Gaussian process single-index models as emulators for computer experiments

TL;DR

This paper introduces a Gaussian process single-index model (GP-SIM) as an efficient emulator for computer experiments, simplifying Bayesian inference and demonstrating superior performance over traditional models on synthetic and real data.

Contribution

It simplifies and generalizes a Bayesian GP-SIM approach, providing practical tools and R packages for improved computer experiment emulation.

Findings

GP-SIM outperforms canonical separable GP models

Simplified Bayesian inference enhances computational efficiency

Effective on both synthetic and real-world data

Abstract

A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process (GP) formulation is simple to work with and ideal as an emulator for some types of computer experiment as it can outperform the canonical separable GP regression model commonly used in this setting. Our contribution focuses on drastically simplifying, re-interpreting, and then generalizing a recently proposed fully Bayesian GP-SIM combination, and then illustrating its favorable performance on synthetic data and a real-data computer experiment. Two R packages, both released on CRAN, have been augmented to facilitate inference under our proposed model(s).