importance-sampled objectives and evaluate it at training generative and structured output prediction models. The resulting estimator, which is based on low-variance per-sample learning signals, is both simpler and more effective than the NVIL estimator proposed for the single-sample variational objective, and is competitive with the currently used biased estimators.