EM Algorithm for Training High-order Hidden Markov Model with Multiple Observation Sequences

摘要

High-order hidden Markov model is known to be more powerful than first-order hidden Markov model and has been applied to a variety of fields. How to better train high-order hidden Markov model is a question of common interest. The EM algorithm together with its derivatives and variations has been the main technique for training hidden Markov model from observational data. We develop a EM algorithm for training any high-order hidden Markov model with multiple observation sequences. In our work, all observation sequences are assumed to be statistically correlated, and the dependence-independence property of them is characterized by combinatorial weights. Furthermore, we show respectively that Li's training equations and Hadar's training equations can be easily derived as two special cases of our conclusion.