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  Entropy numbers, operators and support vector kernels

Williamson, R., Smola, A., & Schölkopf, B. (1999). Entropy numbers, operators and support vector kernels. In R. Fischer, & H. Simon (Eds.), Computational Learning Theory: 4th European Conference, EuroCOLT’99 Nordkirchen, Germany, March 29–31, 1999 (pp. 285-299). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-E759-5 Version Permalink: https://hdl.handle.net/21.11116/0000-0005-C462-F
Genre: Conference Paper

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https://link.springer.com/content/pdf/10.1007%2F3-540-49097-3_23.pdf (Publisher version)
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 Creators:
Williamson, RC, Author
Smola, AJ, Author           
Schölkopf, B1, Author           
Affiliations:
1External Organizations, ou_persistent22              

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 Abstract: We derive new bounds for the generalization error of feature space machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs are based on a viewpoint that is apparently novel in the field of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly infinite dimensional unit ball in feature space into a finite dimensional space. The covering numbers of the class are then determined via the entropy numbers of the operator. These numbers, which characterize the degree of compactness of the operator, can be bounded in terms of the eigenvalues of an integral operator induced by the kernel function used by the machine. As a consequence we are able to theoretically explain the effect of the choice of kernel functions on the generalization performance of support vector machines.

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 Dates: 1999-03
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 807
DOI: 10.1007/3-540-49097-3_23
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Title: 4th European Conference on Computational Learning Theory (EuroCOLT 1999)
Place of Event: Nordkirchen, Germany
Start-/End Date: 1999-03-29 - 1999-03-31

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Title: Computational Learning Theory: 4th European Conference, EuroCOLT’99 Nordkirchen, Germany, March 29–31, 1999
Source Genre: Proceedings
 Creator(s):
Fischer, R, Editor
Simon, HU, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 285 - 299 Identifier: ISBN: 978-3-540-65701-9

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 1572 Sequence Number: - Start / End Page: - Identifier: -