Work

Optimizing Kernel Discrepancies via Subset Selection

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2511.02706

Authors: Chen, Deyao, Clément, François, Doerr, Carola, Kirk, Nathan

Institutions: University of St Andrews, University of Washington, Centre National de la Recherche Scientifique, Sorbonne Université, LIP6, Illinois Institute of Technology

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, European Commission, Sorbonne Université

Award: Collaborative Research: Cost-Efficient and Confident Sampling for Modern Scientific Discovery

OpenAlex ID: W7104054428

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