Conditional Sequential Monte Carlo in High Dimensions

Organizer

Shing Toung Yau

Speaker

Zeju Sun

Time

Wednesday, September 11, 2024 3:00 PM - 3:30 PM

Venue

理科楼A-304

Abstract

In this talk, I will report a paper entitled ‘Conditional Sequential Monte Carlo in High Dimensions’ by A. Finke and A. H. Thiery. The abstract of this paper is as follows: “The iterated conditional sequential Monte Carlo (i-CSMC) algorithm is an MCMC approach for efficiently sampling from the joint posterior distribution of the T latent states in challenging time-series models, e.g. in non-linear or non-Gaussian state space models. It is also the main ingredient in particle Gibbs samplers which infer unknown model parameters alongside the latent states. In this work, we first prove that the i-CSMC algorithm suffers from a curse of dimension in the dimension of the states, D: it breaks down unless the number of samples (‘particles’), N, proposed by the algorithm grows exponentially with D. Then, we present a novel ‘local’ version of the algorithm which proposes particles using Gaussian random-walk moves that are suitably scaled with D. We prove that this iterated random-walk conditional sequential Monte Carlo (i-RW-CSMC) algorithm avoids the curse of dimension: for arbitrary N, its acceptance rates and expected squared jumping distance converge to non-trivial limits as D → ∞. If T = N = 1, our proposed algorithm reduces to a Metropolis–Hastings or Barker’s algorithm with Gaussian random-walk moves and we recover the well-known scaling limits for such algorithms.”