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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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On Sibson's $α$-Mutual Information
Amedeo Roberto Esposito, Adrien Vandenbroucque, Michael Gastpar · 2022-02-09 · via math.ST updates on arXiv.org

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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