Conditions for the existence of a generalization of R\'enyi divergence

Physica A: Statistical Mechanics and its Applications, 2020 We give necessary and sufficient conditions for the existence of a generalization of R\'enyi divergence, which is defined in terms of a deformed exponential function. If the underlying measure $\mu$ is non-atomic, we found that not all...

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Bibliographic Details
Main Authors Vigelis, Rui F, de Andrade, Luiza H. F, Cavalcante, Charles C
Format Journal Article
LanguageEnglish
Published 10.08.2020
Subjects
Computer Science - Information Theory
Mathematics - Information Theory
Mathematics - Probability
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Summary:Physica A: Statistical Mechanics and its Applications, 2020 We give necessary and sufficient conditions for the existence of a generalization of R\'enyi divergence, which is defined in terms of a deformed exponential function. If the underlying measure $\mu$ is non-atomic, we found that not all deformed exponential functions can be used in the generalization of R\'enyi divergence; a condition involving the deformed exponential function is provided. In the case $\mu$ is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.
DOI:10.48550/arxiv.2008.04466