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Maximum Likelihood (ML) criterion

In ML we try to maximize the probability of a given sequence of observations tex2html_wrap_inline2788 , belonging to a given class w, given the HMM tex2html_wrap_inline2792 of the class w, wrt the parameters of the model tex2html_wrap_inline2792 . This probability is the total likelihood of the observations and can be expressed mathematically as


However since we consider only one class w at a time we can drop the subscript and superscript 'w's. Then the ML criterion can be given as,


However there is no known way to analytically solve for the model tex2html_wrap_inline2698 , which maximize the quantity tex2html_wrap_inline2808 . But we can choose model parameters such that it is locally maximized, using an iterative procedure, like Baum-Welch method or a gradient based method, which are described below.

Narada Warakagoda
Fri May 10 20:35:10 MET DST 1996

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