mlsanityData to 14 Oct 2026

Optimal kernel regression bounds under energy-bounded noise

arXiv 2505.22235 ↗First posted 28 May 2025cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic uncertainty bound for kernel-based estimation, which can also handle correlated noise sequences. Its computation relies on a mild norm-boundedness assumption on the unknown function and the noise, returning the worst-case function realization within the hypothesis class at an arbitrary query input location. The value of this function is shown to be given in terms of the posterior mean and covariance of a Gaussian process for an optimal choice of the measurement noise covariance. By rigorously analyzing the proposed approach and comparing it with other results in the literature, we show its effectiveness in returning tight and easy-to-compute bounds for kernel-based estimates.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 22 of its 53 references that are in the map. First posted on arXiv 28 May 2025.

Builds on

22 of 53 references.

References · 22

  1. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 774
  2. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 641
  3. 2019Control Barrier Functions: Theory and Applicationscited by 372
  4. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  5. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  6. 2017A Rewriting System for Convex Optimization Problemscited by 179
  7. 2016Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Roboticscited by 134
  8. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
  9. 2019Uniform Error Bounds for Gaussian Process Regression with Application to Safe Controlcited by 64
  10. 2017Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Controlcited by 53
  11. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  12. 2022Learning with little mixingcited by 33
10 more
  1. 2020Deterministic error bounds for kernel-based learning techniques under bounded noisecited by 24
  2. 2020Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processescited by 20
  3. 2020Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functionscited by 15
  4. 2024On Safety in Safe Bayesian Optimizationcited by 15
  5. 2021Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approachcited by 14
  6. 2014Efficiency of conformalized ridge regressioncited by 13
  7. 2022Nonparametric, Nonasymptotic Confidence Bands with Paley-Wiener Kernels for Band-Limited Functionscited by 8
  8. 2024PACSBO: Probably approximately correct safe Bayesian optimizationcited by 8
  9. 2024Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certificationcited by 6
  10. 2024Towards safe Bayesian optimization with Wiener kernel regressioncited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2026Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual functioncited by 1
  2. 2026Safe learning-based control via function-based uncertainty quantificationcited by 1
  3. 2025A robust and adaptive MPC formulation for Gaussian process modelscited by 0
  4. 2026On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noisecited by 0