Representation of multinomial linear hidden Markov models in the form of algebraic Bayesian networks

Hidden Markov models (HMM) are widespread in simulating of various processes in such fields as bioinformatics, speech recognition and automated translation. Algebraic Bayesian network (ABN) is actively developing model with wide opportunities. Goal of this work is to represent a wider class of HMM as ABN than in the earlier researches. Algorithm for the representation is proposed and its correctness in sense that the probabilistic semantics of them are equal is proven.