  Estimating causal interactions in the brain from functional magnetic
resonance imaging (fMRI) data remains a challenging task. Multiple studies have
demonstrated that all current approaches to determine direction of connectivity
perform poorly even when applied to synthetic fMRI datasets. Recent advances in
this field include methods for pairwise inference, which involve creating a
sparse connectome in the first step, and then using a classifier in order to
determine the directionality of connection between of every pair of nodes in
the second step. In this work, we introduce an advance to the second step of
this procedure, by building a classifier based on fractional moments of the
BOLD distribution combined into cumulants. The classifier is trained on
datasets generated under the Dynamic Causal Modeling (DCM) generative model.
The directionality is inferred based upon statistical dependencies between the
two node time series, e.g. assigning a causal link from time series of low
variance to time series of high variance. Our approach outperforms or performs
as well as other methods for effective connectivity when applied to the
benchmark datasets. Crucially, it is also more resilient to confounding effects
such as differential noise level across different areas of the connectome.
