FINITE SAMPLE COMPLEXITY OF SEQUENTIAL MONTE CARLO ESTIMATORS ON MULTIMODAL TARGET DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Mathews, Joseph; Schmidler, Scott C.
• 署名单位: Duke University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1989
• 发表日期: 2024
• 页码: 1199-1223
• 关键词: logconcave functions; error-bounds; parallel; CONVERGENCE

摘要

We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global mixing of the Markov kernel is slow; in such cases our approach establishes the benefits of SMC over the corresponding Markov chain Monte Carlo (MCMC) estimator. The lack of global mixing is addressed by sequentially controlling the bias introduced by SMC resampling procedures. We apply these results to obtain complexity bounds for approximating expectations under mixtures of log-concave distributions and show that SMC provides a fully polynomial time randomized approximation scheme for some difficult multimodal problems where the corresponding Markov chain sampler is exponentially slow. Finally, we compare the bounds obtained by our approach to existing bounds for tempered Markov chains on the same problems.