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

arXiv: https://arxiv.org/abs/2008.04005 · HTML: https://mlsanity.com/paper/2008.04005/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2020.

## Built on by (most cited first, 24 of 24)

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- [A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems](https://mlsanity.com/paper/2606.13063/) (2026)
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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.