Hidden Markov Models and their Extensions for Proportional Sequential Data

We are facing an all-time high in the worldwide generation of data. Machine learning techniques have proven successful in unveiling patterns within data to further human knowledge. This includes building systems with overall better prediction and accuracy levels. Nonetheless, many areas have yet to be studied which warrants further exploitation of these techniques. Hence, data modeling is one of the topics at the forefront of scientific research. A particularly interesting field of research is the appropriate choice of distribution that corresponds to the nature of the data. In this thesis, we focus on tackling challenges in the approximation of proportional Hidden Markov Models (HMM). We review the main concepts behind HMM; one of the cornerstone probabilistic graphical models for time series or sequential data. We also discuss various modern challenges that exist when training or using HMMs. Nonetheless, we primarily focus on the notorious model estimation process of HMMs as well as the appropriate choice of emission distribution based on the nature of the data. We have tackled these problems using variational inference and Maximum A Posteriori (MAP) approximation with the Dirichlet, the Generalized Dirichlet, and the Beta-Liouville (BL) distributions-based HMMs for proportional data. In this thesis, we develop frameworks for learning these proportional 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 algorithms place priors for the learning of the desired parameters; hence, regularizing the estimation process. We also extend these models into infinity for a data-driven dynamically chosen structure of HMMs. Such a setup enables flexibility in the model structure with a lower computational cost for model selection. We also investigate the fusion of the trained classifiers and witness a consequent improved performance. Moreover, we incorporate a simultaneous feature selection paradigm as well as investigate online deployment. We present our recently proposed methodologies that address the aforementioned problems and discuss the achieved results across a variety of computer vision applications. We also present how a simple novel experimental setup can drastically improve the performance of HMMs in occupancy detection, and estimation by extension, in a smart building for an applied research contribution. Finally, we conclude and recommend potential future work