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

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 BaumWelch algorithm as a framework, including some nested algorithms such as the NewtonRaphson and the ExpectationMaximization (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.