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Entropy 2017, 19(8), 408; https://doi.org/10.3390/e19080408

Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes

1
Bruno Kessler Foundation, 38123 Trento, Italy
2
BIOtech, Department of Industrial Engineering, University of Trento, 38123 Trento, Italy
3
Data Analysis Department, Ghent University, 9000 Ghent, Belgium
4
Dipartimento di Fisica, Universitá degli Studi Aldo Moro, 70126 Bari, Italy
5
Istituto Nazionale di Fisica Nucleare, 70126 Sezione di Bari, Italy
*
Author to whom correspondence should be addressed.
Received: 21 June 2017 / Revised: 3 August 2017 / Accepted: 7 August 2017 / Published: 8 August 2017
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Abstract

Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms, constituting the frameworks known as interaction information decomposition and partial information decomposition, can thus be analytically obtained for different time scales from the parameters of the VAR model that fits the processes. We report the application of the proposed methodology firstly to benchmark Gaussian systems, showing that this class of systems may generate patterns of information decomposition characterized by prevalently redundant or synergistic information transfer persisting across multiple time scales or even by the alternating prevalence of redundant and synergistic source interaction depending on the time scale. Then, we apply our method to an important topic in neuroscience, i.e., the detection of causal interactions in human epilepsy networks, for which we show the relevance of partial information decomposition to the detection of multiscale information transfer spreading from the seizure onset zone. View Full-Text
Keywords: information dynamics; information transfer; multiscale entropy; multivariate time series analysis; redundancy and synergy; state space models; vector autoregressive models information dynamics; information transfer; multiscale entropy; multivariate time series analysis; redundancy and synergy; state space models; vector autoregressive models
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Faes, L.; Marinazzo, D.; Stramaglia, S. Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes. Entropy 2017, 19, 408.

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