Extended Hidden Markov Models And Bayesian Network

The Hidden Markov Models which consist of a hidden Markov process and an observation process are statistical models, and the short form is HMM. They were brought forward by Baum and his colleagues in the late sixties and early seventies. In 1970s, they were applied into speech recognition by Jenik and some other people. They have been developed to be one of the most efficient techniques. Now, they have been widely used in biostatistics, gene recognition, character recognition and image processing etc. Bayesian Network was developed in the late eighties , which was brought by Judea Pearl and his colleagues in 1986. It has been mainly applied to uncertain information of artificial intelligence at first. Gradually it has been developed to be the basic techniques of uncertain information, and it has been widely used in the intelligence system of industry control, medical diagnose etc.In this article, we started with extension of HMM. Firstly, we proposed a new generalized Markov model GHMM and we studied three basic problems of the GHMM. Several new analytic formulae which are similar to forward—backward algorithm,Viterbi algorithm and studying algorithm of HMM for solving three basic problems were theoretically derived and further demonstrated by computer simulation. Considering the best de-noising function, we introduced the wavelet into HMM and introduced wavelet transformation for non-parametric estimation of HMM. Then we discussed 2D-HMM by considering the dimensional extension of HMM. Combined with fuzzy clustering Fuzzy-2D-HMMS algorithm was proposed and convergence of the algorithm was analysed through solving the three basic problems of 2-D HMM. We proposed the continuous 2-D HMM and simply inferred the three basic problems of continuous 2-D HMM . Finally, we studied Bayesian Network by considering a more general HMM. The relation between HMM and DBN had been summarized. Then we solved the reasoning problem of several kinds of separated DBN.