Scalable Computations for Nonstationary Gaussian Processes

TL;DR

This paper introduces a scalable computational framework combining block-diagonal plus low-rank covariance approximation with stochastic trace estimation, enabling efficient maximum likelihood estimation for large nonstationary Gaussian process models with many parameters.

Contribution

It presents a novel computational approach that significantly improves the efficiency of fitting complex nonstationary Gaussian process models with numerous parameters.

Findings

Successfully fitted 192 parameters in a nonstationary model.

Handled 107,600 sea surface temperature measurements efficiently.

Demonstrated scalability and effectiveness of the proposed methods.

Abstract

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods can be slow to converge when estimating many spatially varying parameters. We present here a computational framework that couples an algebraic block-diagonal plus low-rank covariance matrix approximation with stochastic trace estimation to facilitate the efficient use of second-order solvers for maximum likelihood estimation of Gaussian process models with many parameters. We demonstrate the effectiveness of these methods by simultaneously fitting 192 parameters in the popular nonstationary model of Paciorek and Schervish using 107,600 sea surface temperature anomaly measurements.