Dimension-independent convergence rates of randomized nets using median-of-means
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914296782389248 |
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| author | Pan, Zexin |
| author_facet | Pan, Zexin |
| contents | Recent advances in quasi-Monte Carlo integration demonstrate that the median of linearly scrambled digital net estimators achieves near-optimal convergence rates for high-dimensional integrals without requiring a priori knowledge of the integrand's smoothness. Building on this framework, we prove that the median estimator attains dimension-independent convergence, a property known as strong tractability in complexity theory, under tractability conditions characterized by low effective dimensionality. Using a probabilistic, integrand-specific error criterion, our analysis establishes both faster and dimension-independent convergence under weaker assumptions than previously possible in the worst-case setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_13815 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension-independent convergence rates of randomized nets using median-of-means Pan, Zexin Computation Numerical Analysis Recent advances in quasi-Monte Carlo integration demonstrate that the median of linearly scrambled digital net estimators achieves near-optimal convergence rates for high-dimensional integrals without requiring a priori knowledge of the integrand's smoothness. Building on this framework, we prove that the median estimator attains dimension-independent convergence, a property known as strong tractability in complexity theory, under tractability conditions characterized by low effective dimensionality. Using a probabilistic, integrand-specific error criterion, our analysis establishes both faster and dimension-independent convergence under weaker assumptions than previously possible in the worst-case setting. |
| title | Dimension-independent convergence rates of randomized nets using median-of-means |
| topic | Computation Numerical Analysis |
| url | https://arxiv.org/abs/2505.13815 |