# Nearest-Neighbor Radii under Dependent Sampling

arXiv: https://arxiv.org/abs/2605.14343 · HTML: https://mlsanity.com/paper/2605.14343/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 59 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 18 of 18)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Nearest Neighbor Machine Translation](https://mlsanity.com/paper/2010.00710/) (2020)
- [A Comprehensive Survey and Experimental Comparison of Graph-Based Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2101.12631/) (2021)
- [TabR: Tabular Deep Learning Meets Nearest Neighbors in 2023](https://mlsanity.com/paper/2307.14338/) (2023)
- [kNN Prompting: Beyond-Context Learning with Calibration-Free Nearest Neighbor Inference](https://mlsanity.com/paper/2303.13824/) (2023)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Why do Nearest Neighbor Language Models Work?](https://mlsanity.com/paper/2301.02828/) (2023)
- [Learning from many trajectories](https://mlsanity.com/paper/2203.17193/) (2022)
- [RetrievalGuard: Provably Robust 1-Nearest Neighbor Image Retrieval](https://mlsanity.com/paper/2206.11225/) (2022)
- [On boosting the power of Chatterjee's rank correlation](https://mlsanity.com/paper/2108.06828/) (2021)
- [LoRANN: Low-Rank Matrix Factorization for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2410.18926/) (2024)
- [Limit theorems of Chatterjee's rank correlation](https://mlsanity.com/paper/2204.08031/) (2022)
- [k-NNN: Nearest Neighbors of Neighbors for Anomaly Detection](https://mlsanity.com/paper/2305.17695/) (2023)
- [MNN: Mixed Nearest-Neighbors for Self-Supervised Learning](https://mlsanity.com/paper/2311.00562/) (2023)

## 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.