One important property of Rényi divergence is that Dα(T(X)||T(Y )) = Dα(X||Y ) for any invertible transformation T. This follows from the more general data processing inequality (see, e.g., [20, 21]). For example, the Rényi divergence between two lognormal densities is the same as that between two normal densities.
Apr 24, 2014 · We review and extend the most important properties of Rényi divergence and Kullback-Leibler divergence, including convexity, continuity, limits ...
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It was introduced by Rényi as a measure of information that satisfies almost the same axioms as information divergence. We review the most important properties ...
Finally, Rényi divergence plays a role in analyzing the number of binary questions required to guess the values of a sequence of random variables.
The Rényi divergence of order α ∈ ( 0 , 1 ) between probability distributions p and q in P μ is defined as (1.1) D ( α ) ( p ∥ q ) = κ ( α ) α ( α − 1 ) , where ...
The Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy.
We review and extend the most important properties of Rényi divergence and Kullback-Leibler divergence, including convexity, continuity, limits of σ-algebras ...
May 24, 2021 · In this work, we present a systematic study of the geometric Rényi divergence (GRD), also known as the maximal Rényi divergence, from the point of view of ...
The main observations are Theorems 2.4 and 2.5 which show that Lp- affine surface areas and mixed p-affine surface areas are exponentials of Rényi divergences.
We explore properties of the χ2 and more general Rényi (Tsallis) distances to the normal law and in particular propose necessary and sufficient conditions under ...