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Nearest-Neighbor Radii under Dependent Sampling

arXiv 2605.14343 ↗First posted 14 May 2026cs.LG math.ST stat.MLcited by 0

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Abstract (arXiv)

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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References · 18

  1. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  2. 2024MOMENT: A Family of Open Time-series Foundation Modelscited by 482
  3. 2018The UCR Time Series Archivecited by 431
  4. 2019Intrinsic dimension of data representations in deep neural networkscited by 282
  5. 2021Monash Time Series Forecasting Archivecited by 267
  6. 2020Nearest Neighbor Machine Translationcited by 209
  7. 2021A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Searchcited by 82
  8. 2023TabR: Tabular Deep Learning Meets Nearest Neighbors in 2023cited by 74
  9. 2023kNN Prompting: Beyond-Context Learning with Calibration-Free Nearest Neighbor Inferencecited by 47
  10. 2019A simple measure of conditional dependencecited by 38
  11. 2023Why do Nearest Neighbor Language Models Work?cited by 29
  12. 2022Learning from many trajectoriescited by 24
6 more
  1. 2022RetrievalGuard: Provably Robust 1-Nearest Neighbor Image Retrievalcited by 15
  2. 2021On boosting the power of Chatterjee's rank correlationcited by 10
  3. 2024LoRANN: Low-Rank Matrix Factorization for Approximate Nearest Neighbor Searchcited by 4
  4. 2022Limit theorems of Chatterjee's rank correlationcited by 3
  5. 2023k-NNN: Nearest Neighbors of Neighbors for Anomaly Detectioncited by 3
  6. 2023MNN: Mixed Nearest-Neighbors for Self-Supervised Learningcited by 1

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