mlsanityData to 7 Oct 2026

Deterministic error bounds for kernel-based learning techniques under bounded noise

arXiv 2008.04005 ↗First posted 10 Aug 2020eess.SY cs.LG cs.SYcited by 24

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Abstract (arXiv)

We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and varepsilon-support vector regression. By assuming the ground-truth function belongs to the reproducing kernel Hilbert space of the chosen kernel, and the measurement noise affecting the dataset is bounded, we adopt an approximation theory viewpoint to establish textitdeterministic, finite-sample error bounds for the two models. Finally, we discuss their connection with Gaussian processes and two numerical examples are provided. In establishing our inequalities, we hope to help bring the fields of non-parametric kernel learning and system identification for robust control closer to each other.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Aug 2020.

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Citing papers per year: 2021: 5; 2022: 1; 2023: 3; 2024: 5; 2025: 4; 2026: 6.

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  1. 2021Practical and Rigorous Uncertainty Bounds for Gaussian Process Regressioncited by 49
  2. 2021Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applicationscited by 17
  3. 2024Principled Preferential Bayesian Optimizationcited by 16
  4. 2021Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approachcited by 14
  5. 2023Automatic nonlinear MPC approximation with closed-loop guaranteescited by 12
  6. 2025Safe exploration in reproducing kernel Hilbert spacescited by 10
  7. 2022Lower Bounds on the Worst-Case Complexity of Efficient Global Optimizationcited by 7
  8. 2024Error Bounds For Gaussian Process Regression Under Bounded Support Noise With Applications To Safety Certificationcited by 6
  9. 2025Optimal kernel regression bounds under energy-bounded noisecited by 4
  10. 2025Streaming Generated Gaussian Process Experts for Online Learning and Control: Extended Versioncited by 4
  11. 2024Whom to Trust? Elective Learning for Distributed Gaussian Process Regressioncited by 3
  12. 2021Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guaranteescited by 2
12 more
  1. 2021Distributed Bayesian Online Learning for Cooperative Manipulationcited by 1
  2. 2024Safe reinforcement learning in uncertain contextscited by 1
  3. 2026Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual functioncited by 1
  4. 2023Error Bounds for Kernel-Based Linear System Identification with Unknown Hyperparameterscited by 0
  5. 2023Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errorscited by 0
  6. 2024Decentralized Event-Triggered Online Learning for Safe Consensus of Multi-Agent Systems with Gaussian Process Regressioncited by 0
  7. 2025A robust and adaptive MPC formulation for Gaussian process modelscited by 0
  8. 2026On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noisecited by 0
  9. 2026A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systemscited by 0
  10. 2026Mitigating Over-Optimization in PRM-Guided Search in Mathematical Reasoning by Optimizing the Guidecited by 0
  11. 2026COIN-GP: Cooperative Online Learning in Networked Distributed Systems with Partial Measurements via Gaussian Process Regressioncited by 0
  12. 2026Gaussian-process surrogate indicators for residual-based adaptive GMsFEMcited by 0