Rényi Divergence and Majorization

Details Rényi Divergence and Majorization Rényi Divergence and Majorization

2010-01-25

arxiv.org/abs/1001.4448v3

Computer Science

Information Theory

Scientific paper

R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as a measure of information that satisfies almost the same axioms as information divergence. We review the most important properties of R\'enyi divergence, including its relation to some other distances. We show how R\'enyi divergence appears when the theory of majorization is generalized from the finite to the continuous setting. Finally, R\'enyi divergence plays a role in analyzing the number of binary questions required to guess the values of a sequence of random variables.

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