Theory of Parallel Particle Filters for Hidden Markov Models

TL;DR

This paper introduces a parallel particle filtering method for hidden Markov models that segments the latent state sequence, enabling parallel processing, reducing variance, and decreasing computational time.

Contribution

It develops a novel segmented particle filtering algorithm that improves variance properties and computational efficiency for HMMs through parallelization.

Findings

Segmentation reduces variance in latent-state estimators.

Parallelization decreases wall-clock computational time.

Likelihood estimator remains unbiased with proven CLT convergence.

Abstract

The objective of this article is to study the asymptotic behavior of a new particle filtering approach in the context of hidden Markov models (HMMs). In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing. Based upon this approach, we introduce new estimators of the latent states and likelihood which have similar or better variance properties compared to estimators derived from standard particle filters. Moreover due to parallelization there is less wall-clock computational time. We show that the likelihood function estimator is unbiased, prove central limit theorem convergences of estimators, and provide consistent in-sample estimation of the asymptotic variances. The theoretical analyses, supported by a numerical study, show that the segmentation reduces the variances in smoothed latent-state estimators, in addition to the savings in wall-clock time.