Convergence Bounds for Sequential Monte Carlo on Multimodal Distributions using Soft Decomposition

ArXi:2405.19553v2 Announce Type: replace-cross 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 Marko chain mixing dynamics. SMC is a Marko 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 Marko chain for smoothing.