The Convergence Of Two Problem And The Application Of Maximum Model Distance Algorithm In HMM

This paper discussed the parameters estimation of hidden Markov models. At first, we researched the confederated process of the two processes of hidden Markov model, we know the confederated process is a Markov processes from the relationship of the two random processes of HMM. Then we introduced transition probability kernel for the hidden state process and the confederated process. In the deep research, we found that some similar parameters of state transition probability, observation symbol probability and initial state probability were involved in the transition probability kernel of the confederated process. So we can complete the training of traditional HMM parameters by training the transition probability kernel of the confederated process. To our surprised, we got the consistency of transition probability kernel of the confederated process. Meanwhile, we proved the rationality and reliability of the parameters estimation equations under the classical B-W algorithm. Then, we expanded our research to multiplier observations, and obtained the similar estimation equations and proved the convergence as under singer observation. Furthermore, paper discussed prediction filter's exponential forgetting about the initial probability distribution of HMMs too, which is helpful on our estimation, because based on the exponential forgetting only the state transition probability distribution and the observation symbol probability distribution are need to be estimated. At last, paper introduced an efficient algorithm on HMMs training. It is maximum model distance(MMD) algorithm which reduced the error ratio in automatic recognition and overcomed some of shortcoming of the traditional maximum likelihood estimation. Under the new algorithm, we also got the estimation equations, specially, we gave the simple matrix form of the parameters estimation.