Optimizing Kernel Discrepancies via Subset Selection

Deyao Chen; François Clément; Carola Doerr; Nathan Kirk

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arXiv · 2511.02706

Optimizing Kernel Discrepancies via Subset Selection

Deyao Chen·François Clément·Carola Doerr·Nathan Kirk

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Abstract

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.

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stat.ML cs.CG cs.LG cs.NA math.NA

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BibTeX RIS

Deyao Chen, François Clément, Carola Doerr, Nathan Kirk. 2025-11-04. Optimizing Kernel Discrepancies via Subset Selection. https://arxiv.org/abs/2511.02706

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