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CORR
2006
Springer

Functional Bregman Divergence and Bayesian Estimation of Distributions

11 years 11 months ago
Functional Bregman Divergence and Bayesian Estimation of Distributions
Abstract--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.
B. A. Frigyik, Santosh Srivastava, Maya R. Gupta
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CORR
Authors B. A. Frigyik, Santosh Srivastava, Maya R. Gupta
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