Granger Causality among Graphs and Application to Functional Brain Connectivity in Autism Spectrum Disorder

Author(s)

Ribeiro, Adele Helena ^[1] ; Vidal, Maciel Calebe ^[2] ; Sato, Joao Ricardo ^[3] ; Fujita, Andre ^[4]

Affiliation

^[1] Columbia Univ, Data Sci Inst, New York, NY 10027 - USA

^[2] Insper Inst Educ & Res, BR-04546042 Sao Paulo, SP - Brazil

^[3] Univ Fed ABC, Ctr Math Comp & Cognit, BR-09210580 Santo Andre, SP - Brazil

^[4] Univ Sao Paulo, Inst Math & Stat, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Entropy; v. 23, n. 9 SEP 2021.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 18/04654-9 - Time series, wavelets and high dimensional data
• Grantee: Pedro Alberto Morettin
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 18/21934-5 - Network statistics: theory, methods, and applications
• Grantee: André Fujita
• Support Opportunities: Research Projects - Thematic Grants