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On maximum entropy and minimum KL-divergence optimization by Grobner basis methods

Dukkipati, Ambedkar (2012) On maximum entropy and minimum KL-divergence optimization by Grobner basis methods. In: APPLIED MATHEMATICS AND COMPUTATION, 218 (23). pp. 11674-11687.

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Official URL: http://dx.doi.org/10.1016/j.amc.2012.05.052

Abstract

In this paper we study constrained maximum entropy and minimum divergence optimization problems, in the cases where integer valued sufficient statistics exists, using tools from computational commutative algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. We give an implicit description of maximum entropy models by embedding them in algebraic varieties for which we give a Grobner basis method to compute it. In the cases of minimum KL-divergence models we show that implicitization preserves specialization of prior distribution. This result leads us to a Grobner basis method to embed minimum KL-divergence models in algebraic varieties. (C) 2012 Elsevier Inc. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to Elsevier Inc.
Keywords: Shannon entropy;Zariski closure;Implicitization
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 09 Aug 2012 11:22
Last Modified: 09 Aug 2012 11:22
URI: http://eprints.iisc.ernet.in/id/eprint/44911

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