{"ID":2846293,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.02706","arxiv_id":"2511.02706","title":"Optimizing Kernel Discrepancies via Subset Selection","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.","short_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 $...","url_abs":"https://arxiv.org/abs/2511.02706","url_pdf":"https://arxiv.org/pdf/2511.02706v1","authors":"[\"Deyao Chen\",\"François Clément\",\"Carola Doerr\",\"Nathan Kirk\"]","published":"2025-11-04T16:25:08Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.CG\",\"cs.LG\",\"math.NA\"]","methods":"[]","has_code":false}