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Entropy 2016, 18(7), 262; doi:10.3390/e18070262

Greedy Algorithms for Optimal Distribution Approximation

Institute for Communications Engineering, Technical University of Munich, Munich 80290, Germany
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Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 14 June 2016 / Revised: 1 July 2016 / Accepted: 11 July 2016 / Published: 18 July 2016
(This article belongs to the Section Information Theory)
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Abstract

The approximation of a discrete probability distribution t by an M-type distribution p is considered. The approximation error is measured by the informational divergence D ( t p ) , which is an appropriate measure, e.g., in the context of data compression. Properties of the optimal approximation are derived and bounds on the approximation error are presented, which are asymptotically tight. A greedy algorithm is proposed that solves this M-type approximation problem optimally. Finally, it is shown that different instantiations of this algorithm minimize the informational divergence D ( p t ) or the variational distance p t 1 . View Full-Text
Keywords: distribution approximation; finite precision; informational divergence; greedy algorithm distribution approximation; finite precision; informational divergence; greedy algorithm
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Geiger, B.C.; Böcherer, G. Greedy Algorithms for Optimal Distribution Approximation. Entropy 2016, 18, 262.

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