Fast increased fidelity samplers for approximate Bayesian Gaussian process regression

• 成果类型: Article
• 署名作者: Moran, Kelly R.; Wheeler, Matthew W.
• 署名单位: United States Department of Energy (DOE); Los Alamos National Laboratory; National Institutes of Health (NIH) - USA; NIH National Institute of Environmental Health Sciences (NIEHS)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12494
• 发表日期: 2022
• 页码: 1198-1228
• 关键词: process models; hierarchical matrices; algorithms; computation

摘要

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H-matrix approximations that scales at O(nlog2n). We show that this approximation's Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Although multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modelled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets.