Variance Reduction of Resampling for Sequential Monte Carlo

TL;DR

This paper introduces a new resampling method for sequential Monte Carlo that reduces variance, improves efficiency, and enhances accuracy in approximating hidden Markov models, especially in nonlinear scenarios.

Contribution

It proposes a deterministic resampling scheme with median ergodicity that achieves lower variance and faster performance than existing methods.

Findings

Achieves the lowest variance compared to other resampling methods.

Faster than state-of-the-art algorithms for given particle sizes.

Validated through theoretical analysis and experiments on linear and nonlinear hidden Markov models.

Abstract

A resampling scheme provides a way to switch low-weight particles for sequential Monte Carlo with higher-weight particles representing the objective distribution. The less the variance of the weight distribution is, the more concentrated the effective particles are, and the quicker and more accurate it is to approximate the hidden Markov model, especially for the nonlinear case. We propose a repetitive deterministic domain with median ergodicity for resampling and have achieved the lowest variances compared to the other resampling methods. As the size of the deterministic domain $M\ll N$ (the size of population), given a feasible size of particles, our algorithm is faster than the state of the art, which is verified by theoretical deduction and experiments of a hidden Markov model in both the linear and non-linear cases.