Comparison of worst case errors in linear and neural network approximation
From MaRDI portal
Publication:4544781
DOI10.1109/18.971754zbMath1059.62589OpenAlexW2153714959MaRDI QIDQ4544781
Vera Kurková, Marcello Sanguineti
Publication date: 4 August 2002
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/9e2cee625ec47f4409c6f1c994fb40f71e4bc31c
Learning and adaptive systems in artificial intelligence (68T05) Neural networks for/in biological studies, artificial life and related topics (92B20) Neural nets and related approaches to inference from stochastic processes (62M45)
Related Items
Deep learning: a statistical viewpoint ⋮ Linear and nonlinear approximation of spherical radial basis function networks ⋮ When is approximation by Gaussian networks necessarily a linear process? ⋮ Accuracy of suboptimal solutions to kernel principal component analysis ⋮ Two-Layer Neural Networks with Values in a Banach Space ⋮ Lower estimation of approximation rate for neural networks ⋮ Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets ⋮ A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves ⋮ Uniform approximation rates and metric entropy of shallow neural networks ⋮ Optimization of approximating networks for optimal fault diagnosis ⋮ On the tractability of multivariate integration and approximation by neural networks ⋮ Probabilistic lower bounds for approximation by shallow perceptron networks ⋮ Suboptimal solutions to dynamic optimization problems via approximations of the policy functions ⋮ Minimizing sequences for a family of functional optimal estimation problems ⋮ A deep network construction that adapts to intrinsic dimensionality beyond the domain ⋮ Approximation capabilities of neural networks on unbounded domains ⋮ Characterization of the variation spaces corresponding to shallow neural networks ⋮ A comparison between fixed-basis and variable-basis schemes for function approximation and functional optimization ⋮ Complexity estimates based on integral transforms induced by computational units ⋮ Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality ⋮ Accuracy of approximations of solutions to Fredholm equations by kernel methods ⋮ Dynamic programming and value-function approximation in sequential decision problems: error analysis and numerical results ⋮ Estimation of approximating rate for neural network in \(L^p_w\) spaces ⋮ Can dictionary-based computational models outperform the best linear ones? ⋮ Approximate dynamic programming for stochastic \(N\)-stage optimization with application to optimal consumption under uncertainty ⋮ Regularization Techniques and Suboptimal Solutions to Optimization Problems in Learning from Data ⋮ Provable approximation properties for deep neural networks ⋮ Unnamed Item ⋮ Functional optimal estimation problems and their solution by nonlinear approximation schemes ⋮ Approximation and learning by greedy algorithms ⋮ Error bounds for suboptimal solutions to kernel principal component analysis ⋮ Regularized vector field learning with sparse approximation for mismatch removal ⋮ Estimates of variation with respect to a set and applications to optimization problems ⋮ Some comparisons of complexity in dictionary-based and linear computational models ⋮ Learning with generalization capability by kernel methods of bounded complexity ⋮ Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling ⋮ Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison ⋮ Approximating networks and extended Ritz method for the solution of functional optimization problems ⋮ Optimization based on quasi-Monte Carlo sampling to design state estimators for non-linear systems ⋮ Complexity of Gaussian-radial-basis networks approximating smooth functions ⋮ Estimates of the approximation error using Rademacher complexity: Learning vector-valued functions ⋮ Value and Policy Function Approximations in Infinite-Horizon Optimization Problems ⋮ Approximation schemes for functional optimization problems ⋮ Suboptimal Policies for Stochastic $$N$$-Stage Optimization: Accuracy Analysis and a Case Study from Optimal Consumption ⋮ Super-resolution meets machine learning: approximation of measures ⋮ Rates of minimization of error functionals over Boolean variable-basis functions ⋮ Kolmogorov \(n\)-widths of function classes induced by a non-degenerate differential operator: a convex duality approach