Iterated sampling importance resampling with adaptive number of proposals

TL;DR

This paper introduces an adaptive i-SIR algorithm that automatically optimizes the number of proposals for improved efficiency, supported by theoretical insights and empirical validation.

Contribution

It proposes a novel method for adaptively tuning the number of proposals in i-SIR based on asymptotic variance analysis, enhancing efficiency.

Findings

The adaptive i-SIR algorithm effectively tunes proposals during sampling.

The asymptotic variance is convex in the number of proposals.

The method improves sampling efficiency with promising empirical results.

Abstract

Iterated sampling importance resampling (i-SIR) is a Markov chain Monte Carlo (MCMC) algorithm which is based on $N$ independent proposals. As $N$ grows, its samples become nearly independent, but with an increased computational cost. We discuss a method which finds an approximately optimal number of proposals $N$ in terms of the asymptotic efficiency. The optimal $N$ depends on both the mixing properties of the i-SIR chain and the (parallel) computing costs. Our method for finding an appropriate $N$ is based on an approximate asymptotic variance of the i-SIR, which has similar properties as the i-SIR asymptotic variance, and a generalised i-SIR transition having fractional `number of proposals.' These lead to an adaptive i-SIR algorithm, which tunes the number of proposals automatically during sampling. Our experiments demonstrate that our approximate efficiency and the adaptive i-SIR algorithm have promising empirical behaviour. We also present new theoretical results regarding the i-SIR, such as the convexity of asymptotic variance in the number of proposals, which can be of independent interest.