The University of Southampton
University of Southampton Institutional Repository

Complexity of pattern classes and Lipschitz property

Complexity of pattern classes and Lipschitz property
Complexity of pattern classes and Lipschitz property
Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a class of functions with a fixed Lipschitz function may increase its complexity by at most twice the Lipschitz constant. The proof of this property is non-trivial (in contrast to the other properties) and it is believed that the proof in the Gaussian case is conceptually more difficult then the one for the Rademacher case. In this paper we give a detailed prove of the Lipschitz property for the Rademacher case and generalize the same idea to an arbitrary complexity (including the Gaussian). We also discuss a related topic about the Rademacher complexity of a class consisting of all the Lipschitz functions with a given Lipschitz constant. We show that the complexity is surprisingly low in the one-dimensional case. The question for higher dimensions remains open.
181-193
Springer-Verlag, Berlin Heidelberg
Ambroladze, Amiran
86f53c6f-a258-4f34-b7e1-4af90e4d4324
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
David, Shai Ben
Case, John
Maruoka, Akira
Ambroladze, Amiran
86f53c6f-a258-4f34-b7e1-4af90e4d4324
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
David, Shai Ben
Case, John
Maruoka, Akira

Ambroladze, Amiran and Shawe-Taylor, John (2004) Complexity of pattern classes and Lipschitz property. David, Shai Ben, Case, John and Maruoka, Akira (eds.) In Algorithmic Learning Theory: 15th International Conference, ALT 2004, Padova, Italy, October 2-5, 2004. Proceedings. vol. 3244, Springer-Verlag, Berlin Heidelberg. pp. 181-193 .

Record type: Conference or Workshop Item (Paper)

Abstract

Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a class of functions with a fixed Lipschitz function may increase its complexity by at most twice the Lipschitz constant. The proof of this property is non-trivial (in contrast to the other properties) and it is believed that the proof in the Gaussian case is conceptually more difficult then the one for the Rademacher case. In this paper we give a detailed prove of the Lipschitz property for the Rademacher case and generalize the same idea to an arbitrary complexity (including the Gaussian). We also discuss a related topic about the Rademacher complexity of a class consisting of all the Lipschitz functions with a given Lipschitz constant. We show that the complexity is surprisingly low in the one-dimensional case. The question for higher dimensions remains open.

Text
ComplexityOfPatternClasses.pdf - Version of Record
Restricted to Repository staff only

More information

Published date: October 2004
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 259921
URI: http://eprints.soton.ac.uk/id/eprint/259921
PURE UUID: a6c28a03-595f-410b-86bd-1261a327ee04

Catalogue record

Date deposited: 09 Sep 2004
Last modified: 19 Jul 2019 17:00

Export record

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×