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  • title: Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Losses
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            Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Losses
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            Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Losses

            Dec 12, 2019

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            We study the problem of estimating a nonparametric probability distribution under a family of losses called Besov IPMs. This family is quite large, including, for example, L^p distances, total variation distance, and generalizations of both Wasserstein (earthmover's) and Kolmogorov-Smirnov distances. For a wide variety of settings, we provide both lower and upper bounds, identifying precisely how the choice of loss function and assumptions on the data distribution interact to determine the mini-…

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