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

TL;DR

This paper introduces a Network-Weighted Functional Regression model that explicitly incorporates network structure into functional data analysis, improving prediction accuracy and interval validity.

Contribution

It extends existing spatially weighted models to network settings and develops a conformal prediction method for uncertainty quantification.

Findings

Network modeling improves point prediction accuracy.

Conformal prediction provides valid, distribution-free prediction intervals.

Method performs well on simulated and real datasets.

Abstract

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.