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EM Algorithm_English

# EM Algorithm_English - The EM Algorithm Sin-Horng Chen 1...

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1 The EM Algorithm Sin-Horng Chen 2008/5/24

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2 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 (1) where is the observed data sequence. The observed data are generally assumed to be independent, i.e., (2) (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. 1 2 , , , N X x x x = L So, maxlog ( ) max log ( ) n n P X P x Θ Θ Θ = Θ maxlog ( ) L P X Θ = Θ ( ) ( ) n n P X P x Θ = Θ
3 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 equal to zeros. Then, solve the equation set. If the equation set is nonlinear, then use the Newton-Raphson method to solve it.

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EM Algorithm_English - The EM Algorithm Sin-Horng Chen 1...

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