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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

displaymath2798

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,

  equation357

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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