Nested Variational Inference

TL;DR

Nested variational inference (NVI) introduces a flexible framework for learning proposals in nested importance sampling, improving sample quality across various applications by optimizing nested KL divergences.

Contribution

NVI develops a family of methods for learning proposals in nested importance samplers through KL divergence minimization at each nesting level, applicable to multiple importance sampling strategies.

Findings

Enhanced sample quality with optimized nested objectives

Effective learning of intermediate densities as heuristics

Improved performance in multimodal sampling and hierarchical models

Abstract

We develop nested variational inference (NVI), a family of methods that learn proposals for nested importance samplers by minimizing an forward or reverse KL divergence at each level of nesting. NVI is applicable to many commonly-used importance sampling strategies and provides a mechanism for learning intermediate densities, which can serve as heuristics to guide the sampler. Our experiments apply NVI to (a) sample from a multimodal distribution using a learned annealing path (b) learn heuristics that approximate the likelihood of future observations in a hidden Markov model and (c) to perform amortized inference in hierarchical deep generative models. We observe that optimizing nested objectives leads to improved sample quality in terms of log average weight and effective sample size.