Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder
1
Data Science Institute, Columbia University, New York, NY 10027, USA
2
Insper Institute of Education and Research, São Paulo 04546-042, SP, Brazil
3
Center of Mathematics, Computing and Cognition, Universidade Federal do ABC, Santo André 09210-580, SP, Brazil
4
Institute of Mathematics and Statistics, University of São Paulo, São Paulo 05508-090, SP, Brazil
*
Author to whom correspondence should be addressed.
Academic Editors: Daniel Takahashi and Demian Battaglia
Entropy 2021, 23(9), 1204; https://doi.org/10.3390/e23091204
Received: 29 July 2021
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Revised: 6 September 2021
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Accepted: 8 September 2021
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Published: 13 September 2021
(This article belongs to the Special Issue Brain Connectivity and Information Theory)
Graphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks’ time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models’ parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal’s application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain’s right to the left hemisphere is different between ASD and controls.
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Keywords:
Granger causality; random graphs; spectral radius; brain connectivity; autism spectrum disorder
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MDPI and ACS Style
Ribeiro, A.H.; Vidal, M.C.; Sato, J.R.; Fujita, A. Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder. Entropy 2021, 23, 1204. https://doi.org/10.3390/e23091204
AMA Style
Ribeiro AH, Vidal MC, Sato JR, Fujita A. Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder. Entropy. 2021; 23(9):1204. https://doi.org/10.3390/e23091204
Chicago/Turabian StyleRibeiro, Adèle H., Maciel C. Vidal, João R. Sato, and André Fujita. 2021. "Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder" Entropy 23, no. 9: 1204. https://doi.org/10.3390/e23091204
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