Hrushikesh Mhaskar

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TOMASO POGGIOMcDermott Professor in Brain Sciences, MITVerified email at ai.mit.edu
E. B. SaffDistinguished Professor of Mathematics, Vanderbilt UniversityVerified email at vanderbilt.edu
Jürgen PrestinProfessor für Mathematik, Universität zu LübeckVerified email at math.uni-luebeck.de
J. D. WardProfessor emeritus of mathematics, Texas A&M UniversityVerified email at math.tamu.edu
Lorenzo RosascoMaLGa Machine Learning Genoa Center - Università degli Studi di GenovaVerified email at unige.it
Brando MirandaMIT, UIUC, StanfordVerified email at stanford.edu
D.S. LubinskyVerified email at math.gatech.edu
Sergei PereverzevProfessor, Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy ofVerified email at oeaw.ac.at
Maria D. van der WaltWestmont CollegeVerified email at westmont.edu
Karthik Jayaraman RaghuramApple IncVerified email at apple.com
Alexander CloningerAssociate Professor, Department of Mathematics & Halicioglu Data Science Institute, UC San DiegoVerified email at ucsd.edu
Mauro MaggioniBloomberg Distinguished Professor of Mathematics, and Applied Mathematics and StatisticsVerified email at jhu.edu
Mahadevan GaneshColorado School of MinesVerified email at mines.edu
Ian SloanProfessor of Mathematics, University of New South Wales (UNSW Australia)Verified email at unsw.edu.au
Azita MayeliProfessor of Mathematics at the City University of New YorkVerified email at gc.cuny.edu
ISAAC PESENSONProfessor of Mathematics, Temple UniversityVerified email at temple.edu
Xiaosheng ZhuangCity University of Hong KongVerified email at cityu.edu.hk
Valeriya NaumovaSimula Research LaboratoryVerified email at simula.no
Dmitry BatenkovBasis Research InstituteVerified email at basis.ai
Narendra GOVILDepartment of Mathematics and Statistics, Auburn UniversityVerified email at auburn.edu

Hrushikesh Mhaskar

Claremont Graduate University

Verified email at cgu.edu

Applied and computational harmonic analysis approximation theory learning theory data/image processing pdes


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Why and when can deep-but not shallow-networks avoid the curse of dimensionality: a review T Poggio, H Mhaskar, L Rosasco, B Miranda, Q Liao International Journal of Automation and Computing 14 (5), 503-519, 2017	714	2017
Neural networks for optimal approximation of smooth and analytic functions HN Mhaskar Neural computation 8 (1), 164-177, 1996	465	1996
Deep vs. shallow networks: An approximation theory perspective HN Mhaskar, T Poggio Analysis and Applications 14 (06), 829-848, 2016	442	2016
Approximation by superposition of sigmoidal and radial basis functions HN Mhaskar, CA Micchelli Advances in Applied mathematics 13 (3), 350-373, 1992	377	1992
Where does the sup norm of a weighted polynomial live? A Generalization of Incomplete Polynomials HN Mhaskar, EB Saff Constructive Approximation 1, 71-91, 1985	284	1985
Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature H Mhaskar, F Narcowich, J Ward Mathematics of computation 70 (235), 1113-1130, 2001	253	2001
When and why are deep networks better than shallow ones? H Mhaskar, Q Liao, T Poggio Proceedings of the AAAI conference on artificial intelligence 31 (1), 2017	250	2017
Extremal problems for polynomials with exponential weights HN Mhaskar, EB Saff Transactions of the American Mathematical Society 285 (1), 203-234, 1984	243	1984
Introduction to the theory of weighted polynomial approximation HN Mhaskar World Scientific, 1996	220	1996
Approximation properties of a multilayered feedforward artificial neural network HN Mhaskar Advances in Computational Mathematics 1 (1), 61-80, 1993	217	1993
Degree of approximation by neural and translation networks with a single hidden layer HN Mhaskar, CA Micchelli Advances in applied mathematics 16 (2), 151-183, 1995	183	1995
Learning functions: when is deep better than shallow H Mhaskar, Q Liao, T Poggio arXiv preprint arXiv:1603.00988, 2016	178	2016
A deep learning approach to diabetic blood glucose prediction HN Mhaskar, SV Pereverzyev, MD Van der Walt Frontiers in applied mathematics and statistics 3, 14, 2017	147	2017
Fundamentals of approximation theory HN Mhaskar, DV Pai CRC Press, 2000	138	2000
Theory of deep learning III: explaining the non-overfitting puzzle T Poggio, K Kawaguchi, Q Liao, B Miranda, L Rosasco, X Boix, J Hidary, ... arXiv preprint arXiv:1801.00173, 2017	132	2017
Neural networks for localized approximation CK Chui, X Li, HN Mhaskar mathematics of computation 63 (208), 607-623, 1994	129	1994
A proof of Freud's conjecture for exponential weights DS Lubinsky, HN Mhaskar, EB Saff Constructive Approximation 4, 65-83, 1988	124	1988
On trigonometric wavelets CK Chui, HN Mhaskar Constructive Approximation 9, 167-190, 1993	119	1993
Diffusion polynomial frames on metric measure spaces M Maggioni, HN Mhaskar Applied and Computational Harmonic Analysis 24 (3), 329-353, 2008	107	2008
Dimension-independent bounds on the degree of approximation by neural networks HN Mhaskar, CA Micchelli IBM Journal of Research and Development 38 (3), 277-284, 1994	100	1994

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