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Neural network approximation and estimation of classifiers with classification boundary in a Barron class


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Caragea, Andrei ; Petersen, Philipp ; Voigtlaender, Felix:
Neural network approximation and estimation of classifiers with classification boundary in a Barron class.
2022. - 42 S.


Open Access
Volltext Link zum Volltext (externe URL):


We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guarantees for empirical risk minimization using networks of a suitable size, depending on the number of training samples available. The obtained approximation and estimation rates are independent of the dimension of the input, showing that the curse of dimensionality can be overcome in this setting; in fact, the input dimension only enters in the form of a polynomial factor. Regarding the regularity of the target classification function, we assume the interfaces between the different classes to be locally of Barron-type. We complement our results by studying the relations between various Barron-type spaces that have been proposed in the literature. These spaces differ substantially more from each other than the current literature suggests.

Weitere Angaben

Publikationsform:Preprint, Working paper, Diskussionspapier
Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen
Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Reliable Machine Learning
Mathematisch-Geographische Fakultät > Mathematik > Mathematisches Institut für Maschinelles Lernen und Data Science (MIDS)
DOI / URN / ID:arXiv:2011.09363
Open Access: Freie Zugänglichkeit des Volltexts?:Ja
Titel an der KU entstanden:Ja
Eingestellt am: 30. Mär 2022 14:19
Letzte Änderung: 03. Jun 2024 13:59
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