Relative alpha-Entropy Minimizers Subject to Linear Statistical Constraints

Kumar, Ashok M and Sundaresan, Rajesh (2015) Relative alpha-Entropy Minimizers Subject to Linear Statistical Constraints. In: 21st National Conference on Communications (NCC), FEB 27-MAR 01, 2015, Indian Inst Technol, Bombay, INDIA.

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Abstract

We study minimization of a parametric family of relative entropies, termed relative alpha-entropies (denoted I-alpha(P; Q)). These arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimization of I-alpha(P, Q) over the first argument on a set of probability distributions that constitutes a linear family is studied. Such a minimization generalizes the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed I-alpha-projection) for a linear family is shown to have a power-law.

Item Type:	Conference Proceedings
Series.:	National Conference on Communications NCC
Additional Information:	Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	24 Aug 2016 10:10
Last Modified:	24 Aug 2016 10:10
URI:	http://eprints.iisc.ac.in/id/eprint/54563

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