Large-Scale Low-Rank Gaussian Process Prediction with Support Points

• 成果类型: Article
• 署名作者: Song, Yan; Dai, Wenlin; Genton, Marc G.
• 署名单位: Renmin University of China; King Abdullah University of Science & Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2403188
• 发表日期: 2025
• 页码: 1189-1200
• 关键词: spatial sampling design; process regression; approximation; geostatistics; likelihoods

摘要

Low-rank approximation is a popular strategy to tackle the big n problem associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified. Predictive processes simplify the problem by inducing basis functions with a covariance function and a set of knots. The existing literature suggests certain practical implementations of knot selection and covariance estimation; however, theoretical foundations explaining the influence of these two factors on predictive processes are lacking. In this article, the asymptotic prediction performance of the predictive process and Gaussian process predictions are derived and the impacts of the selected knots and estimated covariance are studied. The use of support points as knots, which best represent data locations, is advocated. Extensive simulation studies demonstrate the superiority of support points and verify our theoretical results. Real data of precipitation and ozone are used as examples, and the efficiency of our method over other widely used low-rank approximation methods is verified. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.