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Entropy 2015, 17(4), 1958-1970; doi:10.3390/e17041958

Assessing Coupling Dynamics from an Ensemble of Time Series

1
Netherlands Institute for Neuroscience, Meibergdreef 47, Amsterdam 1105 BA, The Netherlands
2
Lab of Neurophysics and Neurophysiology, Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, 96 JinZhai Rd., Hefei 230026, China
3
Department of Mathematics, Tampere University of Technology, Korkeakoulunkatu 10, Tampere FI-33720, Finland
4
Instituto de Fisica Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat de les Illes Balears E-07122 Palma de Mallorca, Spain
5
Institut für Kognitionswissenschaft, University of Osnabrück, Albrechtstrasse 28, Osnabrück 49076, Germany
6
Institute of Computer Science, University of Tartu, J. Liivi 2, Tartu 50409, Estonia
*
Author to whom correspondence should be addressed.
Academic Editor: Deniz Gencaga
Received: 30 November 2014 / Revised: 28 February 2015 / Accepted: 19 March 2015 / Published: 2 April 2015
(This article belongs to the Special Issue Transfer Entropy)
View Full-Text   |   Download PDF [709 KB, uploaded 2 April 2015]   |  

Abstract

Finding interdependency relations between time series provides valuable knowledge about the processes that generated the signals. Information theory sets a natural framework for important classes of statistical dependencies. However, a reliable estimation from information-theoretic functionals is hampered when the dependency to be assessed is brief or evolves in time. Here, we show that these limitations can be partly alleviated when we have access to an ensemble of independent repetitions of the time series. In particular, we gear a data-efficient estimator of probability densities to make use of the full structure of trial-based measures. By doing so, we can obtain time-resolved estimates for a family of entropy combinations (including mutual information, transfer entropy and their conditional counterparts), which are more accurate than the simple average of individual estimates over trials. We show with simulated and real data generated by coupled electronic circuits that the proposed approach allows one to recover the time-resolved dynamics of the coupling between different subsystems. View Full-Text
Keywords: entropy; transfer entropy; estimator; ensemble; trial; time series entropy; transfer entropy; estimator; ensemble; trial; time series
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

Gómez-Herrero, G.; Wu, W.; Rutanen, K.; Soriano, M.C.; Pipa, G.; Vicente, R. Assessing Coupling Dynamics from an Ensemble of Time Series. Entropy 2015, 17, 1958-1970.

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