On Sibson's α-Mutual Information

02/08/2022

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by   Amedeo Roberto Esposito, et al.

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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.