Scaled Vecchia approximation for fast computer-model emulation
This work addresses the challenge of analyzing large-scale computer experiments for researchers in fields like engineering and science, offering a scalable emulation method that is incremental in its adaptation of spatial statistics techniques.
The authors tackled the computational infeasibility of Gaussian process inference for large computer experiments by adapting Vecchia's approximation with learned input scaling, achieving near-linear time scalability and outperforming existing methods in numerical examples.
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.