Non-parametric estimation of integral probability metrics
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 dis- tance, 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 \phi-divergence estimators.