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arXiv · 2605.14343

Nearest-Neighbor Radii under Dependent Sampling

Yuanyuan Gao·Yilong Hou·Zhexiao Lin
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Abstract

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.

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Yuanyuan Gao, Yilong Hou, Zhexiao Lin. 2026-05-14. Nearest-Neighbor Radii under Dependent Sampling. https://arxiv.org/abs/2605.14343

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