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.

翻译：由于维数灾难，生成确定性空间填充设计通常代价高昂。另一方面，当使用朴素均匀随机采样廉价生成设计时，设计点往往集中在设计空间的较小区域内。尽管在这些情况下，相比均匀随机采样，采用拟随机技术（如Sobol序列和拉丁超立方体设计）更为可取，但这些方法在高维空间中存在自身局限性。本文提出一种通过更新高维分布函数来解决度量集中这一根本问题的技术，以生成更优的空间填充设计。随后，我们证明该技术在生成中等规模高维空间填充样本时，能够在偏差度量指标上优于拉丁超立方体采样和Sobol序列。