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

We study the problem of estimating a nonparametric probability density under a large family of losses called Besov IPMs, which include, for example, $\mathcal{L}^p$ distances, total variation distance, and generalizations of both Wasserstein 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 interact to determine the minimax optimal convergence rate... (read more)

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