Directional statistical graphical modeling of phase-based connectivity

Identifying phase coupling from electrophysiological signals recorded by multiple electrodes, such as electroencephalogram (EEG) and electrocorticography (ECoG), helps neuroscientists and clinicians understand the underlying brain structures or mechanisms. From a statistical perspective, these signals are multi-dimensional circular measurements that are correlated with one another and can be effectively modeled using a torus graph model designed for circular random variables. Using the torus graph model avoids the issue of detecting spurious correlations. However, the naive estimation of this model tends to lead to a dense network structure, which is difficult to interpret. Therefore, to enhance the interpretability of the brain network structure, this paper proposes a sparse estimation method for the torus graph model using regularized score matching combined with information criteria. In numerical simulations, our method successfully recovered the true dependence structure from a synthetic dataset. Furthermore, we present analyses of two real datasets, one involving human EEG and the other marmoset ECoG, demonstrating that our method can be widely applied to phase-coupling analysis across different types of neural data. Using our proposed method, the modularity of the estimated network structure revealed more resolved brain structures and demonstrated differences in trends among individuals.