A Tutorial on the Expectation-Maximization Algorithm Including Maximum-Likelihood Estimation and EM Training of Probabilistic Context-Free Grammars

Details A Tutorial on the Expectation-Maximization Algorithm Including Maximum-Likelihood Estimation and EM Training of Probabilistic Context-Free Grammars A Tutorial on the Expectation-Maximization Algorithm Including Maximum-Likelihood Estimation and EM Training of Probabilistic Context-Free Grammars

2004-12-03

arxiv.org/abs/cs/0412015v2

Computer Science

Computation and Language

Presented at the 15th European Summer School in Logic, Language and Information (ESSLLI 2003). Example 5 extended (and partial

Scientific paper

The paper gives a brief review of the expectation-maximization algorithm (Dempster 1977) in the comprehensible framework of discrete mathematics. In Section 2, two prominent estimation methods, the relative-frequency estimation and the maximum-likelihood estimation are presented. Section 3 is dedicated to the expectation-maximization algorithm and a simpler variant, the generalized expectation-maximization algorithm. In Section 4, two loaded dice are rolled. A more interesting example is presented in Section 5: The estimation of probabilistic context-free grammars.

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