Finite Sample Complexity of Sequential Monte Carlo Estimators on Multimodal Target Distributions

• URL: http://arxiv.org/abs/2208.06672v1
• Date: Sat, 13 Aug 2022 15:06:03 GMT
• Title: Finite Sample Complexity of Sequential Monte Carlo Estimators on Multimodal Target Distributions
• Authors: Joseph Mathews and Scott C. Schmidler
• Abstract summary: We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated kernels. Our bounds are particularly useful when the target distribution is multimodal and global mixing of the kernel is slow.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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