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

Title data

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

Official URL:

Abstract in another language

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.

Further data

Item Type:	Article in a journal
Refereed:	Yes
Keywords:	machine learning; consistency; regression; kernel methods; support vector machines
Institutions of the University:	Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VII - Stochastics and Machine Learning Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VII - Stochastics and Machine Learning > Chair Mathematics VII - Stochastics and mashine learning - Univ.-Prof. Dr. Andreas Christmann
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	05 Aug 2024 08:58
Last Modified:	05 Aug 2024 08:58
URI:	https://eref.uni-bayreuth.de/id/eprint/90141