Nearest-Neighbor Radii under Dependent Sampling
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911684105338880 |
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| author | Gao, Yuanyuan Hou, Yilong Lin, Zhexiao |
| author_facet | Gao, Yuanyuan Hou, Yilong Lin, Zhexiao |
| contents | Nearest-neighbor methods are fundamental to classical and modern machine learning, yet their geometric properties are typically analyzed under independent sampling. In this paper, we study the nearest-neighbor radii under dependent sampling. We consider strong mixing dependent observations and ask whether dependence changes the scale of nearest-neighbor neighborhoods. We establish distribution-free almost sure convergence under polynomial mixing and sharp non-asymptotic moment bounds under geometric mixing. The moment bounds depend on the local intrinsic dimension rather than the ambient dimension, making the results applicable to high-dimensional data concentrated near lower-dimensional manifolds. Synthetic experiments and real-world time-series benchmarks support the theory, showing that nearest-neighbor geometry remains informative under dependence sampling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14343 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nearest-Neighbor Radii under Dependent Sampling Gao, Yuanyuan Hou, Yilong Lin, Zhexiao Machine Learning Statistics Theory Nearest-neighbor methods are fundamental to classical and modern machine learning, yet their geometric properties are typically analyzed under independent sampling. In this paper, we study the nearest-neighbor radii under dependent sampling. We consider strong mixing dependent observations and ask whether dependence changes the scale of nearest-neighbor neighborhoods. We establish distribution-free almost sure convergence under polynomial mixing and sharp non-asymptotic moment bounds under geometric mixing. The moment bounds depend on the local intrinsic dimension rather than the ambient dimension, making the results applicable to high-dimensional data concentrated near lower-dimensional manifolds. Synthetic experiments and real-world time-series benchmarks support the theory, showing that nearest-neighbor geometry remains informative under dependence sampling. |
| title | Nearest-Neighbor Radii under Dependent Sampling |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2605.14343 |