Optimizing Kernel Discrepancies via Subset Selection
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911248655843328 |
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| author | Chen, Deyao Clément, François Doerr, Carola Kirk, Nathan |
| author_facet | Chen, Deyao Clément, François Doerr, Carola Kirk, Nathan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimizing Kernel Discrepancies via Subset Selection Chen, Deyao Clément, François Doerr, Carola Kirk, Nathan Machine Learning Computational Geometry Numerical Analysis 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. |
| title | Optimizing Kernel Discrepancies via Subset Selection |
| topic | Machine Learning Computational Geometry Numerical Analysis |
| url | https://arxiv.org/abs/2511.02706 |