Network Weighted Functional Regression: a method for modeling dependencies between functional data in a network

In this paper, we propose a Network-Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network-structured settings. To asses predictive uncertainity, we develop a functional conformal prediction procedure that yields a distribution free prediction intervals with guaranteed coverage. Through extensive evaluation on both simulated and real-world datasets, we demonstrate that the explicit modeling of network structure yields substantive improvements in point-prediction accuracy and markedly enhances the validity and precision of the resulting prediction intervals.