通过子集选择优化核差异，生成低差异采样点。
Optimizing Kernel Discrepancies via Subset Selection
- 提出新算法，从大样本中高效选小样本以降低核差异。
- 在单位超立方体和一般分布上均实现低差异采样。
- 适用于需要高质量采样的数值积分与机器学习任务。
核差异是分析准蒙特卡洛（QMC）方法最坏情况误差的强大工具。基于近期对这类差异度量的优化进展，我们将子集选择问题拓展至核差异场景，从规模 $n o m$ 的大规模群体中选取大小为 $m$ 的子集。提出一种适用于通用核差异的新子集选择算法，能高效生成来自单位超立方体（经典QMC设置）及具有已知密度函数的更一般分布 $F$ 的低差异样本，采用核Stein差异实现。同时探讨了经典 $L_2$ 星差异与其 $L_ ty$ 对应项之间的关系。
原文摘要 · Abstract (English)
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of kernel discrepancies, selecting an m-element subset from a large population of size $n \gg m$. We introduce a novel subset selection algorithm applicable to general kernel discrepancies to efficiently generate low-discrepancy samples from both the uniform distribution on the unit hypercube, the traditional setting of classical QMC, and from more general distributions $F$ with known density functions by employing the kernel Stein discrepancy. We also explore the relationship between the classical $L_2$ star discrepancy and its $L_\infty$ counterpart.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。