On Sibson's α-Mutual Information

2022/02/08 by Esposito, Amedeo Roberto, Vandenbroucque, Adrien, Gastpar, Michael
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2202.03951

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.

Related

• Sibson α-Mutual Information and Its Variational Representations
• Lower Bounds on the Bayesian Risk via Information Measures
• Robust Generalization via α-Mutual Information
• On conditional Sibson's α-Mutual Information
• Information Processing Equalities and the Information-Risk Bridge