Nested Sequential Monte Carlo Methods
Abstract
We propose nested sequential Monte Carlo (NSMC), a methodology to sample from sequences of probability distributions, even where the random variables are high-dimensional. NSMC generalises the SMC framework by requiring only approximate, properly weighted, samples from the SMC proposal distribution, while still resulting in a correct SMC algorithm. Furthermore, NSMC can in itself be used to produce such properly weighted samples. Consequently, one NSMC sampler can be used to construct an efficient high-dimensional proposal distribution for another NSMC sampler, and this nesting of the algorithm can be done to an arbitrary degree. This allows us to consider complex and high-dimensional models using SMC. We show results that motivate the efficacy of our approach on several filtering problems with dimensions in the order of 100 to 1 000.
Cite
@article{arxiv.1502.02536,
title = {Nested Sequential Monte Carlo Methods},
author = {Christian A. Naesseth and Fredrik Lindsten and Thomas B. Schön},
journal= {arXiv preprint arXiv:1502.02536},
year = {2015}
}
Comments
Extended version of paper published in Proceedings of the 32nd International Conference on Machine Learning (ICML), Lille, France, 2015