A neighbour selection approach for identifying differential networks in conditional functional graphical models
Estimating how different brain regions communicate with each other using EEG data is valuable both for medical research and clinical diagnosis. This involves quantifying the statistical dependencies among the activities of different brain areas, captured by the time-varying electric field recorded by scalp sensors. These dependencies can vary within and across individuals also in relationship with external factors such as age, mental state, or disease severity. Motivated by this problem, we propose a novel neighbor selection approach based on Gaussian functional graphical models and functional-on-functional regression to identify which brain regions interact and how interaction strength changes with individual features or covariates (e.g., age or clinical status). Our approach is fully automated and data-driven, and, in principle, can handle any number of continuous and categorical covariates simultaneously. Unlike existing approaches, it also produces results that are easy to interpret: one can directly assess whether the strength of each estimated interaction increases or decreases as the value of a given covariate varies. We evaluate our method through extensive simulation experiments and an application to real EEG data. The results demonstrate clear advantages over existing approaches, including more accurate estimation of brain connections and reduced computational cost, especially in high-dimensional settings involving a large number of brain regions and large sample sizes.