[2104.03529] Inference of Gaussian Processes by Mattern Covariograms of Compact Riemannian Manifolds

Download the PDF of the paper titled Inference for Gaussian Processes with Mat\’ern Covariogram on Compact Riemannian Manifolds by Didong Li and one other author

Download PDF

overview: Gaussian processes are widely adopted as versatile modeling and prediction tools in a variety of applications in spatial statistics, functional data analysis, computer modeling, and machine learning. They have been extensively studied in Euclidean space, specified using covariance functions or covariate diagrams to model complex dependencies. There is a growing body of literature on Gaussian processes on Riemannian manifolds to develop richer and more flexible inference frameworks for non-Euclidean data. Numerical approximation via graph representation has been well studied for Matérn covariograms and heat kernels, but the behavior of asymptotic inference for covariogram parameters has received relatively little attention. We focus on asymptotic inference of Gaussian processes constructed on compact Riemannian manifolds. Based on the recently introduced Matteln covariogram on compact Riemannian manifolds, we use formal notions and conditions for the equality of two Matteln-Gaussian random measures on compact manifolds to find discernible parameters (microergodic parameters) to determine the consistency of the maximum likelihood estimation and the asymptotic optimality of the best linear unbiased predictor. Circles are studied as specific examples of compact Riemannian manifolds, and numerical experiments explain and support the theory.