Directional statistical graphical modeling of phase-based connectivity

Identifying phase coupling recorded from multiple electrodes during electrophysiological diagnostics, 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 pseudo 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, we propose to induce a sparse solution by implementing a regularized score matching estimation for the torus graph model based on the information criteria. In numerical simulations, our method successfully recovered the true dependence structure of the brain, from a synthetic dataset sampled from a pre-given torus graph model distribution. 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.