On Sibson’s α-Mutual Information

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.