概率上下文无关文法的最大似然估计和EM训练的期望最大化算法
A Tutorial on the Expectation-Maximization Algorithm Including Maximum-Likelihood Estimation and EM Training of Probabilistic Context-Free Grammars
摘要：
本文在离散数学的可理解性框架下对Dempster（1977）的期望最大化算法作了简要的评述。在第二节中，介绍了两种主要的估计方法，相对频率估计和最大似然估计。第3节专门介绍期望最大化算法和一个更简单的变体，广义期望最大化算法。在第4节中，掷出两个装有骰子的骰子。一个更有趣的例子在第5节：概率上下文无关文法的估计中给出。
英文摘要：
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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