关键词: 期望最大（EM）, 极大似然估计（MLE）, 不完全数据, 隐变量

Abstract: EM algorithm is an effective method for maximum-likelihood estimate（MLE），which is mainly used to estimate parameters of incomplete data.On the one hand，by assuming the existence of hidden variable in EM algorithm，the likelihood function are greatly simplified；on the other hand，some special parameters estimation can be easily realized by virtue of EM algorithm.MLE is a common parameters estimation method and EM algorithm makes its application more extensive.This tutorial is organized from users’ points of view and its content is self-contained.

Key words: expectation-maximization（EM）, maximum likelihood estimation（MLE）, incomplete data, hidden variable