Consider the complete log-likelihood of the Gaussian mixture model: n K log P(x, z) = ziklogak...

 

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Consider the complete log-likelihood of the Gaussian mixture model: n K log P(x, z) = ziklogak i=1 k=1 (b) n K CE i=1 k=1 1 2 n K 1 1 ziklog(2?) zik log(270) Czuk (21 14k) . Zik - 2 ok i=1 k=1 (a) Suppose z is observed, compute the maximum likelihood estimator for ,..., K and o,..., ok (i.e., maximize log P(x, z) over the parameters). Given the parameters T1,..., TK, 1,..., K and o1, ..., ok, compute P(Zik = 1|xi) Consider the complete log-likelihood of the Gaussian mixture model: n K log P(x, z) = ziklogak i=1 k=1 (b) n K CE i=1 k=1 1 2 n K 1 1 ziklog(2?) zik log(270) Czuk (21 14k) . Zik - 2 ok i=1 k=1 (a) Suppose z is observed, compute the maximum likelihood estimator for ,..., K and o,..., ok (i.e., maximize log P(x, z) over the parameters). Given the parameters T1,..., TK, 1,..., K and o1, ..., ok, compute P(Zik = 1|xi)