# 最大期望算法

2018-07-27 10:05:04     所属分类：算法

## 目录

• 1 历史
• 2 EM简单教程
• 3 最大期望过程说明
• 3.1 估计无法观测的数据
• 4 参见
• 5 参考文献

## EM简单教程

EM是一个在已知部分相关变量的情况下，估计未知变量的迭代技术。EM的算法流程如下：

1. 初始化分布参数
2. 重复直到收敛：
1. E步骤：根据隐含数据的假设值，给出当前的参数的极大似然估计。
2. M步骤：重新给出未知变量的期望估计。应用于缺失值。

• 估计理论
• 数据聚类

## 参考文献

• Arthur Dempster, Nan Laird, and Donald Rubin. "Maximum likelihood from incomplete data via the EM algorithm". Journal of the Royal Statistical Society, Series B, 39 (1):1–38, 1977 1.
• Robert Hogg, Joseph McKean and Allen Craig. Introduction to Mathematical Statistics. pp. 359-364. Upper Saddle River, NJ: Pearson Prentice Hall, 2005.
• Radford Neal, Geoffrey Hinton. "A view of the EM algorithm that justifies incremental, sparse, and other variants". In Michael I. Jordan (editor), Learning in Graphical Models pp 355-368. Cambridge, MA: MIT Press, 1999.
• The on-line textbook: Information Theory, Inference, and Learning Algorithms，by David J.C. MacKay includes simple examples of the E-M algorithm such as clustering using the soft K-means algorithm, and emphasizes the variational view of the E-M algorithm.
• A Gentle Tutorial of the EM Algorithm and its Application to Parameter Estimation for Gaussian Mixture and Hidden Markov Models，by J. Bilmes includes a simplified derivation of the EM equations for Gaussian Mixtures and Gaussian Mixture Hidden Markov Models.
• Information Geometry of the EM and em Algorithms for Neural Networks，by Shun-Ichi Amari give a view of EM algorithm from geometry view point.