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Entropy 2016, 18(1), 13; doi:10.3390/e18010013

Improvement of the k-nn Entropy Estimator with Applications in Systems Biology

1
Institute of Computer Science Polish Academy of Sciences, Jana Kazimierza Street 5, 01-248 Warsaw, Poland
2
Laboratory of Bioinformatics, Nencki Institute of Experimental Biology Polish Academy of Sciences, Pasteura Street 3, 02-093 Warsaw, Poland
3
Institute of Informatics, University of Warsaw, Banacha Street 2, 02-097 Warsaw, Poland
*
Authors to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 5 October 2015 / Revised: 8 December 2015 / Accepted: 21 December 2015 / Published: 29 December 2015
(This article belongs to the Section Information Theory)
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Abstract

In this paper, we investigate efficient estimation of differential entropy for multivariate random variables. We propose bias correction for the nearest neighbor estimator, which yields more accurate results in higher dimensions. In order to demonstrate the accuracy of the improvement, we calculated the corrected estimator for several families of random variables. For multivariate distributions, we considered the case of independent marginals and the dependence structure between the marginal distributions described by Gaussian copula. The presented solution may be particularly useful for high dimensional data, like those analyzed in the systems biology field. To illustrate such an application, we exploit differential entropy to define the robustness of biochemical kinetic models. View Full-Text
Keywords: differential entropy; k-NN estimator; bias correction; Gaussian copula; mutual information; sensitivity indices; p53-Mdm2 feedback loop model differential entropy; k-NN estimator; bias correction; Gaussian copula; mutual information; sensitivity indices; p53-Mdm2 feedback loop model
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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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Charzyńska, A.; Gambin, A. Improvement of the k-nn Entropy Estimator with Applications in Systems Biology. Entropy 2016, 18, 13.

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