Nearest-Neighbor Radii under Dependent Sampling
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 ...
| Authors | Yuanyuan Gao, Yilong Hou, Zhexiao Lin |
|---|---|
| Primary category | cs.LG |
| Published | 14 May 2026 |
| Last updated at source | 14 May 2026 |
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