Hrushikesh Mhaskar

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E. B. SaffProfessor of Mathematics, Vanderbilt UniversityVerified email at vanderbilt.edu
TOMASO POGGIOMcDermott Professor in Brain Sciences, MITVerified email at ai.mit.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 WaltAssistant Professor of Mathematics, Westmont CollegeVerified email at westmont.edu
Karthik Jayaraman RaghuramUniversity of California, Santa BarbaraVerified email at ece.ucsb.edu
Mauro MaggioniBloomberg Distinguished Professor of Mathematics, and Applied Mathematics and StatisticsVerified email at jhu.edu
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
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
Alexander CloningerAssociate Professor, Department of Mathematics & Halicioglu Data Science Institute, UC San DiegoVerified email at ucsd.edu
Xiaosheng ZhuangCity University of Hong KongVerified email at cityu.edu.hk
Valeriya NaumovaSimula Research LaboratoryVerified email at simula.no
Dmitry BatenkovAssistant Professor of Applied Mathematics, Tel-Aviv University, IsraelVerified email at tauex.tau.ac.il
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	557	2017
Neural networks for optimal approximation of smooth and analytic functions HN Mhaskar Neural computation 8 (1), 164-177, 1996	405	1996
Approximation by superposition of sigmoidal and radial basis functions HN Mhaskar, CA Micchelli Advances in Applied mathematics 13 (3), 350-373, 1992	357	1992
Deep vs. shallow networks: An approximation theory perspective HN Mhaskar, T Poggio Analysis and Applications 14 (06), 829-848, 2016	354	2016
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	272	1985
Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature H Mhaskar, F Narcowich, J Ward Mathematics of computation 70 (235), 1113-1130, 2001	234	2001
Extremal problems for polynomials with exponential weights HN Mhaskar, EB Saff Transactions of the American Mathematical Society 285 (1), 203-234, 1984	234	1984
Introduction to the theory of weighted polynomial approximation HN Mhaskar World Scientific, 1996	208	1996
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	195	2017
Approximation properties of a multilayered feedforward artificial neural network HN Mhaskar Advances in Computational Mathematics 1 (1), 61-80, 1993	182	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	167	1995
Learning functions: when is deep better than shallow H Mhaskar, Q Liao, T Poggio arXiv preprint arXiv:1603.00988, 2016	157	2016
Fundamentals of approximation theory HN Mhaskar, DV Pai CRC Press, 2000	124	2000
Neural networks for localized approximation CK Chui, X Li, HN Mhaskar mathematics of computation 63 (208), 607-623, 1994	122	1994
On trigonometric wavelets CK Chui, HN Mhaskar Constructive Approximation 9, 167-190, 1993	118	1993
A proof of Freud's conjecture for exponential weights DS Lubinsky, HN Mhaskar, EB Saff Constructive Approximation 4, 65-83, 1988	117	1988
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	115	2017
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	112	2017
Diffusion polynomial frames on metric measure spaces M Maggioni, HN Mhaskar Applied and Computational Harmonic Analysis 24 (3), 329-353, 2008	98	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	97	1994

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