Functional Bregman Divergence and Bayesian Estimation of Distributions

被引：59

作者：

Frigyik, Bela A. ^{[1
]}

Srivastava, Santosh ^{[2
]}

Gupta, Maya R. ^{[3
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Univ Washington, Dept Appl Math, Seattle, WA 98195 USA

[3] Univ Washington, Dept Elect Engn, Seattle, WA 98195 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2008年 / 54卷 / 11期

关键词：

Bayesian estimation; Bregman divergence; convexity; Frechet derivative; uniform distribution;

D O I：

10.1109/TIT.2008.929943

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A class of distortions termed functional Bregman divergences is defined, which includes squared error and relative entropy. A functional Bregman divergence acts on functions or distributions, and generalizes the standard Bregman divergence for vectors and a previous pointwise Bregman divergence that was defined for functions. A recent result showed that the mean minimizes the expected Bregman divergence. The new functional definition enables the extension of this result to the continuous case to show that the mean minimizes the expected functional Bregman divergence over a set of functions or distributions. It is shown how this theorem applies to the Bayesian estimation of distributions. Estimation of the uniform distribution from independent and identically drawn samples is presented as a case study.

引用

页码：5130 / 5139

页数：10

共 28 条

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