A Multinomial Hidden Markov Model and its training by a combined iterative procedure

Article type: Research Article

Authors: Cidota, Marina A.^; | Dumitrescu, Monica

Affiliations: Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania. E-mails: {cidota, mdumi}@fmi.unibuc.ro

Note: [] Corresponding author: Marina A. Cidota, University of Bucharest, Faculty of Mathematics and Computer Science, Str. Academiei No.14, Bucharest, 010014, Romania.

Abstract: The paper proposes a new extension of Hidden Markov Models (HMM) for communication systems by allowing the Markovian transitions between the channel's states to be influenced by some external “catalyzers” (e.g. environmental or experimental conditions). The stochastic influence of the catalyzers is expressed by multinomial link functions. We introduce a combined iterative training procedure, with the Baum–Welch algorithm as a framework, including some nested algorithms such as the Newton–Raphson and the Expectation–Maximization (EM) algorithms. The monotony of the log-likelihood function associated with our procedure is proven. A simulation study is provided in order to prove the good performances of the proposed combined iterative training procedure. We consider that the Multinomial HMM will be an important and useful extension of HMM in bioinformatics and biostatistics, due to the possible applications in modeling the “hidden” ion channels whose states could be influenced by external factors.

Keywords: Communication channel, Hidden Markov Model, multinomial response model, nested optimization algorithms

DOI: 10.3233/AIC-130589

Journal: AI Communications, vol. 27, no. 2, pp. 143-155, 2014