  It is a challenging research endeavor to infer causal relationships in
multivariate observational time-series. Such data may be represented by graphs,
where nodes represent time-series, and edges directed causal influence scores
between them. If the number of nodes exceeds the number of temporal
observations, conventional methods, such as standard Granger causality, are of
limited value, because estimating free parameters of time-series predictors
lead to underdetermined problems. A typical example for this situation is
functional Magnetic Resonance Imaging (fMRI), where the number of nodal
observations is large, usually ranging from $10^2$ to $10^5$ time-series, while
the number of temporal observations is low, usually less than $10^3$. Hence,
innovative approaches are required to address the challenges arising from such
data sets. Recently, we have proposed the large-scale Extended Granger
Causality (lsXGC) algorithm, which is based on augmenting a
dimensionality-reduced representation of the system's state-space by
supplementing data from the conditional source time-series taken from the
original input space. Here, we apply lsXGC on synthetic fMRI data with known
ground truth and compare its performance to state-of-the-art methods by
leveraging the benefits of information-theoretic approaches. Our results
suggest that the proposed lsXGC method significantly outperforms existing
methods, both in diagnostic accuracy with Area Under the Receiver Operating
Characteristic (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 for
analyzing large-scale networks in neuroimaging studies of the human brain.
