The -EM Algorithm: Surrogate Likelihood Maximization Using -Logarithmic Information Measures
The -EM Algorithm: Surrogate Likelihood Maximization Using -Logarithmic Information Measures
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发表时间：
2001
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通讯作者：
Y. Matsuyama
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作者：
Y. Matsuyama
提出了一种新的似然最大化算法，称为 -EM 算法（-Expectation–Maximization 算法）。在适当的设计参数范围内，该算法的收敛速度优于传统或对数 EM 算法。 log-EM 算法是对应于 = 1 的特殊情况。-EM 算法背后的主要思想是寻找有效的代理函数或次要函数来最大化观测数据的似然比。本文采用的代理函数基于与凸散度相关的-对数。通过相关更新矩阵对-EM算法的收敛速度进行了理论分析，并通过数值模拟进行了说明。最后，给出了使用对数方法的一般准则。还讨论了替代代理函数的选择。
A new likelihood maximization algorithm called the -EM algorithm ( -Expectation–Maximization algorithm) is presented. This algorithm outperforms the traditional or logarithmic EM algorithm in terms of convergence speed for an appropriate range of the design parameter . The log-EM algorithm is a special case corresponding to = 1. The main idea behind the -EM algorithm is to search for an effective surrogate function or a minorizer for the maximization of the observed data’s likelihood ratio. The surrogate function adopted in this paper is based upon the -logarithm which is related to the convex divergence. The convergence speed of the-EM algorithm is theoretically analyzed through -dependent update matrices and illustrated by numerical simulations. Finally, general guidelines for using the -logarithmic methods are given. The choice of alternative surrogate functions is also discussed.