Emergent Mind
On Sibson's $α$-Mutual Information
(2202.03951)
Published Feb 8, 2022
in
cs.IT
,
math.IT
,
math.ST
,
and
stat.TH
Abstract
We explore a family of information measures that stems from R\'enyi's $\alpha$-Divergences with $\alpha<0$. In particular, we extend the definition of Sibson's $\alpha$-Mutual Information to negative values of $\alpha$ 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.
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