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Non-parametric estimation of integral probability metrics

2010

Conference Paper

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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.

Author(s): Sriperumbudur, BK. and Fukumizu, K. and Gretton, A. and Schölkopf, B. and Lanckriet, GRG.
Journal: Proceedings of the IEEE International Symposium on Information Theory (ISIT 2010)
Pages: 1428-1432
Year: 2010
Month: June
Day: 0
Publisher: IEEE

Department(s): Empirical Inference
Research Project(s): Kernel Methods
Bibtex Type: Conference Paper (inproceedings)

Address: Piscataway, NJ, USA
Digital: 0
DOI: 10.1109/ISIT.2010.5513626
Event Name: IEEE International Symposium on Information Theory (ISIT 2010)
Event Place: Austin, TX, USA
Institution: Institute of Electrical and Electronics Engineers
ISBN: 978-1-424-47890-3
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF
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BibTex

@inproceedings{6773,
  title = {Non-parametric estimation of integral probability metrics},
  author = {Sriperumbudur, BK. and Fukumizu, K. and Gretton, A. and Sch{\"o}lkopf, B. and Lanckriet, GRG.},
  journal = {Proceedings of the IEEE International Symposium on Information Theory (ISIT 2010)},
  pages = {1428-1432},
  publisher = {IEEE},
  organization = {Max-Planck-Gesellschaft},
  institution = {Institute of Electrical and Electronics Engineers},
  school = {Biologische Kybernetik},
  address = {Piscataway, NJ, USA},
  month = jun,
  year = {2010},
  month_numeric = {6}
}