Hidden Markov model estimation based on alpha-EM algorithm: Discrete and continuous alpha-HMMs

Fast estimation algorithms for Hidden Markov models (HMMs) for given data are presented. These algorithms start from the alpha-EM algorithm which includes the traditional log-EM as its proper subset. Since existing or traditional HMMs are the outcome of the log-EM, it had been expected that the alpha-HMM would exist. In this paper, it is shown that this foresight is true by using methods of the iteration index shift and likelihood ratio expansion. In each iteration, new update equations utilize one-step past terms which are computed and stored during the previous maximization step. Therefore, iteration speedup directly appears as that of CPU time. Since the new method is theoretically based on the alpha-EM, all of its properties are inherited. There are eight types of alpha-HMMs derived. They are discrete, continuous, semi-continuous and discrete-continuous alpha-HMMs, and both for single and multiple sequences. Using the properties of the alpha-EM algorithm, the speedup property is theoretically analyzed. Experimental results including real world data are given.