Strategies for scaling iterated conditional Sequential Monte Carlo methods for high dimensional state space models
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 the MCMC run. 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 that relies only on data up to time t. In high dimensions and in the presence of informative data, such proposals become inefficient, and can considerably slow down sampling. I will introduce a principled approach to incorporating future observations in the cSMC proposal at time t. By considering several examples, I will demonstrate that both strategies improve the performance of iterated cSMC for sequence sampling in high-dimensional state space models.
