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On Sibson's $\alpha$-Mutual Information

Information Theory 2022-02-09 v1 math.IT Statistics Theory Statistics Theory

Abstract

We explore a family of information measures that stems from R\'enyi's α\alpha-Divergences with α<0\alpha<0. In particular, we extend the definition of Sibson's α\alpha-Mutual Information to negative values of α\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.

Keywords

Cite

@article{arxiv.2202.03951,
  title  = {On Sibson's $\alpha$-Mutual Information},
  author = {Amedeo Roberto Esposito and Adrien Vandenbroucque and Michael Gastpar},
  journal= {arXiv preprint arXiv:2202.03951},
  year   = {2022}
}

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Submitted to ISIT 2022

R2 v1 2026-06-24T09:26:34.203Z