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On The Equivalence of Projections In Relative α-Entropy and Rényi Divergence

2017/01/23 by P. N. Karthik, Karthik, P. N., Rajesh Sundaresan +1
Physics and Astronomy · #FOS: Computer and information sciences #Information Theory (cs.IT) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1701.06347

openalex publication_date 2017/01/23 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

The aim of this work is to establish that two recently published projection theorems, one dealing with a parametric generalization of relative entropy and another dealing with Rényi divergence, are equivalent under a correspondence on the space of probability measures. Further, we demonstrate that the associated "Pythagorean" theorems are equivalent under this correspondence. Finally, we apply Eguchi's method of obtaining Riemannian metrics from general divergence functions to show that the geometry arising from the above divergences are equivalent under the aforementioned correspondence.

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