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Further results on geometric properties of a family of relative entropies

Moses, Ashok Kumar and Sundaresan, Rajesh (2011) Further results on geometric properties of a family of relative entropies. In: International Symposium on Information Theory (ISIT), July 31 2011-Aug. 5 2011, St. Petersburg.

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Official URL: http://dx.doi.org/10.1109/ISIT.2011.6033890

Abstract

This paper extends some geometric properties of a one-parameter family of relative entropies. These arise as redundancies when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the Kullback-Leibler divergence. They satisfy the Pythagorean property and behave like squared distances. This property, which was known for finite alphabet spaces, is now extended for general measure spaces. Existence of projections onto convex and certain closed sets is also established. Our results may have applications in the Rényi entropy maximization rule of statistical physics.

Item Type: Conference Proceedings
Additional Information: Copyright of this article belongs to IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 02 Apr 2013 08:38
Last Modified: 02 Apr 2013 08:38
URI: http://eprints.iisc.ac.in/id/eprint/46145

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