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

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 the mean parameter of the probability distribution of the responses (for a given state) depend on the set of up to 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 4p 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.