Construction of orthogonal-MaxPro Latin hypercube designs

Abstract

Orthogonal Latin hypercube designs (LHDs) and maximum projection (MaxPro) LHDs are widely used in computer experiments. They are efficient for estimating the trend part and the Gaussian process part of the universal Kriging (i.e., the Gaussian process) model, respectively, especially when only some of the factors are active. Yet, the orthogonality and the MaxPro criteria often do not agree with each other. In this work, we propose a new class of optimal designs, called orthogonal-MaxPro LHDs, optimizing a well-defined multi-objective criterion combining the correlation and the MaxPro metrics. An efficient parallel algorithm via level permutations and expansions is developed, whose efficiency is guaranteed by theories. Numerical results are presented to show that the construction is fast and the obtained designs are attractive, especially for large computer experiments.

Keywords:

• computer experiment
• maximum projection criterion
• orthogonality
• space-filling design

Acknowledgments

The authors thank the editor, associate editor, and reviewers for their constructive comments that significantly improved the manuscript.

Data availability statement

In this paper, all data were simulated using the code provided.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China Nos. 12271166 and 32030063, Young Elite Scientists Sponsorship Program by CAST No. 2022QNRC001, and Natural Science Foundation of Beijing No. 1244041.

Notes on contributors

Yaping Wang

Dr. Yaping Wang received his Ph.D. degree in Probability and Statistics from Peking University (Beijing, China) in 2018. Currently, he is a research fellow at School of Statistics, East China Normal University (Shanghai, China). His research focuses on experimental design, computer experiment, screening experiment and response surface experiment. His email address is [email protected].

Sixu Liu

Dr. Sixu Liu received her Ph.D. degree in Mathematics from Peking University (Beijing, China) in 2019. Currently, she is an assistant professor at Beijing Institute of Mathematical Sciences and Applications (Beijing, China). Her main research interests include dynamical systems and ergodic theory, as well as statistical experimental design. Her email address is [email protected].

Qian Xiao

Dr. Qian Xiao received his Ph.D. degree in Statistics from University of California Los Angeles (CA, USA) in 2017. He joined Dept. of Statistics at University of Georgia (GA, USA) as an Assistant Professor (2017 to 2023) and an Associate Professor with tenure (2023-2024). Effective from July 2024, he is an Associate Professor with tenure in the Dept. of Statistics at Shanghai Jiao Tong University (Shanghai, China). His research focuses on the interface between experimental design and machine learning. He can be reached via email [email protected].