A spectral approach for the design of experiments: Design, analysis and algorithms

Bhavya Kailkhura, Jayaraman J. Thiagarajan, Charvi Rastogi, Pramod Kumar Varshney, Peer Timo Bremer

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-of uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatial domain) to the quality metric of the design performance (defined in the spectral domain). This connection serves as an analytic framework for evaluating the qualitative properties of space-filling designs in general. Us- ing the theoretical insights provided by this spatial-spectral analysis, we derive the notion of optimal space-filling designs, which we refer to as space-filling spectral designs. Third, we propose an efficient estimator to evaluate the space-filling properties of sample designs in arbitrary dimensions and use it to develop an optimization framework for generating high quality space-filling designs. Finally, we carry out a detailed performance comparison on two different applications in varying dimensions: A) image reconstruction and b) surro- gate modeling for several benchmark optimization functions and a physics simulation code for inertial confinement fusion (ICF). Our results clearly evidence the superiority of the proposed space-filling designs over existing approaches, particularly in high dimensions.

Original languageEnglish (US)
JournalJournal of Machine Learning Research
Volume19
StatePublished - Aug 1 2018

Keywords

  • Design of experiments
  • Poisson-disk sampling
  • Regression
  • Space-filling
  • Surrogate modeling

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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