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This paper studies the universal approximation property of deep neural networks for representing probability distributions.
Mode collapse and regularity of optimal transportation maps, 2019
Y. Guo, D. An, X. Qi, Z. Luo, S.-T. Yau, and X. Gu · 1902
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Deep network approximation characterized by number of neurons, 2019
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K.-I. Funahashi · 1989
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Multilayer feedforward networks are universal approximators
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Approximation of distributions of von mises statistics with multidimensional kernels
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Universal approximation bounds for superpositions of a sigmoidal function
A. R. Barron · 1993
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Deep network approximation for smooth functions, 2020
J. Lu, Z. Shen, H. Yang, and S. Zhang · 2001
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Topics in optimal transportation
C. Villani · 2003
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Power diagrams and their applications
D. Siersma and M. Van Manen · 2005
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Optimal transport, old and new
C. Villani · 2009
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Hilbert space embeddings and metrics on probability measures
B. K. Sriperumbudur, A. Gretton, K. Fukumizu, B. Schölkopf, and G. R. Lanckriet · 2010
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A kernel two-sample test
A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. Smola · 2012
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A tail inequality for quadratic forms of subgaussian random vectors
D. Hsu, S. Kakade, T. Zhang, et al · 2012
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Auto-encoding variational bayes
D. P. Kingma and M. Welling · 2013
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Spatial variation
B. Matérn · 2013
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Generative adversarial nets
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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Training generative neural networks via maximum mean discrepancy optimization
G. K. Dziugaite, D. M. Roy, and Z. Ghahramani · 2015
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Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
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Variational inference with normalizing flows
D. Rezende and S. Mohamed · 2015
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Representation benefits of deep feedforward networks
M. Telgarsky · 2015
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A kernel test of goodness of fit
K. Chwialkowski, H. Strathmann, and A. Gretton · 2016
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The power of depth for feedforward neural networks
R. Eldan and O. Shamir · 2016
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Variational principles for minkowski type problems, discrete optimal transport, and discrete monge–ampère equations
X. Gu, F. Luo, J. Sun, and S.-T. Yau · 2016
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Error bounds for approximations with deep relu networks
D. Yarotsky · 2017
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Approximability of discriminators implies diversity in gans
Y. Bai, T. Ma, and A. Risteski · 2018
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Size-noise tradeoffs in generative networks
B. Bailey and M. J. Telgarsky · 2018
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M. Bińkowski, D. J. Sutherland, M. Arbel, and A. Gretton · 2018
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Stein points
W. Chen, L. Mackey, J. Gorham, F.-X. Briol, and C. Oates · 2018
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Stein variational gradient descent: A general purpose bayesian inference algorithm
Q. Liu and D. Wang · 2016
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On the optimal estimation of probability measures in weak and strong topologies
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On the depth of deep neural networks: A theoretical view
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Wasserstein generative adversarial networks
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Notions of optimal transport theory and how to implement them on a computer
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On how well generative adversarial networks learn densities: Nonparametric and parametric results
T. Liang · 2018
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Resnet with one-neuron hidden layers is a universal approximator
H. Lin and S. Jegelka · 2018
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Optimal approximation of piecewise smooth functions using deep relu neural networks
P. Petersen and F. Voigtlaender · 2018
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Provable approximation properties for deep neural networks
U. Shaham, A. Cloninger, and R. R. Coifman · 2018
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Optimal approximation of continuous functions by very deep relu networks
D. Yarotsky · 2018
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Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics
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One-dimensional empirical measures, order statistics, and Kantorovich transport distances
S. Bobkov and M. Ledoux · 2019
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Nonlinear approximation and (deep) relu networks
I. Daubechies, R. DeVore, S. Foucart, B. Hanin, and G. Petrova · 2019
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A geometric view of optimal transportation and generative model
N. Lei, K. Su, L. Cui, S.-T. Yau, and X. D. Gu · 2019
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Optimal transport mapping via input convex neural networks
A. V. Makkuva, A. Taghvaei, S. Oh, and J. D. Lee · 2019
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A. Taghvaei and A. Jalali · 2019
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The expressive power of a class of normalizing flow models
Z. Kong and K. Chaudhuri · 2020
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Convergence and concentration of empirical measures under wasserstein distance in unbounded functional spaces
J. Lei · 2020
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