Maximum projection designs for computer experiments
Abstract
Space-filling properties are important in designing computer experiments. The traditional maximin and minimax distance designs only consider space-filling in the full dimensional space. This can result in poor projections onto lower dimensional spaces, which is undesirable when only a few factors are active. Restricting maximin distance design to the class of Latin hypercubes can improve one-dimensional projections, but cannot guarantee good space-filling properties in larger subspaces. We propose designs that maximize space-filling properties on projections to all subsets of factors. We call our designs maximum projection designs. As a result, our design criterion can be computed at a cost no more than a design criterion that ignores projection properties.
- Authors:
-
- Georgia Inst. of Technology, Atlanta, GA (United States)
- The Procter & Gamble Co., Mason, OH (United States)
- Publication Date:
- Research Org.:
- Georgia Institute of Technology, Atlanta, GA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1405144
- Report Number(s):
- DOE-GT-0010548-3
Journal ID: ISSN 0006-3444; FG02-13ER26159
- Grant/Contract Number:
- SC0010548
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Biometrika
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 2; Journal ID: ISSN 0006-3444
- Publisher:
- Oxford University Press
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Experimental design; Gaussian process; Latin hypercube design; Screening design; Space-filling design
Citation Formats
Joseph, V. Roshan, Gul, Evren, and Ba, Shan. Maximum projection designs for computer experiments. United States: N. p., 2015.
Web. doi:10.1093/biomet/asv002.
Joseph, V. Roshan, Gul, Evren, & Ba, Shan. Maximum projection designs for computer experiments. United States. https://doi.org/10.1093/biomet/asv002
Joseph, V. Roshan, Gul, Evren, and Ba, Shan. Wed .
"Maximum projection designs for computer experiments". United States. https://doi.org/10.1093/biomet/asv002. https://www.osti.gov/servlets/purl/1405144.
@article{osti_1405144,
title = {Maximum projection designs for computer experiments},
author = {Joseph, V. Roshan and Gul, Evren and Ba, Shan},
abstractNote = {Space-filling properties are important in designing computer experiments. The traditional maximin and minimax distance designs only consider space-filling in the full dimensional space. This can result in poor projections onto lower dimensional spaces, which is undesirable when only a few factors are active. Restricting maximin distance design to the class of Latin hypercubes can improve one-dimensional projections, but cannot guarantee good space-filling properties in larger subspaces. We propose designs that maximize space-filling properties on projections to all subsets of factors. We call our designs maximum projection designs. As a result, our design criterion can be computed at a cost no more than a design criterion that ignores projection properties.},
doi = {10.1093/biomet/asv002},
journal = {Biometrika},
number = 2,
volume = 102,
place = {United States},
year = {Wed Mar 18 00:00:00 EDT 2015},
month = {Wed Mar 18 00:00:00 EDT 2015}
}
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Figures / Tables:
Fig. 1: Plot of Mmq (larger-the-better) against q for maximum projection (squares), maximum projection Latin hypercube (triangles), maximin Latin hypercube (circles), uniform (pluses), and generalized maximin Latin hypercube(crosses) designs.
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Works referenced in this record:
Algorithms for Generating Maximin Latin Hypercube and Orthogonal Designs
journal, March 2011
- Moon, Hyejung; Dean, Angela; Santner, Thomas
- Journal of Statistical Theory and Practice, Vol. 5, Issue 1
Design and analysis of computer experiments
conference, September 1998
- Booker, Andrew
- 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization
Noncollapsing Space-Filling Designs for Bounded Nonrectangular Regions
journal, May 2012
- Draguljić, Danel; Santner, Thomas J.; Dean, Angela M.
- Technometrics, Vol. 54, Issue 2
Design and analysis of computer experiments
journal, December 2010
- Kuhnt, Sonja; Steinberg, David M.
- AStA Advances in Statistical Analysis, Vol. 94, Issue 4
Generalized latin hypercube design for computer experiments
text, January 2009
- Dette, Holger; Pepelyshev, Andrey
- Technische Universität Dortmund
Orthogonal Array-Based Latin Hypercubes
journal, December 1993
- Tang, Boxin
- Journal of the American Statistical Association, Vol. 88, Issue 424
Generalized Latin Hypercube Design for Computer Experiments
journal, November 2010
- Dette, Holger; Pepelyshev, Andrey
- Technometrics, Vol. 52, Issue 4
Exploratory designs for computational experiments
journal, February 1995
- Morris, Max D.; Mitchell, Toby J.
- Journal of Statistical Planning and Inference, Vol. 43, Issue 3
A generalized discrepancy and quadrature error bound
journal, January 1998
- Hickernell, Fred J.
- Mathematics of Computation of the American Mathematical Society, Vol. 67, Issue 221
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code
journal, May 1979
- McKay, M. D.; Beckman, R. J.; Conover, W. J.
- Technometrics, Vol. 21, Issue 2
Design and Analysis of Computer Experiments
journal, November 1989
- Sacks, Jerome; Welch, William J.; Mitchell, Toby J.
- Statistical Science, Vol. 4, Issue 4
Maximum entropy sampling
journal, January 1987
- Shewry, M. C.; Wynn, H. P.
- Journal of Applied Statistics, Vol. 14, Issue 2
Minimax and maximin distance designs
journal, October 1990
- Johnson, M. E.; Moore, L. M.; Ylvisaker, D.
- Journal of Statistical Planning and Inference, Vol. 26, Issue 2
A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code
journal, February 2000
- Mckay, M. D.; Beckman, R. J.; Conover, W. J.
