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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.00202 |
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| _version_ | 1866914377287860224 |
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| author | Xu, Xiaoda |
| author_facet | Xu, Xiaoda |
| contents | We study the expected star discrepancy under a newly designed class of non-equal volume partitions. The main contributions are twofold. First, we establish a strong partition principle for the star discrepancy, showing that our newly designed non-equal volume partitions yield stratified sampling point sets with lower expected star discrepancy than classical jittered sampling. Specifically, we prove that $\mathbb{E}(D^{*}_{N}(Z)) < \mathbb{E}(D^{*}_{N}(Y))$, where $Y$ and $Z$ represent jittered sampling and our non-equal volume partition sampling, respectively. Second, we derive explicit upper bounds for the expected star discrepancy under our non-equal volume partition models, which improve upon existing bounds for jittered sampling. Our results provide a theoretical foundation for using non-equal volume partitions in high-dimensional numerical integration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00202 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Partition Principle Revisited: Non-Equal Volume Designs Achieve Minimal Expected Star Discrepancy Xu, Xiaoda Machine Learning Probability We study the expected star discrepancy under a newly designed class of non-equal volume partitions. The main contributions are twofold. First, we establish a strong partition principle for the star discrepancy, showing that our newly designed non-equal volume partitions yield stratified sampling point sets with lower expected star discrepancy than classical jittered sampling. Specifically, we prove that $\mathbb{E}(D^{*}_{N}(Z)) < \mathbb{E}(D^{*}_{N}(Y))$, where $Y$ and $Z$ represent jittered sampling and our non-equal volume partition sampling, respectively. Second, we derive explicit upper bounds for the expected star discrepancy under our non-equal volume partition models, which improve upon existing bounds for jittered sampling. Our results provide a theoretical foundation for using non-equal volume partitions in high-dimensional numerical integration. |
| title | The Partition Principle Revisited: Non-Equal Volume Designs Achieve Minimal Expected Star Discrepancy |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2603.00202 |