An accuracy-runtime trade-off comparison of scalable Gaussian process approximations for spatial data

TL;DR

This paper systematically compares various scalable Gaussian process approximation methods, evaluating their accuracy and computational efficiency on simulated and real-world spatial data.

Contribution

It provides a comprehensive analysis of the accuracy-runtime trade-offs of different GP approximations, highlighting Vecchia methods as consistently effective.

Findings

Vecchia approximations offer the best accuracy-runtime trade-off in most scenarios.

The study evaluates the impact of approximation methods on likelihood, estimation, and prediction.

Large-scale data sets demonstrate the practical advantages of specific GP approximations.

Abstract

Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$ memory complexity, which makes them prohibitive for large data sets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations with respect to likelihood evaluation, parameter estimation, and prediction, explicitly accounting for the computational time required. We analyze the trade-off between accuracy and runtime on multiple simulated and large-scale real-world data sets and find that Vecchia approximations consistently provide the best accuracy-runtime trade-off across most settings considered.