Sparseness Achievement in Hidden Markov Models

In this paper, a novel learning algorithm for Hidden Markov Models (HMMs) has been devised. The key issue is the achievement of a sparse model, i.e., a model in which all irrelevant parameters are set exactly to zero. Alternatively to standard maximum likelihood estimation (Baum Welch training), in the proposed approach the parameters estimation problem is cast into a Bayesian framework, with the introduction of a negative Dirichlet prior, which strongly encourages sparseness of the model. A modified Expectation Maximization algorithm has been devised, able to determine a MAP (maximum a posteriori probability) estimate of HMM parameters in this Bayesian formulation. Theoretical considerations and experimental comparative evaluations on a 2D shape classification task contribute to validate the proposed technique.