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Non-parametric estimation of integral probability metrics

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84233

Sriperumbudur,  BK
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Dept. Empirical Inference, Max Planck Institute for Intelligent System, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83923

Fukumizu,  K
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83946

Gretton,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

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.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-BFA0-2
Zusammenfassung
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.