Statistical Distance Based Deterministic Offspring Selection in SMC Methods

TL;DR

This paper introduces two deterministic offspring selection methods for sequential Monte Carlo that minimize statistical distances, leading to improved performance over traditional resampling schemes in benchmark models.

Contribution

It proposes novel deterministic offspring selection techniques based on minimizing KL divergence and TV distance, enhancing SMC performance.

Findings

Outperforms traditional resampling methods in benchmark tests

Consistently better or comparable results in SMC and pMCMC applications

Reduces statistical distance between particle distributions

Abstract

Over the years, sequential Monte Carlo (SMC) and, equivalently, particle filter (PF) theory has gained substantial attention from researchers. However, the performance of the resampling methodology, also known as offspring selection, has not advanced recently. We propose two deterministic offspring selection methods, which strive to minimize the Kullback-Leibler (KL) divergence and the total variation (TV) distance, respectively, between the particle distribution prior and subsequent to the offspring selection. By reducing the statistical distance between the selected offspring and the joint distribution, we obtain a heuristic search procedure that performs superior to a maximum likelihood search in precisely those contexts where the latter performs better than an SMC. For SMC and particle Markov chain Monte Carlo (pMCMC), our proposed offspring selection methods always outperform or compare favorably with the two state-of-the-art resampling schemes on two models commonly used as benchmarks from the literature.