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的成本往往过高。另一方面，当使用朴素均匀随机采样廉价生成设计时，设计点往往集中于设计空间的某一小区域内。尽管在此类情况下，使用Sobol序列和拉丁超立方设计等准随机技术比均匀随机采样更优，但这些方法在高维空间中存在自身局限性。本文提出一种技术，通过更新高维分布函数以改善测度集中这一根本问题，从而生成更优的空间填充设计。我们证明，在生成中等规模的高维问题空间填充样本时，本技术能在差异度量指标上优于拉丁超立方采样和Sobol序列。