Lower-bounds on the Bayesian Risk in Estimation Procedures via $f$-Divergences
Information Theory
2022-05-19 v3 math.IT
Probability
Statistics Theory
Statistics Theory
Abstract
We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of -Divergences. The results are then applied to specific settings of interest and compared to other notable results in the literature. In particular, we show that the known bounds using Mutual Information can be improved by using, for example, Maximal Leakage, Hellinger divergence, or generalizations of the Hockey-Stick divergence.
Keywords
Cite
@article{arxiv.2202.02557,
title = {Lower-bounds on the Bayesian Risk in Estimation Procedures via $f$-Divergences},
author = {Adrien Vandenbroucque and Amedeo Roberto Esposito and Michael Gastpar},
journal= {arXiv preprint arXiv:2202.02557},
year = {2022}
}
Comments
Submitted to ISIT 2022