Variational Rejection Particle Filtering

TL;DR

This paper introduces Variational Rejection Particle Filtering (VRPF), a novel VI framework combining particle filtering with rejection sampling and resampling techniques to improve inference in sequential models.

Contribution

The paper proposes VRPF, a new variational inference method that unifies particle filtering and rejection sampling, providing tighter bounds and better performance for sequential data models.

Findings

VRPF outperforms existing VI methods on sequential models.

The framework provides new variational bounds on marginal likelihood.

Theoretical analysis supports the effectiveness of VRPF.

Abstract

We present a variational inference (VI) framework that unifies and leverages sequential Monte-Carlo (particle filtering) with \emph{approximate} rejection sampling to construct a flexible family of variational distributions. Furthermore, we augment this approach with a resampling step via Bernoulli race, a generalization of a Bernoulli factory, to obtain a low-variance estimator of the marginal likelihood. Our framework, Variational Rejection Particle Filtering (VRPF), leads to novel variational bounds on the marginal likelihood, which can be optimized efficiently with respect to the variational parameters and generalizes several existing approaches in the VI literature. We also present theoretical properties of the variational bound and demonstrate experiments on various models of sequential data, such as the Gaussian state-space model and variational recurrent neural net (VRNN), on which VRPF outperforms various existing state-of-the-art VI methods.