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Nonparametric Density Estimation under Adversarial Losses
Shashank Singh · Ananya Uppal · Boyue Li · Chun-Liang Li · Manzil Zaheer · Barnabas Poczos

Thu Dec 06 02:00 PM -- 04:00 PM (PST) @ Room 210 #84

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.

Author Information

Shashank Singh (Carnegie Mellon University)
Ananya Uppal (Carnegie Mellon University)
Boyue Li (Carnegie Mellon University)
Chun-Liang Li (Carnegie Mellon University)
Manzil Zaheer (Google)
Barnabas Poczos (Carnegie Mellon University)

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