Resampling Strategy in Sequential Monte Carlo for Constrained Sampling Problems

TL;DR

This paper introduces a general framework for applying Sequential Monte Carlo methods to constrained sampling problems, utilizing forward and backward pilot resampling strategies to improve sampling efficiency in constrained high-dimensional spaces.

Contribution

The paper formulates a unified framework for constrained sampling with SMC, reviews existing methods, and develops new algorithms based on pilot resampling strategies.

Findings

Framework unifies constrained sampling approaches

New algorithms improve sampling efficiency

Applicable to various constrained high-dimensional problems

Abstract

Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different types of constraints. These constraints can make the problem much more challenging. In this paper, we formulate a general framework of using SMC for constrained sampling problems based on forward and backward pilot resampling strategies. We review some existing methods under the framework and develop several new algorithms. It is noted that all information observed or imposed on the underlying system can be viewed as constraints. Hence the approach outlined in this paper can be useful in many applications.