Empirical Inference Conference Paper 2010

Non-parametric estimation of integral probability metrics

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

BibTex

@inproceedings{6773,
  title = {Non-parametric estimation of integral probability metrics},
  journal = {Proceedings of the IEEE International Symposium on Information Theory (ISIT 2010)},
  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.},
  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},
  slug = {6773},
  author = {Sriperumbudur, BK. and Fukumizu, K. and Gretton, A. and Sch{\"o}lkopf, B. and Lanckriet, GRG.},
  month_numeric = {6}
}