Bounds on rates of variable-basis and neural-network approximation

IEEE Transactions on Information Theory

Volumn 47, Issue 6, 2001, Pages 2659-2665

  Kůrková, Věra ^a   Sanguineti, Marcello ^b  

^a INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

Approximation by variable basis functions; Bounds on rates of approximation; Complexity of neural networks; High dimensional optimal decision problems

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER ARCHITECTURE; FEEDFORWARD NEURAL NETWORKS; FUNCTIONS; PROBLEM SOLVING;

HIGH-DIMENSIONAL OPTIMAL DECISION PROBLEMS; VARIABLE-BASIS FUNCTIONS;

APPROXIMATION THEORY;

EID: 0035443484     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.945285     Document Type: Letter

References (32)

1. Approximating networks and extended Ritz method for the solution of functional optimization problems
2. Neural approximations for infinite-horizon optimal control of nonlinear stochastic systems
3. Parallel networks that learn to pronounce English text
4. A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
5. Remarques sur un resultat non publié de B. Maurey
6. Universal approximation bounds for superpositions of a sigmoidal function
7. Regularization theory and neural networks architectures
8. Representations and rates of approximation of real-valued Boolean functions by neural networks
9. Rate of approximation results motivated by robust neural network learning
10. Neural net approximation
11. Approximation error bounds that use VC-bounds
12. Approximation and learning of convex superpositions
13. Uniform approximation by neural networks
14. Random approximants and neural networks
15. A note on error bounds for approximation in inner product spaces
16. Constructive function approximation: Theory and practice
17. New results on convex constructive function approximation
18. Comparison of worst-case errors in linear and neural network approximation
19. Dimension-independent bounds on the degree of approximation by neural networks
20. Tightness of upper bounds on rates of neural-network approximation
21. The unreasonable effectiveness of neural network approximation
22. Direct and converse theorems for spline and rational approximation and Besov spaces
23. Constructive approximation
24. q
25. Approximation of functions of several variables by trigonometric polynomials with given number of harmonics, and estimates of ε-entropy
26. Nonlinear approximation by trigonometric sums
27. Compression of wavelet decompositions
28. Dimension-independent rates of approximation by neural networks
29. Author's reply: Comments on 'The unreasonable effectiveness of neural networks approximation
30. Comments on 'The unreasonable effectiveness of neural networks approximation'