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Unformatted text preview: The EM Algorithm • The EM algorithm is used in the case of estimating model parameters Θ from incomplete data. It is an optimal ML (maximum likelihood) estimation method with goal max log ( ) L P X Θ = Θ (1) where 1 2 N X x x x = L is the observed data sequence. • The observed data are generally assumed to be independent, i.e., ( ) ( ) n n P X P x Θ = Θ (2) n So, maxlog ( ) max log ( ) n P X P x Θ Θ Θ = Θ . (3) • Here, “incomplete data” means that some properties of the data are unknown or unobserved. For instances, the mixture component that a feature vector belongs, the HMM state it is staying, etc. • If the data is complete, then the above goal L can be reached via directly optimizing it with respect to the parameters. The method is to take the derivatives of L w.r.t. parameters and set them to zeros. Then, solve the equation set. If the equation set is nonlinear, then use the NewtonRaphson method to solve it. • The EM algorithm is a twostep iterative procedure containing the following two steps: Expectation and Maximization.steps: Expectation and Maximization....
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This note was uploaded on 07/21/2009 for the course CM EM5102 taught by Professor Sinhorngchen during the Fall '08 term at National Chiao Tung University.
 Fall '08
 SinHorngChen

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