教程：EM算法

[编者的话]

EM算法即期望最大化算法，在生物信息学中多有应用。在这里向大家推荐一篇关于EM的教程，希望大家对EM能有所了解。下面是教程的摘要。

We describe the maximum-likelihood parameter estimation problem and how the Expectation-Maximization (EM) algorithm can be used for its solution. We first describe the abstract form of the EM algorithm as it is often given in the literature. We then develop the EM parameter estimation procedure for two applications: 1) finding the parameters of a mixture of Gaussian densities, and 2) finding the parameters of a hidden Markov model (HMM) (i.e.,the Baum-Welch algorithm) for both discrete and Gaussian mixture observation models.We derive the update equations in fairly explicit detail but we do not prove any convergence properties. We try to emphasize intuition rather than mathematical rigor.