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Entropy 2011, 13(12), 2013-2023; doi:10.3390/e13122013

Coincidences and Estimation of Entropies of Random Variables with Large Cardinalities

Departments of Physics and Biology and Computational and Life Sciences Initiative, Emory University, 400 Dowman Dr., Atlanta, GA 30322, USA
Received: 1 November 2011 / Revised: 8 December 2011 / Accepted: 15 December 2011 / Published: 19 December 2011
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Abstract

We perform an asymptotic analysis of the NSB estimator of entropy of a discrete random variable. The analysis illuminates the dependence of the estimates on the number of coincidences in the sample and shows that the estimator has a well defined limit for a large cardinality of the studied variable. This allows estimation of entropy with no a priori assumptions about the cardinality. Software implementation of the algorithm is available.
Keywords: entropy estimation; coincidences; bias-variance tradeoff; model selection entropy estimation; coincidences; bias-variance tradeoff; model selection
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Nemenman, I. Coincidences and Estimation of Entropies of Random Variables with Large Cardinalities. Entropy 2011, 13, 2013-2023.

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