High-dimensional Filtering using Nested Sequential Monte Carlo

TL;DR

This paper introduces nested sequential Monte Carlo (NSMC), a novel method that enhances high-dimensional Bayesian filtering by enabling efficient and accurate inference with approximate proposals.

Contribution

The paper presents NSMC, a generalization of SMC that allows using approximate proposals while maintaining correctness, improving inference in high-dimensional models.

Findings

NSMC outperforms existing methods on spatio-temporal models.

It enables exact approximation of the locally optimal proposal.

The approach extends the applicability of SMC to more complex models.

Abstract

Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo (NSMC), a methodology that generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. This way we can exactly approximate the locally optimal proposal, and extend the class of models for which we can perform efficient inference using SMC. We show improved accuracy over other state-of-the-art methods on several spatio-temporal state space models.