On Maximum A Posteriori Approximation of Hidden Markov Models for Proportional Data

Hidden Markov models (HMM) have recently risen as a key generative machine learning approach for time series data study and analysis. While early works focused only on applying HMMs for speech recognition, HMMs are now prominent in various fields such as video classification and genomics. In this paper, we develop a Maximum A Posteriori framework for learning the Generalized Dirichlet HMMs that have been proposed recently as an efficient way for modeling sequential proportional data. In contrast to the conventional Baum Welch algorithm, commonly used for learning HMMs, the proposed algorithm places priors for the learning of the desired parameters; hence, regularizing the estimation process. We validate our proposed approach on a challenging video processing application; namely, dynamic texture classification.