Scaled Vecchia approximation for fast computer-model emulation

2020/05/01 by Matthias Katzfuß, Joseph Guinness, Katzfuss, Matthias +3 · 8 citations
Computer Science · #Advanced Multi-Objective Optimization Algorithms #Computation (stat.CO) #Data Analysis with R #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (stat.ML) #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2005.00386

openalex publication_date 2020/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia's ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data, by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.

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