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Rényi Divergence and Kullback-Leibler Divergence

Abstract : Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Rényi divergence of order 1 equals the Kullback-Leibler divergence. We review and extend the most important properties of Rényi divergence and Kullback-Leibler divergence, including convexity, continuity, limits of {\sigma}-algebras and the relation of the special order 0 to the Gaussian dichotomy and contiguity. We also extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs (for all orders), and present several other minimax results.
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https://hal.inria.fr/hal-00758191
Contributor : Tim Van Erven Connect in order to contact the contributor
Submitted on : Wednesday, November 28, 2012 - 11:54:41 AM
Last modification on : Sunday, June 26, 2022 - 11:57:30 AM

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  • HAL Id : hal-00758191, version 1
  • ARXIV : 1206.2459

Citation

Tim van Erven, Peter Harremoës. Rényi Divergence and Kullback-Leibler Divergence. 2013. ⟨hal-00758191⟩

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