Exploring the Application of Gaussian Process Regression in Spatial and Functional Data Prediction

Posted: Feb 22, 2019

• Eric Jenkins
• Ethan Parker
• Eva Ramirez

Abstract

The integration of spatial and functional data analysis represents a significant frontier in statistical methodology and machine learning. Gaussian Process Regression (GPR) has emerged as a powerful framework for modeling complex relationships in various domains, yet its application to combined spatial-functional data remains underexplored. Traditional approaches often treat spatial and functional components separately, leading to suboptimal models that fail to capture the intricate interplay between these dimensions. This research addresses this gap by developing a unified GPR framework that simultaneously models spatial dependencies and functional relationships. Our work is motivated by the increasing availability of datasets that exhibit both spatial structure and functional characteristics. Examples include environmental monitoring networks that track pollutant concentrations over time across geographic locations, agricultural field trials measuring crop growth curves at different spatial positions, and neurological studies recording brain activity patterns across electrode arrays over time. In each case, the spatial arrangement of measurement points and the functional nature of the recorded signals are intrinsically linked, necessitating methodologies that can handle both aspects concurrently. This paper makes several key contributions. First, we develop a novel covariance structure that integrates spatial kernel functions with functional basis representations, enabling the model to capture complex spatio-functional patterns. Second, we introduce an adaptive bandwidth selection technique that dynamically adjusts to local data density, overcoming limitations of traditional fixed-bandwidth approaches. Third, we demonstrate the practical utility of our