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Activity Number: 187 - Contributed Poster Presentations: Section on Nonparametric Statistics
Type: Contributed
Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #306913
Title: Nonparametric Density Estimation Under Adversarial Losses
Author(s): Shashank Singh* and Ananya Uppal and Barnabas Poczos
Companies: Carnegie Mellon University and Carnegie Mellon University and Carnegie Mellon University
Keywords: Nonparametric Density Estimation; Adversarial Loss; Integral Probability Metric; IPM; Generative Adversarial Network; GAN

We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called adversarial losses, which, besides classical Lp losses, include maximum mean discrepancy (MMD), Wasserstein distance, total variation distance, and Kolmorogov-Smirnov distance. In a general framework, we study how the choice of loss and the assumed smoothness of the underlying density together determine the minimax rate. Adversarial losses are also closely related to the losses encoded by discriminator networks in generative adversarial networks (GANs), and we discuss implications for training and evaluating GANs.

Authors who are presenting talks have a * after their name.

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