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We develop a minimax rate analysis to describe the reason that deep neural networks (DNNs) perform better than other standard methods.
Metric entropy of some classes of sets with differentiable boundaries
Richard M Dudley · 1974
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Optimal global rates of convergence for nonparametric regression
CJ Stone · 1982
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Concrete mathematics: a foundation for computer science
Ronald L Graham, Donald E Knuth, Oren Patashnik, and Stanley Liu · 1989
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Asymptotical minimax recovery of sets with smooth boundaries
E Mammen and AB Tsybakov · 1995
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Neural networks for optimal approximation of smooth and analytic functions
HN Mhaskar · 1996
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Weak Convergence and Empirical Processes: With Applications to Statistics
AW van der Vaart and Jon Wellner · 1996
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The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network
Peter L Bartlett · 1998
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Minimax estimation via wavelet shrinkage
David L Donoho and Iain M Johnstone · 1998
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Smooth discrimination analysis
Enno Mammen and Alexandre B Tsybakov · 1999
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Information-theoretic determination of minimax rates of convergence
Yuhong Yang and Andrew Barron · 1999
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Recovering edges in ill-posed inverse problems: Optimality of curvelet frames
Emmanuel J Candes and David L Donoho · 2002
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New tight frames of curvelets and optimal representations of objects with piecewise c2 singularities
Emmanuel J Candès and David L Donoho · 2004
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A fast learning algorithm for deep belief nets
Geoffrey E Hinton, Simon Osindero, and Yee-Whye Teh · 2006
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Local rademacher complexities and oracle inequalities in risk minimization
Vladimir Koltchinskii · 2006
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All of nonparametric statistics: with 52 illustrations
Larry Alan Wasserman · 2006
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Neural network learning: Theoretical foundations
Martin Anthony and Peter L Bartlett · 2009
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Introduction to nonparametric estimation, 2009
Alexandre B Tsybakov · 2009
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Compactly supported shearlets are optimally sparse
Gitta Kutyniok and Wang-Q Lim · 2011
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Deep learning
Yann LeCun, Yoshua Bengio, and Geoffrey Hinton · 2015
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Deep learning in neural networks: An overview
Jürgen Schmidhuber · 2015
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Deep learning without poor local minima
Kenji Kawaguchi · 2016
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Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2017
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Optimal approximation of piecewise smooth functions using deep relu neural networks
Philipp Petersen and Felix Voigtlaender · 2018
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A convergence theory for deep learning via over-parameterization
Zeyuan Allen-Zhu, Yuanzhi Li, and Zhao Song · 2019
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On optimization methods for deep learning
Quoc V Le, Jiquan Ngiam, Adam Coates, Abhik Lahiri, Bobby Prochnow, and Andrew Y Ng · 2011
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Aleksandr Petrovich Korostelev and Alexandre B Tsybakov · 2012
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Shearlets: Multiscale analysis for multivariate data
Gitta Kutyniok and Demetrio Labate · 2012
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Richard M Dudley · 2014
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On deep learning as a remedy for the curse of dimensionality in nonparametric regression
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Deep neural networks learn non-smooth functions effectively
Masaaki Imaizumi and Kenji Fukumizu · 2019
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Adaptivity of deep relu network for learning in besov and mixed smooth besov spaces: optimal rate and curse of dimensionality
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On the minimax optimality and superiority of deep neural network learning over sparse parameter spaces
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Adaptive approximation and generalization of deep neural network with intrinsic dimensionality
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