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

Manisha Garg; Tyler Chang; Krishnan Raghavan

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arXiv · 2305.12043

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

Manisha Garg·Tyler Chang·Krishnan Raghavan

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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.

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BibTeX RIS

Manisha Garg, Tyler Chang, Krishnan Raghavan. 2023-05-20. SF-SFD: Stochastic Optimization of Fourier Coefficients to Generate Space-Filling Designs. https://arxiv.org/abs/2305.12043

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