Sparse Graphical Modeling for Electrophysiological Phase-Based Connectivity Using Circular Statistics

Identifying phase coupling from electrophysiological signals recorded by multiple electrodes, such as electroencephalogram (EEG) and electrocorticography (ECoG), helps neuroscientists and clinicians understand underlying brain structures or mechanisms. From a statistical perspective, these signals are multidimensional 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 that is difficult to interpret. Therefore, to enhance the interpretability of the brain network structure, this review 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 data set. Furthermore, we present analyses of two real data sets, 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. We found that when we used our proposed method, the modularity of the estimated network structure revealed more resolved brain structures and demonstrated differences in trends among individuals.