GPfit: An R package for Gaussian Process Model Fitting using a New Optimization Algorithm

TL;DR

GPfit is an R package that offers a robust and faster method for fitting Gaussian process models to deterministic simulators, improving stability and efficiency over previous approaches.

Contribution

It introduces a novel parameterization and a gradient-based optimization algorithm for Gaussian process fitting, enhancing robustness and speed compared to genetic algorithm methods.

Findings

GPfit outperforms mlegp in speed and stability.

The new optimization approach is robust for close design points.

Examples demonstrate practical application and improved performance.

Abstract

Gaussian process (GP) models are commonly used statistical metamodels for emulating expensive computer simulators. Fitting a GP model can be numerically unstable if any pair of design points in the input space are close together. Ranjan, Haynes, and Karsten (2011) proposed a computationally stable approach for fitting GP models to deterministic computer simulators. They used a genetic algorithm based approach that is robust but computationally intensive for maximizing the likelihood. This paper implements a slightly modified version of the model proposed by Ranjan et al. (2011), as the new R package GPfit. A novel parameterization of the spatial correlation function and a new multi-start gradient based optimization algorithm yield optimization that is robust and typically faster than the genetic algorithm based approach. We present two examples with R codes to illustrate the usage of the main functions in GPfit. Several test functions are used for performance comparison with a popular R package mlegp. GPfit is a free software and distributed under the general public license, as part of the R software project (R Development Core Team 2012).