Poster
Nonparametric Density Estimation under Adversarial Losses
Shashank Singh · Ananya Uppal · Boyue Li · Chun-Liang Li · Manzil Zaheer · Barnabas Poczos
Room 210 #84
Keywords: [ Information Theory ] [ Learning Theory ] [ Density Estimation ] [ Generative Models ] [ Frequentist Statistics ] [ Spaces of Functions and Kernels ]
We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called ``adversarial losses'', which, besides classical L^p losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs). In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. We also discuss implications for training GANs based on deep ReLU networks, and more general connections to learning implicit generative models in a minimax statistical sense.
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