An adaptive simulated annealing EM algorithm for inference on non-homogeneous hidden Markov models

TL;DR

This paper introduces an adaptive simulated annealing EM algorithm designed to efficiently perform model selection and parameter estimation in non-homogeneous hidden Markov models, which involve complex covariate-dependent structures.

Contribution

It proposes a novel ASA-EM algorithm that jointly optimizes model structure and parameters for NHHMMs, addressing the combinatorial complexity of covariate influence.

Findings

Demonstrates effective model selection in NHHMMs

Improves parameter estimation accuracy

Reduces computational complexity for large covariate sets

Abstract

Non-homogeneous hidden Markov models (NHHMM) are a subclass of dependent mixture models used for semi-supervised learning, where both transition probabilities between the latent states and mean parameter of the probability distribution of the responses (for a given state) depend on the set of $p$ covariates. A priori we do not know which (and how) covariates influence the transition probabilities and the mean parameters. This induces a complex combinatorial optimization problem for model selection with $4^p$ potential configurations. To address the problem, in this article we propose an adaptive (A) simulated annealing (SA) expectation maximization (EM) algorithm (ASA-EM) for joint optimization of models and their parameters with respect to a criterion of interest.