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  Non-parametric estimation of integral probability metrics

Sriperumbudur, B., Fukumizu, K., Gretton, A., Schölkopf, B., & Lanckriet, G. (2010). Non-parametric estimation of integral probability metrics. In IEEE International Symposium on Information Theory (ISIT 2010) (pp. 1428-1432). Piscataway, NJ, USA: IEEE.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-BFA0-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-81E5-9
Genre: Conference Paper

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 Creators:
Sriperumbudur, BK, Author              
Fukumizu, K, Author              
Gretton, A, Author              
Schölkopf, B1, 2, Author              
Lanckriet, GRG, 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: In this paper, we develop and analyze a nonparametric method for estimating the class of integral probability metrics (IPMs), examples of which include the Wasserstein distance, Dudley metric, and maximum mean discrepancy (MMD). We show that these distances can be estimated efficiently by solving a linear program in the case of Wasserstein distance and Dudley metric, while MMD is computable in a closed form. All these estimators are shown to be strongly consistent and their convergence rates are analyzed. Based on these results, we show that IPMs are simple to estimate and the estimators exhibit good convergence behavior compared to fi-divergence estimators.

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 Dates: 2010-06
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: -
 Identifiers: DOI: 10.1109/ISIT.2010.5513626
BibTex Citekey: 6773
 Degree: -

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Title: IEEE International Symposium on Information Theory (ISIT 2010)
Place of Event: Austin, TX, USA
Start-/End Date: 2010-06-13 - 2010-06-18

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Title: IEEE International Symposium on Information Theory (ISIT 2010)
Source Genre: Proceedings
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Publ. Info: Piscataway, NJ, USA : IEEE
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 1428 - 1432 Identifier: ISBN: 978-1-424-47890-3