Bayesian Risk With Bregman Loss: A Cramer-Rao Type Bound and Linear Estimation

被引：3
|
作者：
Dytso, Alex [1 ]
Fauss, Michael [2 ]
Poor, H. Vincent [2 ]
机构：
[1] New Jersey Inst Technol NJIT, Dept Elect & Comp Engn, Newark, NJ 07102 USA
[2] Princeton Univ, Dept Elect & Comp Engn, Princeton, NJ 08544 USA
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2022年 / 68卷 / 03期
基金：
美国国家科学基金会;
关键词：
Bayes methods; Estimation; Symmetric matrices; Random variables; Upper bound; Probability density function; Wireless communication; Cramer-Rao; minimum mean squared error (MMSE); Bregman divergence; linear estimation; Poisson noise; Gaussian Noise; MUTUAL INFORMATION; VECTOR POISSON; ENTROPY; ERROR; DIVERGENCE; GRADIENT;
D O I：
10.1109/TIT.2021.3130381
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 general class of Bayesian lower bounds when the underlying loss function is a Bregman divergence is demonstrated. This class can be considered as an extension of the Weinstein-Weiss family of bounds for the mean squared error and relies on finding a variational characterization of Bayesian risk. This approach allows for the derivation of a version of the Cramer-Rao bound that is specific to a given Bregman divergence. This new generalization of the Cramer-Rao bound reduces to the classical one when the loss function is taken to be the Euclidean norm. In order to evaluate the effectiveness of the new lower bounds, the paper also develops upper bounds on Bayesian risk, which are based on optimal linear estimators. The effectiveness of the new bound is evaluated in the Poisson noise setting.
引用
收藏
页码：1985 / 2000
页数：16
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