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Entropy 2017, 19(5), 232; doi:10.3390/e19050232

A Kullback–Leibler View of Maximum Entropy and Maximum Log-Probability Methods

1
Industrial & Systems Engineering and Public Policy, University of Southern California, Los Angeles, CA 90089, USA
2
Supply Chain & Analytics, University of Missouri-St. Louis, St. Louis, MO 63121, USA
3
Industrial & Systems Engineering, University of Southern California, Los Angeles, CA 90007, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 2 March 2017 / Revised: 30 April 2017 / Accepted: 15 May 2017 / Published: 19 May 2017
(This article belongs to the Section Information Theory)
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Abstract

Entropy methods enable a convenient general approach to providing a probability distribution with partial information. The minimum cross-entropy principle selects the distribution that minimizes the Kullback–Leibler divergence subject to the given constraints. This general principle encompasses a wide variety of distributions, and generalizes other methods that have been proposed independently. There remains, however, some confusion about the breadth of entropy methods in the literature. In particular, the asymmetry of the Kullback–Leibler divergence provides two important special cases when the target distribution is uniform: the maximum entropy method and the maximum log-probability method. This paper compares the performance of both methods under a variety of conditions. We also examine a generalized maximum log-probability method as a further demonstration of the generality of the entropy approach. View Full-Text
Keywords: entropy; minimum cross entropy; joint probability distribution entropy; minimum cross entropy; joint probability distribution
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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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Abbas, A.E.; H. Cadenbach, A.; Salimi, E. A Kullback–Leibler View of Maximum Entropy and Maximum Log-Probability Methods. Entropy 2017, 19, 232.

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