Non-parametric estimation of integral probability metrics

Bharath K. Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Bernhard Schölkopf, Gert R.G. Lanckriet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (SciVal)


In this paper, we develop and analyze a non-parametric 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 ø-divergence estimators.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Number of pages5
StatePublished - 2010
Event2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States
Duration: Jun 13 2010Jun 18 2010

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8103


Other2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/TerritoryUnited States
CityAustin, TX

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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