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On the Connection between Lp- and Risk Consistency and its Implications on Regularized Kernel Methods

Titelangaben

Köhler, Hannes:
On the Connection between Lp- and Risk Consistency and its Implications on Regularized Kernel Methods.
In: Journal of Machine Learning Research. Bd. 25 (2024) Heft 213 . - S. 1-33.
ISSN 1533-7928

Volltext

Link zum Volltext (externe URL): Volltext

Abstract

As a predictor's quality is often assessed by means of its risk, it is natural to regard risk consistency as a desirable property of learning methods, and many such methods have indeed been shown to be risk consistent. The first aim of this paper is to establish the close connection between risk consistency and Lp-consistency for a considerably wider class of loss functions than has been done before. The attempt to transfer this connection to shifted loss functions surprisingly reveals that this shift does not reduce the assumptions needed on the underlying probability measure to the same extent as it does for many other results. The results are applied to regularized kernel methods such as support vector machines.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Keywords: machine learning; consistency; regression; kernel methods; support vector machines
Institutionen der Universität: Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik VII - Stochastik und maschinelles Lernen
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik VII - Stochastik und maschinelles Lernen > Lehrstuhl Mathematik VII - Stochastik und maschinelles Lernen - Univ.-Prof. Dr. Andreas Christmann
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 05 Aug 2024 08:58
Letzte Änderung: 05 Aug 2024 08:58
URI: https://eref.uni-bayreuth.de/id/eprint/90141