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Open AccessArticle

A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations

Department of Biomedicine and Prevention, University of Rome Tor Vergata, 00133 Rome, Italy
Department of Information Engineering and Research Centre “E. Piaggio”, University of Pisa, 56122 Pisa, Italy
Institute of Bioimaging and Molecular Physiology, National Research Council, 20090 Milano, Italy
Department of Clinical Neurosciences, University of Cambridge, Cambridge CB2 0QQ, UK
Department of Experimental and Clinical Medicine, Magna Graecia University, 88100 Catanzaro, Italy
Department of Health Sciences, Magna Graecia University, 88100 Catanzaro, Italy
Department of Electronics, Informatics and Bioengineering, Politecnico di Milano, 20133 Milano, Italy
Department of Radiology, Martinos Center for Biomedical Imaging and Harvard Medical School, Boston, MA 02129, USA
Authors to whom correspondence should be addressed.
Entropy 2019, 21(7), 629;
Received: 3 May 2019 / Revised: 23 June 2019 / Accepted: 24 June 2019 / Published: 26 June 2019
(This article belongs to the Special Issue Information Dynamics in Brain and Physiological Networks)
High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener–Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions. View Full-Text
Keywords: Granger causality; directed brain connectivity; MEG connectivity; laguerre polynomials Granger causality; directed brain connectivity; MEG connectivity; laguerre polynomials
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Duggento, A.; Valenza, G.; Passamonti, L.; Nigro, S.; Bianco, M.G.; Guerrisi, M.; Barbieri, R.; Toschi, N. A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations. Entropy 2019, 21, 629.

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