Inference of collective Gaussian hidden Markov models

TL;DR

This paper introduces a collective Gaussian forward-backward algorithm for inference in continuous state collective hidden Markov models, extending Sinkhorn belief propagation with convergence guarantees and applicability to large populations.

Contribution

It presents a novel aggregate inference algorithm for collective HMMs with Gaussian densities, extending Sinkhorn belief propagation and ensuring convergence.

Findings

Algorithm demonstrates effective inference in experiments.

Reduces to Kalman filter for single individual observations.

Convergence is theoretically guaranteed.

Abstract

We consider inference problems for a class of continuous state collective hidden Markov models, where the data is recorded in aggregate (collective) form generated by a large population of individuals following the same dynamics. We propose an aggregate inference algorithm called collective Gaussian forward-backward algorithm, extending recently proposed Sinkhorn belief propagation algorithm to models characterized by Gaussian densities. Our algorithm enjoys convergence guarantee. In addition, it reduces to the standard Kalman filter when the observations are generated by a single individual. The efficacy of the proposed algorithm is demonstrated through multiple experiments.