Revisiting Unbiased Implicit Variational Inference

TL;DR

This paper revisits unbiased implicit variational inference (UIVI), demonstrating that its MCMC loop can be replaced with importance sampling and learned via KL divergence minimization, leading to improved or comparable performance on benchmarks.

Contribution

The authors show that UIVI's MCMC loop can be replaced with importance sampling and the proposal distribution can be learned through KL divergence minimization, enhancing efficiency and stability.

Findings

UIVI's MCMC loop can be replaced with importance sampling.

The proposal distribution can be learned via KL divergence minimization.

The refined UIVI achieves superior or comparable results on benchmarks.

Abstract

Recent years have witnessed growing interest in semi-implicit variational inference (SIVI) methods due to their ability to rapidly generate samples from complex distributions. However, since the likelihood of these samples is non-trivial to estimate in high dimensions, current research focuses on finding effective SIVI training routines. Although unbiased implicit variational inference (UIVI) has largely been dismissed as imprecise and computationally prohibitive because of its inner MCMC loop, we revisit this method and show that UIVI's MCMC loop can be effectively replaced via importance sampling and the optimal proposal distribution can be learned stably by minimizing an expected forward Kullback-Leibler divergence without bias. Our refined approach demonstrates superior performance or parity with state-of-the-art methods on established SIVI benchmarks.