Expectation Maximization – Link (35/365)

Dan Piponi has written up a simple to follow derivation of the Expectation-Maximization algorithm. It give a very practical derivation of the algorithm which also makes it easy to remember.

What it clarifies for me is the step in the EM algorithm where one introduces auxilliary variables \beta_z – one for each value hidden value z that the hidden variable can take on – which somehow turns out to be the conditional probability of z given everything else. Why this turns out to be the case has always been a little fuzzy to me. And Dan’s post clarifies it greatly. The step that determines the auxilliary variables comes from equating the derivative of the log-likelihood and the derivative of the simpler function involving \beta_z’s and solving for \beta_z. Please have a read.

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