Dimension-independent bounds on the degree of approximation by neural networks

Keywords

Dimension (graph theory), Univariate, Degree (music), Artificial neural network, Function (biology)

References

• Theory of Approximation of Functions of a Real VariableA. Timan — 1994
• Optimal nonlinear approximationRonald DeVore, Ralph Howard, Charles A. Micchelli — 1989
• Approximation properties of a multilayered feedforward artificial neural networkH. N. Mhaskar — 1993
• A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network TrainingLee Jones — 1992
• Theory of the backpropagation neural networkRobert Hecht-Nielsen — 1989
• Approximation by superposition of sigmoidal and radial basis functionsH. N. Mhaskar, Charles A. Micchelli — 1992
• The Chebyshev polynomialsT. J. Rivlin — 1974
• Multilayer feedforward networks are universal approximatorsKurt Hornik, Maxwell B. Stinchcombe, Halbert White — 1989
• Universal approximation bounds for superpositions of a sigmoidal functionAndrew R. Barron — 1993
• Approximation by superpositions of a sigmoidal functionGeorge Cybenko — 1992
• Multilayer feedforward networks are universal approximatorsHornikK., StinchcombeM., WhiteH. — 1989

Cited by

• Generalization bounds for function approximation from scattered noisy dataPartha Niyogi, Federico Girosi — 1999
• Multivariate data approximation with preprocessing of dataWitold Kosiński, D. Kowalczyk, M. Weigl — 2007
• Approximation Error Bounds via Rademacher's ComplexityGiorgio Gnecco, Marcello Sanguineti — 2008
• Implementing size-optimal discrete neural networks require analog circuitryValeriu Beiu — 1998
• On the near optimality of the stochastic approximation of smooth functions by neural networksV. Maiorov, Ron Meir — 2000
• The essential order of approximation for nearly exponential type neural networksZongben Xu, Jianjun Wang — 2006
• System identification using neural networksH. N. Mhaskar, Nahmwoo Hahm — 1996
• Functional optimization by variable-basis approximation schemesGiorgio Gnecco — 2011
• Neural networks and approximation theoryH. N. Mhaskar — 1996
• Complexity of Gaussian-radial-basis networks approximating smooth functionsPaul C. Kainen, Věra Kůrková, Marcello Sanguineti — 2009
• Universal Approximation Using Feedforward Neural Networks: A Survey of Some Existing Methods, and Some New ResultsFranco Scarselli, Ah Chung Tsoi — 1998
• On Best Approximation by Ridge FunctionsV. Maiorov — 1999
• Rates of approximation of real-valued boolean functions by neural networksVěra Kůrková, Petr Savický, Kateřina Hlaváčková — 1998
• Lower estimation of approximation rate for neural networksFeilong Cao, YongQuan Zhang, Zongben Xu — 2009
• Degree of Approximation by Neural and Translation Networks with a Single Hidden LayerH. N. Mhaskar, Charles A. Micchelli — 1995
• A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane wavesPaul C. Kainen, Věra Kůrková, Andrew Vogt — 2007
• Applications of classical approximation theory to periodic basis function networks and computational harmonic analysisH. N. Mhaskar, Paul Nevai, Eugene Shvarts — 2013
• Using a neural network based method to solve the vibrational Schrödinger equation for H2OSergei Manzhos, Koichi Yamashita, Tucker Carrington — 2009
• Rates of Minimization of Error Functionals over Boolean Variable-Basis FunctionsPaul C. Kainen, V. K rkov, Marcello Sanguineti — 2005
• Best approximation by ridge functions in Lp-spacesV. Maiorov — 2010

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