A Global-Local Approximation Framework for Large-Scale Gaussian Process Modeling

Abstract

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ a combined global-local approach in building the approximation. Our framework uses a subset-of-data approach where the subset is a union of a set of global points designed to capture the global trend in the data, and a set of local points specific to a given testing location to capture the local trend around the testing location. The correlation function is also modeled as a combination of a global, and a local kernel. The predictive performance of our framework, which we refer to as TwinGP, is comparable to the state-of-the-art GP modeling methods, but at a fraction of their computational cost.

KEYWORDS:

• Big data
• Computer experiments
• Emulation
• Inducing points
• Kriging
• Nonparametric regression

Supplementary Materials

The zip file contains the R codes and data to reproduce part of the results in Figure 7. The R package twingp can be downloaded from GitHub (Vakayil and Joseph 2023).

Disclosure Statement

The authors report that there are no competing interests to declare.

Additional information

Funding

This research is supported by U.S. National Science Foundation grants CMMI-1921646 and DMREF-1921873.