Theory and application of absolute discrepancy in experimental designs

Yao Xiao (), Hong Qin (), Kashinath Chatterjee () and Na Zou ()
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Yao Xiao: Beijing Institute of Technology
Hong Qin: Zhongnan University of Economics and Law
Kashinath Chatterjee: Visva-Bharati University
Na Zou: Zhongnan University of Economics and Law

Statistical Papers, 2024, vol. 65, issue 9, No 14, 5775-5795

Abstract: Abstract In many practical experiments, the number of possible levels for each experimental factor is often limited to a finite number. Various discrepancies, like discrete discrepancy and Lee discrepancy, have been proposed to measure the uniformity on the discrete experimental domain. However, these two discrepancies can yield unreasonable results when multiple levels are involved. In this paper, a new discrepancy, termed absolute discrepancy (AD), is proposed as a more reasonable measure of uniformity on a discrete experimental domain, particularly for discrete-numerical factors. Moreover, connections between AD and other design optimality criteria, such as generalized minimum aberration and orthogonality, are established. These connections provide strong statistical justification for AD. Some lower bounds of AD are also obtained, serving as important benchmarks for the design uniformity. In addition, uniform designs based on the AD criterion have produced better prediction performance by fitting statistical surrogate models of complex surfaces compared to their competitors. Furthermore, the application in hyperparameter optimization for machine learning algorithms also validates the superiority of uniform designs with the proposed AD criterion.

Keywords: Uniform designs; Discrepancy; Computer experiments; Hyperparameter optimization; 62K15; 62K99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01617-2

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