Bayesian Risk with Bregman Loss: A Cramér-Rao Type Bound and Linear Estimation

Document Type

Conference Proceeding

Publication Date

3-1-2022

Abstract

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 Cramér-Rao bound that is specific to a given Bregman divergence. This new generalization of the Cramér-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.

Identifier

85120070124 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/TIT.2021.3130381

e-ISSN

15579654

ISSN

00189448

First Page

1985

Last Page

2000

Issue

3

Volume

68

Grant

CCF-1908308

Fund Ref

National Science Foundation

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