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Entropy 2015, 17(1), 438-470; doi:10.3390/e17010438

A Recipe for the Estimation of Information Flow in a Dynamical System

1
NOAA-CREST, The City College of New York, New York, NY, 10031, USA
2
Depts. of Physics and Informatics, University at Albany (SUNY), Albany, NY 12222, USA
*
Author to whom correspondence should be addressed.
Received: 7 February 2014 / Revised: 8 December 2014 / Accepted: 8 January 2015 / Published: 19 January 2015
(This article belongs to the Special Issue Transfer Entropy)
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Abstract

Information-theoretic quantities, such as entropy and mutual information (MI), can be used to quantify the amount of information needed to describe a dataset or the information shared between two datasets. In the case of a dynamical system, the behavior of the relevant variables can be tightly coupled, such that information about one variable at a given instance in time may provide information about other variables at later instances in time. This is often viewed as a flow of information, and tracking such a flow can reveal relationships among the system variables. Since the MI is a symmetric quantity; an asymmetric quantity, called Transfer Entropy (TE), has been proposed to estimate the directionality of the coupling. However, accurate estimation of entropy-based measures is notoriously difficult. Every method has its own free tuning parameter(s) and there is no consensus on an optimal way of estimating the TE from a dataset. We propose a new methodology to estimate TE and apply a set of methods together as an accuracy cross-check to provide a reliable mathematical tool for any given data set. We demonstrate both the variability in TE estimation across techniques as well as the benefits of the proposed methodology to reliably estimate the directionality of coupling among variables. View Full-Text
Keywords: transfer entropy; information flow; statistical dependency; mutual information; Shannon entropy; information-theoretical quantities; Lorenz equations transfer entropy; information flow; statistical dependency; mutual information; Shannon entropy; information-theoretical quantities; Lorenz equations
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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

Gencaga, D.; Knuth, K.H.; Rossow, W.B. A Recipe for the Estimation of Information Flow in a Dynamical System. Entropy 2015, 17, 438-470.

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