Maximum A Posteriori Approximation of Dirichlet and Beta-Liouville Hidden Markov Models for Proportional Sequential Data Modeling

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 stock market forecasting, video classification, and genomics. In this paper, we develop a Maximum A Posteriori (MAP) framework for learning the Dirichlet and Beta-Liouville 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 two challenging real applications; namely, dynamic texture classification and infrared action recognition.