On Sibson's $\alpha$-Mutual Information
Information Theory
2022-02-09 v1 math.IT
Statistics Theory
Statistics Theory
Abstract
We explore a family of information measures that stems from R\'enyi's -Divergences with . In particular, we extend the definition of Sibson's -Mutual Information to negative values of and show several properties of these objects. Moreover, we highlight how this family of information measures is related to functional inequalities that can be employed in a variety of fields, including lower-bounds on the Risk in Bayesian Estimation Procedures.
Keywords
Cite
@article{arxiv.2202.03951,
title = {On Sibson's $\alpha$-Mutual Information},
author = {Amedeo Roberto Esposito and Adrien Vandenbroucque and Michael Gastpar},
journal= {arXiv preprint arXiv:2202.03951},
year = {2022}
}
Comments
Submitted to ISIT 2022