2025/11/04 by Chen, Deyao, Clément, François, Doerr, Carola +1
Decision Sciences · Mathematics · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design
paper · doi:10.48550/arxiv.2511.02706
openalex publication_date 2025/11/04 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
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 ≫ 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 L2 star discrepancy and its L_∞ counterpart.