EM Algorithm Motiviation Notation:ExampleExampleXi Chen(based on the notes from Ajit) Expectation-Maximization (EM) is a technique used in point estimation. Given a set of observable variables Xand unknown (latent) variables Z, we want to estimate parameters θin a model.E-step: Evaluation: M-step:Evaluation: (Binomial Mixture Model) You have two coins with unknown probabilities of heads, denoted pand qrespectively. The first coin is chosen with probability πand the second coin is chosen with probability 1−π. The chosen coin is flipped once and the result is recorded. x= {1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1} (Heads = 1, Tails = 0). Hidden Variables: Zi=1: the coin tossed with the head probability pZi=0: the coin tossed with the head probability qParameters: θ=(p, q, π) E-step: Evaluation
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