Mixed-input Gaussian process emulators for computer experiments with a large number of categorical levels

Abstract

Computer models with both quantitative and qualitative inputs frequently arise in science, engineering and business. Mixed-input Gaussian process models have been used for emulating such models. The key in building this emulator is to accurately estimate the covariance between different categorical levels of the qualitative inputs. This problem is challenging when the number of categorical levels is large. We propose a sparse covariance estimation approach to estimating the covariance matrix with a large number of categorical levels for the mixed-input Gaussian process emulator. The effectiveness of this approach is illustrated with an application of IO operation modes in high performance computing systems.

Keywords:

• computer experiments
• qualitative and quantitative inputs
• uncertainty quantification

Acknowledgments

The authors would like to thank the Editor, Associate Editor and two reviewers for their comments and suggestions that have led to improvement of this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Chien is supported by NSF Grant DMS 1564376. The work by Xu and Hong was partially supported by funds from NSF under Grant CNS-1565314 and CNS-1838271 to Virginia Tech.

Notes on contributors

Qiong Zhang

Qiong Zhang is an Assistant Professor in Statistics at Clemson University, Clemson, SC.

Peter Chien

Peter Chien is a Professor in Statistics at the University of Wisconsin-Madison.

Qing Liu

Qing Liu is an Associate Professor in Marketing at the University of Wisconsin-Madison, WI.

Li Xu

Li Xu is a fourth year PhD student in the department of statistics at Virginia Tech.

Yili Hong

Yili Hong is an Associate Professor of Statistics at Virginia Tech. His research interests include machine learning and engineering applications, reliability analysis, and spatial statistics.