Finite Sample Complexity of Sequential Monte Carlo Estimators

TL;DR

This paper provides finite sample error bounds for sequential Monte Carlo methods, relating their performance to distribution properties and Markov kernel mixing, and compares their complexity to other Monte Carlo schemes.

Contribution

It introduces the first finite sample bounds for SMC estimators on static spaces, connecting performance to distribution properties and Markov kernel mixing.

Findings

Finite sample bounds for SMC on various distributions

Comparison of SMC complexity with MCMC

Applicability to Bayesian logistic regression

Abstract

We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions including finite spaces, product measures, and log-concave distributions including Bayesian logistic regression. The bounds obtained are within a logarithmic factor of similar bounds obtainable for Markov chain Monte Carlo.