Non-parametric estimation of integral probability metrics

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

doi:10.1109/ISIT.2010.5513626

Non-parametric estimation of integral probability metrics

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

Statistics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

19 Scopus citations

Abstract

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 language	English (US)
Title of host publication	2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Pages	1428-1432
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2010.5513626
State	Published - 2010
Event	2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States Duration: Jun 13 2010 → Jun 18 2010

Publication series

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

Other

Other	2010 IEEE International Symposium on Information Theory, ISIT 2010
Country/Territory	United States
City	Austin, TX
Period	6/13/10 → 6/18/10

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT.2010.5513626

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Sriperumbudur, B. K., Fukumizu, K., Gretton, A., Schölkopf, B., & Lanckriet, G. R. G. (2010). Non-parametric estimation of integral probability metrics. In 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings (pp. 1428-1432). Article 5513626 (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2010.5513626

@inproceedings{df485bb2047345c4bc71d60d77421844,

title = "Non-parametric estimation of integral probability metrics",

abstract = "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 {\o}-divergence estimators.",

author = "Sriperumbudur, {Bharath K.} and Kenji Fukumizu and Arthur Gretton and Bernhard Sch{\"o}lkopf and Lanckriet, {Gert R.G.}",

year = "2010",

doi = "10.1109/ISIT.2010.5513626",

language = "English (US)",

isbn = "9781424469604",

series = "IEEE International Symposium on Information Theory - Proceedings",

pages = "1428--1432",

booktitle = "2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings",

note = "2010 IEEE International Symposium on Information Theory, ISIT 2010 ; Conference date: 13-06-2010 Through 18-06-2010",

}

Sriperumbudur, BK, Fukumizu, K, Gretton, A, Schölkopf, B & Lanckriet, GRG 2010, Non-parametric estimation of integral probability metrics. in 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings., 5513626, IEEE International Symposium on Information Theory - Proceedings, pp. 1428-1432, 2010 IEEE International Symposium on Information Theory, ISIT 2010, Austin, TX, United States, 6/13/10. https://doi.org/10.1109/ISIT.2010.5513626

Non-parametric estimation of integral probability metrics. / Sriperumbudur, Bharath K.; Fukumizu, Kenji; Gretton, Arthur et al.
2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings. 2010. p. 1428-1432 5513626 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Non-parametric estimation of integral probability metrics

AU - Sriperumbudur, Bharath K.

AU - Fukumizu, Kenji

AU - Gretton, Arthur

AU - Schölkopf, Bernhard

AU - Lanckriet, Gert R.G.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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M3 - Conference contribution

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SN - 9781424469604

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1428

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BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

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Y2 - 13 June 2010 through 18 June 2010

ER -

Non-parametric estimation of integral probability metrics

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