On the mathematical foundations of learning

On the mathematical foundations of learning (2002)

Cached

Download Links

by Felipe Cucker , Steve Smale

Venue:	Bulletin of the American Mathematical Society
Citations:	175 - 10 self

BibTeX

@ARTICLE{Cucker02onthe,
    author = {Felipe Cucker and Steve Smale},
    title = {On the mathematical foundations of learning},
    journal = {Bulletin of the American Mathematical Society},
    year = {2002},
    volume = {39},
    pages = {1--49}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

The problem of learning is arguably at the very core of the problem of intelligence, both biological and arti cial. T. Poggio and C.R. Shelton

Citations

6696	The Nature of Statistical Learning Theory - Vapnik - 1995
3909	Neural Networks for Pattern Recognition - Bishop - 1995
1515	A Theory of the Learnable - Valiant - 1984
989	Spline models for observational data - Wahba - 1990
560	Theory of reproducing kernels - Aronszajn - 1950
549	A logical calculus of the ideas immanent in nervous activity - McCulloch, Pitts - 1943
478	Constructive Approximation - Devore, Lorentz - 1993
457	Convergence of Stochastic Processes - Pollard - 1984
418	Numerical Methods for Least Squares Problems - Björck - 1996
332	Smoothing noisy data with spline functions - CRAVEN, WAHBA - 1979
328	Decision theoretic generalization of the PAC model for neural net and other learning applications - Haussler - 1992
283	Interpolation Spaces, An Introduction - Bergh, Löfstrom - 1976
263	Complexity and Real Computation - Blum, Cucker, et al. - 1998
210	Basic algebraic geometry - Shafarevich - 1974
205	Splines Minimizing Rotation-invariant Seminorms in Sobolev space,” in Constructive Theory of Functions of Several Variables - Duchon - 1977
120	Introductory Real Analysis - Kolmogorov, Fomin - 1970
115	On the parabolic kernel of the Schrödinger operator - Li, Yau - 1986
106	n-Widths in Approximation Theory - Pinkus - 1985
96	Metric spaces and completely monotone functions - Schoenberg - 1938
82	Partial Differential Equations I: Basic Theory. 2nd corrected printing - Taylor - 1999
73	Multivariate Interpolation at Arbitrary Points Made Simple - Meinguet - 1979
66	Complexity regularization with applications to artificial neural networks - BARRON - 1991
59	Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators - Williamson, Smola, et al. - 1998
51	Entropy, compactness and the approximation of operators - Carl, Stephani - 1990
45	Tihomirov V: ε-entropy and ε-capacity of sets of functional spaces - Kolmogorov - 1961
41	Function Spaces, Entropy Numbers and Differential Operetors - Edmunds, Triebel - 1996
36	The importance of convexity in learning with squared loss - Lee, Bartlett, et al. - 1998
34	Constructive approximation: advanced problems. Grundlehren der mathematischen Wissenschaften - Lorentz, Golitschek, et al. - 1996
34	Eigenvalues and s-numbers - Pietsch - 1987
34	Estimating the approximation error in learning theory - Smale, Zhou - 2003
33	Introduction to Hilbert Spaces, with Applications, second edition - See, Mikusiński - 1999
30	Integral Equations - Hochstadt - 1973
23	Piece-wise polynomial approximations of functions of the classes W α p - Birman, Solomjak - 1967
22	Constructive Approximation, Grundlehren der Mathematischen Wissenschaften, 303 - DeVore, Lorentz - 1993
20	Newton’s method for overdetermined systems of equations - Dedieu, Shub
19	The Informational Complexity of Learning - Niyogi - 1998
15	Rates of convex approximation in non-Hilbert spaces - Donahue, Gurvits, et al. - 1997
13	On the Morse index theorem - Smale - 1965
9	On the parabolic kernel of the Schrodinger operators, Acta.Math - Li
7	de Geer, Empirical Processes in M-Estimation - van - 2000
6	Function spaces, entropy numbers, and di#erential operators. Cambridge Univ - Edmunds, Triebel - 1996
6	Partial Di#erential Equations: Basic Theory - Taylor - 1996
4	Partial differential equations. VII. Spectral theory of differential operators - Rozenblum, Shubin, et al. - 1994
4	Complexity regularization with applications to arti cial neural networks - Barron - 1991
4	entropy and "-capacity of sets in functional spaces - Kolmogorov, Tihomirov - 1961
1	Intelligent production machines: benefiting from synergy amongst modelling, sensing and learning - Venuvinod
1	Estimation of the complexity of the tabulation problem, Nauka (in Russian), 1959, English Translation appeared as Theory of the Transmission and Processing of the Information - Vitushkin - 1961
1	Partial di erential equations vii: Spectral theory of di erential operators - Rozenblum, Shubin, et al. - 1994
1	Intelligent production machines: bene ting from synergy amongst modelling, sensing and learning - Venuvinod
1	Rates of convex approximation - Darken, Donahue, et al. - 1997