Advances in functional regression for network-structured data

We propose a Network-Weighted Functional Regression (NWFR) model, a rigorous extension of Spatially Weighted Functional Regression (SWFR) that directly addresses the challenges of functional data distributed over complex, network-structured domains. Unlike traditional methods limited to spatial or Euclidean contexts, NWFR is designed to capture the often irregular dependencies embedded in real-world networks. To rigorously quantify predictive uncertainty in such settings, we develop a functional conformal prediction framework that delivers distribution-free prediction intervals with guaranteed coverage. Through comprehensive evaluations on both simulated and real-world datasets, we show that explicitly modeling network complexity leads to accuracy and improves the validity of the resulting prediction intervals.