Hilbertian Metrics and Positive Definite Kernels on Probability Measures

Hein, M; Bousquet, O

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Hilbertian Metrics and Positive Definite Kernels on Probability Measures

Hein, M., & Bousquet, O. (2005). Hilbertian Metrics and Positive Definite Kernels on Probability Measures. In R. Cowell, & Z. Ghahramani (Eds.), AISTATS 2005: Tenth International Workshop onArtificial Intelligence and Statistics (pp. 136-143). The Society for Artificial Intelligence and Statistics.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-D68F-5 Version Permalink: https://hdl.handle.net/21.11116/0000-0005-3A85-4

Genre: Conference Paper

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http://www.gatsby.ucl.ac.uk/aistats/aistats2005_eproc.pdf (Any fulltext) Open Access status unknown

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Creators:
Hein, M^{1, 2}, Author
Bousquet, O^{1, 2}, Author

Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794

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Abstract: We investigate the problem of defining Hilbertian metrics resp.
positive definite kernels on probability measures, continuing previous work. This type of kernels has shown very good
results in text classification and has a wide range of possible
applications. In this paper we extend the two-parameter family of
Hilbertian metrics of Topsoe such that it now includes all
commonly used Hilbertian metrics on probability measures. This
allows us to do model selection among these metrics in an elegant
and unified way. Second we investigate further our approach to
incorporate similarity information of the probability space into
the kernel. The analysis provides a better understanding of these
kernels and gives in some cases a more efficient way to compute
them. Finally we compare all proposed kernels in two text and two
image classification problems.

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Dates: Date issued: 2005-01

Publication Status: Issued

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Identifiers: BibTex Citekey: 3013

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Title: Tenth International Workshop on Artificial Intelligence and Statistics (AI Statistics 2005)

Place of Event: Barbados

Start-/End Date: 2005-01-06 - 2005-01-08

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Title: AISTATS 2005: Tenth International Workshop onArtificial Intelligence and Statistics

Source Genre: Proceedings

Creator(s):
Cowell, R, Editor
Ghahramani, Z, Editor

Affiliations:
-

Publ. Info: The Society for Artificial Intelligence and Statistics

Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 136 - 143 Identifier: ISBN: 0-9727358-1-X