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This paper studies the rates of convergence for learning distributions implicitly with the adversarial framework and Generative Adversarial Networks (GANs), which subsume Wasserstein, Sobolev, MMD GAN, and Generalized/Simulated Method of Moments (GMM/SMM) as special cases.
Large Sample Properties of Generalized Method of Moments Estimators
Lars Peter Hansen · 1982
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Optimal global rates of convergence for nonparametric regression
Charles J Stone · 1982
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Fundamentals of statistical exponential families: with applications in statistical decision theory
Lawrence D Brown · 1986
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A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration
Daniel McFadden · 1989
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Simulation and the Asymptotics of Optimization Estimators
Ariel Pakes and David Pollard · 1989
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Empirical processes: theory and applications
David Pollard · 1990
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Some regularity properties of solutions of Monge Ampere equation
Luis A Caffarelli · 1991
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The regularity of mappings with a convex potential
Luis A Caffarelli · 1992
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Implied Probabilities in GMM Estimators
Kerry Back and David P. Brown · 1993
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Information theoretic approaches to inference in moment condition models
Guido W Imbens, Phillip Johnson, and Richard H Spady · 1995
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Statistical inverse estimation in hilbert scales
Bernard A Mair and Frits H Ruymgaart · 1996
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Topics in non-parametric
Arkadi Nemirovski · 2000
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All of nonparametric statistics
Larry Wassermann · 2006
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Optimal rates for the regularized least-squares algorithm
Andrea Caponnetto and Ernesto De Vito · 2007
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Bracketing metric entropy rates and empirical central limit theorems for function classes of besov-and sobolev-type
Richard Nickl and Benedikt M Pötscher · 2007
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Neural network learning: Theoretical foundations
Martin Anthony and Peter L Bartlett · 2009
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Introduction to nonparametric estimation
Alexandre B Tsybakov · 2009
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Learning probability measures with respect to optimal transport metrics
Guillermo Canas and Lorenzo Rosasco · 2012
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A user’s guide to optimal transport
Luigi Ambrosio and Nicola Gigli · 2013
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Stability
Bin Yu · 2013
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Probability in high dimension
Ramon van Handel · 2014
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Law of log determinant of sample covariance matrix and optimal estimation of differential entropy for high-dimensional gaussian distributions
T. Tony Cai, Tengyuan Liang, and Harrison H. Zhou · 2015
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Training generative neural networks via maximum mean discrepancy optimization
Gintare Karolina Dziugaite, Daniel M Roy, and Zoubin Ghahramani · 2015
Lars Mescheder, Sebastian Nowozin, and Andreas Geiger · 2017
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Youssef Mroueh, Chun-Liang Li, Tom Sercu, Anant Raj, and Yu Cheng · 2017
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Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2017
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On gradient regularizers for mmd gans
Michael Arbel, Dougal J Sutherland, Mikołaj Bińkowski, and Arthur Gretton · 2018
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Approximability of discriminators implies diversity in gans
Yu Bai, Tengyu Ma, and Andrej Risteski · 2018
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Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
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Do gans actually learn the distribution? an empirical study
Sanjeev Arora and Yi Zhang · 2017
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Generalization and equilibrium in generative adversarial nets (gans)
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The inductive bias of restricted f-gans
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Which training methods for gans do actually converge?
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Nonparametric density estimation under adversarial losses
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Sgd learns one-layer networks in wgans
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Estimating certain integral probability metric (IPM) is as hard as estimating under the IPM
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Statistical guarantees of generative adversarial networks for distribution estimation
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Deep neural networks for estimation and inference
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