Optimizing Kernel Discrepancies via Subset Selection

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 L2 star discrepancy and its L_∞ counterpart.