  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.
