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  Learning with Non-Positive Kernels

Ong, C., Mary, X., Cnu, S., & Smola, A. (2004). Learning with Non-Positive Kernels. In R. Greiner, & D. Schuurmans (Eds.), ICML '04: Twenty-First International Conference on Machine Learning (pp. 639-646). New York, NY, USA: ACM Press.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-D8A7-C Version Permalink: http://hdl.handle.net/21.11116/0000-0005-52D0-3
Genre: Conference Paper

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 Creators:
Ong, CS1, Author              
Mary , X, Author
Cnu, S, Author
Smola, AJ1, Author              
Affiliations:
1External Organizations, ou_persistent22              

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 Abstract: n this paper we show that many kernel methods can be adapted to deal with indefinite kernels, that is, kernels which are not positive semidefinite. They do not satisfy Mercer‘s condition and they induce associated functional spaces called Reproducing Kernel Kreicaron;n Spaces (RKKS), a generalization of Reproducing Kernel Hilbert Spaces (RKHS).Machine learning in RKKS shares many "nice" properties of learning in RKHS, such as orthogonality and projection. However, since the kernels are indefinite, we can no longer minimize the loss, instead we stabilize it. We show a general representer theorem for constrained stabilization and prove generalization bounds by computing the Rademacher averages of the kernel class. We list several examples of indefinite kernels and investigate regularization methods to solve spline interpolation. Some preliminary experiments with indefinite kernels for spline smoothing are reported for truncated spectral factorization, Landweber-Fridman iterations, and MR-II.

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 Dates: 2004-07
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1145/1015330.1015443
BibTex Citekey: 3416
 Degree: -

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Title: Twenty-First International Conference on Machine Learning (ICML 2004)
Place of Event: Banff, Canada
Start-/End Date: 2004-07-04 - 2004-07-08

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Title: ICML '04: Twenty-First International Conference on Machine Learning
Source Genre: Proceedings
 Creator(s):
Greiner, R, Editor
Schuurmans, D, Editor
Affiliations:
-
Publ. Info: New York, NY, USA : ACM Press
Pages: - Volume / Issue: - Sequence Number: 81 Start / End Page: 639 - 646 Identifier: ISBN: 1-58113-838-5