SF-SFD: Stochastic Optimization of Fourier Coefficients to Generate Space-Filling Designs

arXiv2305.12043MaRDI QIDQ6437292

Author name not available (Why is that?)

Publication date: 19 May 2023

Abstract: Due to the curse of dimensionality, it is often prohibitively expensive to generate deterministic space-filling designs. On the other hand, when using na{"i}ve uniform random sampling to generate designs cheaply, design points tend to concentrate in a small region of the design space. Although, it is preferable in these cases to utilize quasi-random techniques such as Sobol sequences and Latin hypercube designs over uniform random sampling in many settings, these methods have their own caveats especially in high-dimensional spaces. In this paper, we propose a technique that addresses the fundamental issue of measure concentration by updating high-dimensional distribution functions to produce better space-filling designs. Then, we show that our technique can outperform Latin hypercube sampling and Sobol sequences by the discrepancy metric while generating moderately-sized space-filling samples for high-dimensional problems.

Has companion code repository: https://github.com/sfdsampling/sfsfd

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