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It is a challenging research endeavor to infer causal relationships inmultivariate observational time-series. Such data may be represented by graphs,where nodes represent time-series, and edges directed causal influence scoresbetween them. If the number of nodes exceeds the number of temporalobservations, conventional methods, such as standard Granger causality, are oflimited value, because estimating free parameters of time-series predictorslead to underdetermined problems. A typical example for this situation isfunctional Magnetic Resonance Imaging (fMRI), where the number of nodalobservations is large, usually ranging from $10^2$ to $10^5$ time-series, whilethe number of temporal observations is low, usually less than $10^3$. Hence,innovative approaches are required to address the challenges arising from suchdata sets. Recently, we have proposed the large-scale Extended GrangerCausality (lsXGC) algorithm, which is based on augmenting adimensionality-reduced representation of the system's state-space bysupplementing data from the conditional source time-series taken from theoriginal input space. Here, we apply lsXGC on synthetic fMRI data with knownground truth and compare its performance to state-of-the-art methods byleveraging the benefits of information-theoretic approaches. Our resultssuggest that the proposed lsXGC method significantly outperforms existingmethods, both in diagnostic accuracy with Area Under the Receiver OperatingCharacteristic (AUROC = $0.849$ vs.~$[0.727, 0.762]$ for competing methods,$p<\!10^{-8}$), and computation time ($3.4$ sec vs.~[$9.7$, $4.8 \times 10^3$]sec for competing methods) benchmarks, demonstrating the potential of lsXGC foranalyzing large-scale networks in neuroimaging studies of the human brain.

Investigation of large-scale extended Granger causality (lsXGC) on synthetic functional MRI data