Matti Vihola: On the forgetting of particle filters

Abstract

We discuss the forgetting properties of the particle filter (a sequential Monte Carlo algorithm) when its state — the collection of particles — is regarded as a Markov chain. Under a strong mixing assumption on the particle filter's underlying Feynman–Kac model, we find that the particle filter forgets its state (in total variation sense) in O(log N) time, where N is the number of particles and time refers to the number of particle filter algorithm steps, each comprising a selection (or resampling) and mutation (or prediction) operation. An example shows that the rate is optimal. We discuss implications of our findings e.g. to coupling particle filters and mixing time of a conditional backward sampling particle filter.

The talk is based on two joint works with Joona Karjalainen, Sumeetpal S. Singh and Anthony Lee:
https://arxiv.org/abs/2309.08517
https://arxiv.org/abs/2312.17572