Seminar Details
2020-10-06 (14:00) : Scaling Monte Carlo inference for State-Space Models
At MS Teams
Organized by Mathematical Engineering
Speaker :
Alexander Shestopaloff (School of Mathematical Sciences, Queen Mary University of London, UK )
Abstract :
The iterated conditional Sequential Monte Carlo (cSMC) method is a particle MCMC method commonly used for state inference in non-linear, non-Gaussian state space models. Standard implementations of iterated cSMC provide an efficient way to sample state sequences in low-dimensional state space models. However, efficiently scaling iterated cSMC methods to perform well in models with a high-dimensional state remains a challenge. One reason for this is the use of a global proposal, without reference to the current state sequence. In high dimensions, such a proposal will typically not be well-matched to the posterior and impede efficient sampling. I will describe a technique based on the embedded HMM (Hidden Markov Model) framework to construct efficient proposals in high dimensions that are local relative to the current state sequence. A second obstacle to scalability of iterated cSMC is not using the entire observed sequence to construct the proposal. Typical implementations of iterated cSMC use a proposal at time t that relies only on data up to time t, even when data after time t is available. In high dimensions and in the presence of informative data, such proposals can become inefficient and slow down sampling. I will introduce a principled approach to incorporating all data in the cSMC proposal at time t. By considering several examples, I will demonstrate that both strategies improve the performance of iterated cSMC for state sequence sampling in high-dimensional state space models.