mlsanityData to 14 Oct 2026

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

arXiv 2605.09757 ↗First posted 10 May 2026cs.LG stat.MLcited by 0

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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.

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References · 22

  1. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 774
  2. 2017On Kernelized Multi-armed Banditscited by 352
  3. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  4. 2016Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Roboticscited by 134
  5. 2020Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planningcited by 86
  6. 2018Information Directed Sampling and Bandits with Heteroscedastic Noisecited by 76
  7. 2019Uniform Error Bounds for Gaussian Process Regression with Application to Safe Controlcited by 64
  8. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  9. 2022How do noise tails impact on deep ReLU networks?cited by 25
  10. 2020Deterministic error bounds for kernel-based learning techniques under bounded noisecited by 24
  11. 2019Bayesian Optimization under Heavy-tailed Payoffscited by 21
  12. 2024On Safety in Safe Bayesian Optimizationcited by 15
10 more
  1. 2021Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approachcited by 14
  2. 2020Learning-based Symbolic Abstractions for Nonlinear Control Systemscited by 11
  3. 2020Risk Bounds for Robust Deep Learningcited by 9
  4. 2024Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guaranteescited by 7
  5. 2024Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certificationcited by 6
  6. 2024Towards safe Bayesian optimization with Wiener kernel regressioncited by 4
  7. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  8. 2025Stochastic Model Predictive Control for Sub-Gaussian Noisecited by 4
  9. 2025Optimal kernel regression bounds under energy-bounded noisecited by 4
  10. 2025Regularized least squares learning with heavy-tailed noise is minimax optimalcited by 3

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