# Generalization bounds for nonparametric regression with β-mixing samples

arXiv: https://arxiv.org/abs/2108.00997 · HTML: https://mlsanity.com/paper/2108.00997/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 34 references that are in the map.
- First posted on arXiv 2 Aug 2021.

## Built on by (most cited first, 5 of 5)

- [Offline Reinforcement Learning with Instrumental Variables in Confounded Markov Decision Processes](https://mlsanity.com/paper/2209.08666/) (2022)
- [Trade-off Between Dependence and Complexity for Nonparametric Learning -- an Empirical Process Approach](https://mlsanity.com/paper/2401.08978/) (2024)
- [Fast Rates for Nonstationary Weighted Risk Minimization](https://mlsanity.com/paper/2602.05742/) (2026)
- [Confidence intervals for nonparametric regression](https://mlsanity.com/paper/2203.10643/) (2022)
- [Beyond Discrepancy: Oracle Drift in Nonstationary Weighted Risk Minimization](https://mlsanity.com/paper/2610.13598/) (2026)

## Abstract (arXiv)

In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of β-mixing coefficients associated to the training sample. We then apply these results to some previously obtained inequalities for independent samples associated to the deviation of the least-squared error in nonparametric regression to derive corresponding generalization bounds for regression schemes in which the training sample may not be independent. These results provide a framework to analyze the error associated to regression schemes whose training sample comes from a large class of β-mixing sequences, including geometrically ergodic Markov samples, using only the independent case. More generally, they permit a meaningful extension of the Vapnik-Chervonenkis and similar theories for independent training samples to this class of β-mixing samples.