An algorithm for information projection to an affine subspace

被引：0
|
作者：
D. V. Vinogradov
机构：
[1] Russian Academy of Sciences,Institute of Informatics Problems
[2] Russian State University for the Humanities,undefined
来源：
Automatic Documentation and Mathematical Linguistics | 2016年 / 50卷 / 3期
关键词：
KL-distance; positive orthant; affine subspace; exponential family; maximum likelihood estimates;
D O I：
10.3103/S0005105516030109
中图分类号：
学科分类号：
摘要：
We investigate an algorithm to find a point of an affine subspace in the positive orthant such that it is the closest one to the original point with respect to the Kullback–Leibler distance. This problem is solved by means of the classical Darroch–Ratcliff algorithm (see [1]), while we use ideas of the information geometry founded by Chentsov (see [2]) and Csiszar (see [3]). The main theorem of the present work proves the convergence of that algorithm (the method of the proof is different from previous ones). The proposed algorithm can be applied, e.g., to find the maximum likelihood estimates in an exponential family (see the last section of the paper).
引用
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页码：133 / 138
页数：5
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