On the approximation of functional classes equipped with a uniform measure using ridge functions

DOI10.1006/jath.1998.3305zbMath0940.41009OpenAlexW2118774596MaRDI QIDQ1300147

Joel Ratsaby, Ron Meir, Vitaly Maiorov

Publication date: 10 May 2000

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/86443ba0c1addebf18966e54fbf0cace5ecc9f9c

zbMATH Keywords

nonlinear approximationuniform measureprobabilistic widthapproximation by ridge functionsapproximation of Besov-type class

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximation by other special function classes (41A30) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (10)

On the error of approximation by ridge functions with two fixed directions ⋮ Characterization of an extremal sum of ridge functions ⋮ Approximation of Sobolev classes by polynomials and ridge functions ⋮ The Kolmogorov-Arnold representation theorem revisited ⋮ Phase transitions in rate distortion theory and deep learning ⋮ On the representation by linear superpositions ⋮ The ridge function representation of polynomials and an application to neural networks ⋮ Some problems in the theory of ridge functions ⋮ Limitations of shallow nets approximation ⋮ On best approximation of classes by radial functions

Cites Work

• Networks and the best approximation property
• On best approximation by ridge functions
• Approximation and estimation bounds for artificial neural networks
• Fundamentality of ridge functions
• Linear widths of function spaces equipped with the Gaussian measure
• Harmonics on homogeneous manifolds
• Probabilistic and average linear width in \(L_ \infty\)-norm with respect to \(r\)-fold Wiener measure
• On the near optimality of the stochastic approximation of smooth functions by neural networks
• Approximation by Ridge Functions and Neural Networks
• Probability Inequalities for Sums of Bounded Random Variables
• Lower Bounds for Approximation by Nonlinear Manifolds
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