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

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 ɛ-support vector regression. By assuming the ground-truth function belongs to the reproducing kernel Hilbert space of the chosen k...

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Bibliographic Details
Published in:Automatica (Oxford) 2021-12, Vol.134, p.109896, Article 109896
Main Authors: Maddalena, Emilio Tanowe, Scharnhorst, Paul, Jones, Colin N.
Format: Article
Language:English
Subjects:
Deterministic error bounds
Generalization error
Kernel ridge regression
Support vector machines
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Summary: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 ɛ-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 deterministic, 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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2021.109896