Effective Dimension and Generalization of Kernel Learning

Tong Zhang

Effective Dimension and Generalization of Kernel Learning

Tong Zhang^*

^*Corresponding author for this work

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

16 Citations (Scopus)

Abstract

We investigate the generalization performance of some learning problems in Hilbert function Spaces. We introduce a concept of scale-sensitive effective data dimension, and show that it characterizes the convergence rate of the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to non-parametric kernel learning methods. We derive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.

Original language	English
Title of host publication	NIPS 2002
Subtitle of host publication	Proceedings of the 15th International Conference on Neural Information Processing Systems
Editors	Suzanna Becker, Sebastian Thrun, Klaus Obermayer
Publisher	MIT Press Journals
Pages	454-461
Number of pages	8
ISBN (Electronic)	0262025507, 9780262025508
Publication status	Published - 2002
Externally published	Yes
Event	15th International Conference on Neural Information Processing Systems, NIPS 2002 - Vancouver, Canada Duration: 9 Dec 2002 → 14 Dec 2002

Publication series

Name	NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems

Conference

Conference	15th International Conference on Neural Information Processing Systems, NIPS 2002
Country/Territory	Canada
City	Vancouver
Period	9/12/02 → 14/12/02

Bibliographical note

Publisher Copyright:
© NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems. All rights reserved.

Cite this

Zhang, Tong. / Effective Dimension and Generalization of Kernel Learning. NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems. editor / Suzanna Becker ; Sebastian Thrun ; Klaus Obermayer. MIT Press Journals, 2002. pp. 454-461 (NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems).

@inproceedings{987c65708ca14f238dd4dda845977dc1,

title = "Effective Dimension and Generalization of Kernel Learning",

abstract = "We investigate the generalization performance of some learning problems in Hilbert function Spaces. We introduce a concept of scale-sensitive effective data dimension, and show that it characterizes the convergence rate of the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to non-parametric kernel learning methods. We derive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.",

author = "Tong Zhang",

note = "Publisher Copyright: {\textcopyright} NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems. All rights reserved.; 15th International Conference on Neural Information Processing Systems, NIPS 2002 ; Conference date: 09-12-2002 Through 14-12-2002",

year = "2002",

language = "English",

series = "NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems",

publisher = "MIT Press Journals",

pages = "454--461",

editor = "Suzanna Becker and Sebastian Thrun and Klaus Obermayer",

booktitle = "NIPS 2002",

}

Zhang, T 2002, Effective Dimension and Generalization of Kernel Learning. in S Becker, S Thrun & K Obermayer (eds), NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems. NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems, MIT Press Journals, pp. 454-461, 15th International Conference on Neural Information Processing Systems, NIPS 2002, Vancouver, Canada, 9/12/02.

Effective Dimension and Generalization of Kernel Learning. / Zhang, Tong.
NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems. ed. / Suzanna Becker; Sebastian Thrun; Klaus Obermayer. MIT Press Journals, 2002. p. 454-461 (NIPS 2002: Proceedings of the 15th International Conference on Neural Information Processing Systems).

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

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PY - 2002

Y1 - 2002

N2 - We investigate the generalization performance of some learning problems in Hilbert function Spaces. We introduce a concept of scale-sensitive effective data dimension, and show that it characterizes the convergence rate of the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to non-parametric kernel learning methods. We derive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.

AB - We investigate the generalization performance of some learning problems in Hilbert function Spaces. We introduce a concept of scale-sensitive effective data dimension, and show that it characterizes the convergence rate of the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to non-parametric kernel learning methods. We derive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.

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M3 - Conference Paper published in a book

AN - SCOPUS:85140618492

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SP - 454

EP - 461

BT - NIPS 2002

A2 - Becker, Suzanna

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T2 - 15th International Conference on Neural Information Processing Systems, NIPS 2002

Y2 - 9 December 2002 through 14 December 2002

ER -

Effective Dimension and Generalization of Kernel Learning

Abstract

Publication series

Conference

Bibliographical note

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