Developments in Functional Regression Model for Network Structured Data

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 assess predictive uncertainty, we develop a functional conformal prediction procedure that yields a distribution-free prediction interval 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.