A neighbour selection approach for identifying differential networks in conditional functional graphical models

Estimation of brain functional connectivity from EEG data is of great importance both for medical research and diagnosis. It involves quantifying the conditional dependencies among the activity of different brain areas from the time-varying electric field recorded by sensors placed outside the scalp. These dependencies may vary within and across individuals and be influenced by covariates such as age, mental status, or disease severity. Motivated by this problem, we propose a novel neighbour selection approach based on functional-on-functional regression for the characterization of conditional Gaussian functional graphical models. We provide a fully automated, data-driven procedure for inferring conditional dependence structures among observed functional variables. In particular, pairwise interactions are directly identified and allowed to vary as a function of covariates, enabling covariate-specific modulation of connectivity patterns. Our proposed method accommodates an arbitrary number of continuous and discrete covariates. Moreover, unlike existing methods for direct estimation of differential graphical models, the proposed approach yields directly interpretable coefficients, allowing discrimination between covariate-induced increases and decreases in interaction strength. The methodology is evaluated through extensive simulation studies and an application to experimental EEG data. The results demonstrate clear advantages over existing approaches, including higher estimation accuracy and substantially reduced computational cost, especially in high-dimensional settings.