A leave-one-out cross validation bound for kernel methods with applications in learning

Tong Zhang

doi:10.1007/3-540-44581-1_28

A leave-one-out cross validation bound for kernel methods with applications in learning

Tong Zhang^*

^*Corresponding author for this work

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

15 Citations (Scopus)

Abstract

In this paper, we prove a general leave-one-out style crossvalidation bound for Kernel methods. We apply this bound to some classification and regression problems, and compare the results with previously known bounds. One aspect of our analysis is that the derived expected generalization bounds reflect both approximation (bias) and learning (variance) properties of the underlying kernel methods. We are thus able to demonstrate the universality of certain learning formulations.

Original language	English
Title of host publication	Computational Learning Theory - 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Proceedings
Editors	David Helmbold, Bob Williamson
Publisher	Springer Verlag
Pages	427-443
Number of pages	17
ISBN (Print)	9783540423430
DOIs	https://doi.org/10.1007/3-540-44581-1_28
Publication status	Published - 2001
Externally published	Yes
Event	14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001 - Amsterdam, Netherlands Duration: 16 Jul 2001 → 19 Jul 2001

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2111
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001
Country/Territory	Netherlands
City	Amsterdam
Period	16/07/01 → 19/07/01

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2001.

Access to Document

10.1007/3-540-44581-1_28

Cite this

Zhang, T. (2001). A leave-one-out cross validation bound for kernel methods with applications in learning. In D. Helmbold, & B. Williamson (Eds.), Computational Learning Theory - 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Proceedings (pp. 427-443). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2111). Springer Verlag. https://doi.org/10.1007/3-540-44581-1_28

Zhang, Tong. / A leave-one-out cross validation bound for kernel methods with applications in learning. Computational Learning Theory - 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Proceedings. editor / David Helmbold ; Bob Williamson. Springer Verlag, 2001. pp. 427-443 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this paper, we prove a general leave-one-out style crossvalidation bound for Kernel methods. We apply this bound to some classification and regression problems, and compare the results with previously known bounds. One aspect of our analysis is that the derived expected generalization bounds reflect both approximation (bias) and learning (variance) properties of the underlying kernel methods. We are thus able to demonstrate the universality of certain learning formulations.",

author = "Tong Zhang",

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Zhang, T 2001, A leave-one-out cross validation bound for kernel methods with applications in learning. in D Helmbold & B Williamson (eds), Computational Learning Theory - 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2111, Springer Verlag, pp. 427-443, 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Amsterdam, Netherlands, 16/07/01. https://doi.org/10.1007/3-540-44581-1_28

A leave-one-out cross validation bound for kernel methods with applications in learning. / Zhang, Tong.
Computational Learning Theory - 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Proceedings. ed. / David Helmbold; Bob Williamson. Springer Verlag, 2001. p. 427-443 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2111).

Research output: Chapter in Book/Conference Proceeding/Report › Conference Paper published in a book › peer-review

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AB - In this paper, we prove a general leave-one-out style crossvalidation bound for Kernel methods. We apply this bound to some classification and regression problems, and compare the results with previously known bounds. One aspect of our analysis is that the derived expected generalization bounds reflect both approximation (bias) and learning (variance) properties of the underlying kernel methods. We are thus able to demonstrate the universality of certain learning formulations.

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Zhang T. A leave-one-out cross validation bound for kernel methods with applications in learning. In Helmbold D, Williamson B, editors, Computational Learning Theory - 14th Annual Conference on Computational Learning Theory, COLT 2001 and 5th European Conference on Computational Learning Theory, EuroCOLT 2001, Proceedings. Springer Verlag. 2001. p. 427-443. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-44581-1_28

A leave-one-out cross validation bound for kernel methods with applications in learning

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