Comparison of worst case errors in linear and neural network approximation

IEEE Transactions on Information Theory

Volumn 48, Issue 1, 2002, Pages 264-275

  Kůrková, Věra ^a   Sanguineti, Marcello ^b  

^a INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

Complexity of neural networks; Curse of dimensionality; High dimensional optimization; Linear and nonlinear approximation; Rates of approximation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; ERRORS; MULTIVARIABLE SYSTEMS; NEURAL NETWORKS; OPTIMIZATION;

CURSE OF DIMENSIONALITY; NONLINEAR APPROXIMATION; WORST CASE ERRORS;

INFORMATION THEORY;

EID: 0036165028     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.971754     Document Type: Article

References (36)

1. Nonlinear stabilization by receding-horizon neural regulators
2. Parallel networks that learn to pronounce English text
3. Approximating networks and extended Ritz method for the solution of functional optimization problems
4. Universal approximation bounds for superpositions of a sigmoidal function
5. