Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition
<|reference_start|>Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition: We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics. SMC is a Markov Chain Monte Carlo (MCMC) method, which starts by drawing $N$ particles from a known distribution, and then, through a sequence of distributions, re-weights and re-samples the particles, at each instance applying a Markov chain for smoothing. In principle, SMC tries to alleviate problems from multi-modality. However, most theoretical guarantees for SMC are obtained by assuming global mixing time bounds, which are only efficient in the uni-modal setting. We show that bounds can be obtained in the truly multi-modal setting, with mixing times that depend only on local MCMC dynamics.<|reference_end|>
@article{lee2024convergence,
    title={Convergence Bounds for Sequential Monte Carlo on Multimodal
  Distributions using Soft Decomposition},
    author={Holden Lee and Matheau Santana-Gijzen},
    journal={arXiv preprint arXiv:2405.19553},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.19553},
    primaryClass={math.ST cs.LG math.PR stat.ML stat.TH}
}