On adaptive resampling strategies for sequential Monte Carlo methods

TL;DR

This paper analyzes the convergence of adaptive resampling strategies in sequential Monte Carlo methods, providing theoretical guarantees for algorithms that determine resampling times based on online criteria like effective sample size.

Contribution

It introduces a novel convergence analysis using semigroup techniques and coupling arguments for adaptive resampling in SMC methods, filling a gap in theoretical understanding.

Findings

Established functional central limit theorems for adaptive SMC algorithms.

Derived uniform exponential concentration estimates for resampling times.

Provided rigorous convergence guarantees for practical adaptive resampling strategies.

Abstract

Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed online using criteria such as the effective sample size. This is a popular approach amongst practitioners but there are very few convergence results available for these methods. By combining semigroup techniques with an original coupling argument, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms.