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arXiv · 2202.03951

On Sibson's $α$-Mutual Information

Amedeo Roberto Esposito·Adrien Vandenbroucque·Michael Gastpar
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Abstract

We explore a family of information measures that stems from Rényi's $α$-Divergences with $α<0$. In particular, we extend the definition of Sibson's $α$-Mutual Information to negative values of $α$ 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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Amedeo Roberto Esposito, Adrien Vandenbroucque, Michael Gastpar. 2022-02-08. On Sibson's $α$-Mutual Information. https://arxiv.org/abs/2202.03951

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