Learning Hidden Markov Models from Aggregate Observations

TL;DR

This paper introduces a new algorithm for estimating hidden Markov model parameters from aggregate population data, leveraging expectation-maximization and Sinkhorn belief propagation, with proven convergence and extensions to continuous observations.

Contribution

The paper presents a novel aggregate inference-based algorithm for HMM parameter estimation with convergence guarantees, extending standard methods to aggregate and continuous data.

Findings

Algorithm outperforms existing methods in convergence and accuracy.

Successfully applied to diverse datasets demonstrating effectiveness.

Extends to HMMs with continuous observations.

Abstract

In this paper, we propose an algorithm for estimating the parameters of a time-homogeneous hidden Markov model from aggregate observations. This problem arises when only the population level counts of the number of individuals at each time step are available, from which one seeks to learn the individual hidden Markov model. Our algorithm is built upon expectation-maximization and the recently proposed aggregate inference algorithm, the Sinkhorn belief propagation. As compared with existing methods such as expectation-maximization with non-linear belief propagation, our algorithm exhibits convergence guarantees. Moreover, our learning framework naturally reduces to the standard Baum-Welch learning algorithm when observations corresponding to a single individual are recorded. We further extend our learning algorithm to handle HMMs with continuous observations. The efficacy of our algorithm is demonstrated on a variety of datasets.