# On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise

arXiv: https://arxiv.org/abs/2605.09757 · HTML: https://mlsanity.com/paper/2605.09757/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 10 May 2026.

## Builds on (most cited first, 22 of 22)

- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [Information Directed Sampling and Bandits with Heteroscedastic Noise](https://mlsanity.com/paper/1801.09667/) (2018)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [How do noise tails impact on deep ReLU networks?](https://mlsanity.com/paper/2203.10418/) (2022)
- [Deterministic error bounds for kernel-based learning techniques under bounded noise](https://mlsanity.com/paper/2008.04005/) (2020)
- [Bayesian Optimization under Heavy-tailed Payoffs](https://mlsanity.com/paper/1909.07040/) (2019)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [Learning-based Symbolic Abstractions for Nonlinear Control Systems](https://mlsanity.com/paper/2004.01879/) (2020)
- [Risk Bounds for Robust Deep Learning](https://mlsanity.com/paper/2009.06202/) (2020)
- [Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees](https://mlsanity.com/paper/2411.00656/) (2024)
- [Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certification](https://mlsanity.com/paper/2408.09033/) (2024)
- [Towards safe Bayesian optimization with Wiener kernel regression](https://mlsanity.com/paper/2411.02253/) (2024)
- [Outlier-Robust Linear System Identification Under Heavy-tailed Noise](https://mlsanity.com/paper/2501.00421/) (2024)
- [Stochastic Model Predictive Control for Sub-Gaussian Noise](https://mlsanity.com/paper/2503.08795/) (2025)
- [Optimal kernel regression bounds under energy-bounded noise](https://mlsanity.com/paper/2505.22235/) (2025)
- [Regularized least squares learning with heavy-tailed noise is minimax optimal](https://mlsanity.com/paper/2505.14214/) (2025)

## Abstract (arXiv)

Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this work, we propose novel non-asymptotic probabilistic uniform error bounds for kernel-based regression. Compared to related bounds in the literature that are restricted to (conditionally) independent sub-Gaussian noise, our bounds allow to consider a broad class of non-Gaussian distributions, such as sub-Gaussian, bounded, sub-exponential, and variance/moment-bounded noise. Moreover, our results apply to correlated and uncorrelated noise. We compare our proposed error bounds with existing results in terms of the induced uncertainty region and their performance in safe control, demonstrating the tightness of the proposed bounds.