- Technometrics, Vol. 42, Issue 1
Works referencing / citing this record:
Space-filling designs for computer experiments: A review
journal, January 2016
- Joseph, V. Roshan
- Quality Engineering, Vol. 28, Issue 1
On the road to per cent accuracy – II. Calibration of the non-linear matter power spectrum for arbitrary cosmologies
journal, September 2019
- Giblin, Benjamin; Cataneo, Matteo; Moews, Ben
- Monthly Notices of the Royal Astronomical Society, Vol. 490, Issue 4
The importance of thermal modelling and prototyping in shelter design
text, January 2020
- Fosas, D.; Moran, F.; Natarajan, S.
- Apollo - University of Cambridge Repository
Advanced Methodology for Uncertainty Propagation in Computer Experiments with Large Number of Inputs
journal, March 2019
- Iooss, Bertrand; Marrel, Amandine
- Nuclear Technology, Vol. 205, Issue 12
Space-Filling Designs for Robustness Experiments
journal, June 2018
- Joseph, V. Roshan; Gu, Li; Ba, Shan
- Technometrics, Vol. 61, Issue 1
Controlling Sources of Inaccuracy in Stochastic Kriging
preprint, January 2017
- Wang, Wenjia; Haaland, Benjamin
- arXiv
The importance of thermal modelling and prototyping in shelter design
journal, November 2019
- Fosas, Daniel; Moran, Francis; Natarajan, Sukumar
- Building Research & Information, Vol. 48, Issue 4
An Efficient Surrogate Model for Emulation and Physics Extraction of Large Eddy Simulations
journal, June 2018
- Mak, Simon; Sung, Chih-Li; Wang, Xingjian
- Journal of the American Statistical Association, Vol. 113, Issue 524
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs
text, January 2019
- Joseph, V. Roshan; Wang, Dianpeng; Gu, Li
- Taylor & Francis
Minimax and minimax projection designs using clustering
preprint, January 2016
- Mak, Simon; Joseph, V. Roshan
- arXiv
Kernel-Smoothed Proper Orthogonal Decomposition–Based Emulation for Spatiotemporally Evolving Flow Dynamics Prediction
journal, December 2019
- Chang, Yu-Hung; Zhang, Liwei; Wang, Xingjian
- AIAA Journal, Vol. 57, Issue 12
Global Fitting of the Response Surface via Estimating Multiple Contours of a Simulator
journal, December 2019
- Yang, F.; Lin, C. Devon; Ranjan, P.
- Journal of Statistical Theory and Practice, Vol. 14, Issue 1
Controlling Sources of Inaccuracy in Stochastic Kriging
journal, October 2018
- Wang, Wenjia; Haaland, Benjamin
- Technometrics, Vol. 61, Issue 3
Advanced methodology for uncertainty propagation in computer experiments with large number of inputs
book, June 2018
- Marrel, A.; Iooss, B.
- Safety and Reliability – Safe Societies in a Changing World
Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints
journal, December 2018
- Piepel, Greg F.; Stanfill, Bryan A.; Cooley, Scott K.
- Quality Engineering, Vol. 31, Issue 3
Design and analysis of computer experiments with quantitative and qualitative inputs: A selective review
journal, February 2020
- Kang, Xiaoning; Deng, Xinwei
- WIREs Data Mining and Knowledge Discovery, Vol. 10, Issue 3
Nonintrusive approximation of parametrized limits of matrix power algorithms – application to matrix inverses and log-determinants
journal, January 2019
- Casenave, Fabien; Akkari, Nissrine; Charles, Alexandre
- ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 53, Issue 1
Variable selection using Gaussian process regression-based metrics for high-dimensional model approximation with limited data
journal, November 2018
- Lee, Kyungeun; Cho, Hyunkyoo; Lee, Ikjin
- Structural and Multidisciplinary Optimization, Vol. 59, Issue 5
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs
journal, March 2019
- Joseph, V. Roshan; Wang, Dianpeng; Gu, Li
- Technometrics, Vol. 61, Issue 3
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs
text, January 2019
- Joseph, V. Roshan; Wang, Dianpeng; Gu, Li
- Taylor & Francis
On the road to percent accuracy II: calibration of the non-linear matter power spectrum for arbitrary cosmologies
text, January 2019
- Giblin, Benjamin; Cataneo, Matteo; Moews, Ben
- arXiv
Stochastic coordinate-exchange optimal designs with complex constraints
journal, December 2018
- Kang, Lulu
- Quality Engineering, Vol. 31, Issue 3
Rotated Sphere Packing Designs
journal, July 2017
- He, Xu
- Journal of the American Statistical Association, Vol. 112, Issue 520
Deterministic Sampling of Expensive Posteriors Using Minimum Energy Designs
text, January 2018
- Joseph, V. Roshan; Wang, Dianpeng; Gu, Li
- Taylor & Francis
Space-Filling Designs for Robustness Experiments
text, January 2017
- Joseph, V. Roshan; Gu, Li; Ba, Shan
- arXiv
Minimax and Minimax Projection Designs Using Clustering
journal, July 2017
- Mak, Simon; Joseph, V. Roshan
- Journal of Computational and Graphical Statistics, Vol. 27, Issue 1
Uncertainty quantification of machining simulations using an in situ emulator
journal, July 2018
- Gul, Evren; Joseph, V. Roshan; Yan, Huan
- Journal of Quality Technology, Vol. 50, Issue 3
Surrogate model–based optimal feed-forward control for dimensional-variation reduction in composite parts' assembly processes
journal, July 2018
- Yue, Xiaowei; Shi, Jianjun
- Journal of Quality Technology, Vol. 50, Issue 3
Bi-criteria multiple knapsack problem with grouped items
journal, June 2021
- Castillo-Zunino, Francisco; Keskinocak, Pinar
- Journal of Heuristics, Vol. 27, Issue 5
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