A multinomial - Hidden Markov model for communication systems influenced by external factors

The paper proposes an extension of Hidden Markov models for communication systems that are influenced by external "catalyzers" (e.g. environmental or experimental conditions). A simpler version of the model, the Logistic HMM (LHMM), was already introduced by the authors. In comparison with LHMM, this new extension of HMM allows the catalyzer to have multiple components, expressing the influence over the system through multinomial link functions. A possible application of the Multinomial Hidden Markov model (MHMM) could be in bio-informatics for example, to predict under different external conditions (different quantities of calcium channel blockers CCB and some antioxidants AO) the behavior of the calcium channel that holds an essential part in controlling the blood pressure. We introduce a training algorithm for MHMM based on the BaumWelch scheme, including nested algorithms for optimization such as the Newton - Raphson and the Expectation-Maximization technique for updating the parameters of the model. In order to explore the convergence of the proposed training procedure, a simulation study is provided.