Non-parametric estimation of integral probability metrics

Sriperumbudur, BK; Fukumizu, K; Gretton, A; Schölkopf, B; Lanckriet, GRG

doi:10.1109/ISIT.2010.5513626

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Non-parametric estimation of integral probability metrics

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

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Citation

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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-BFA0-2

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.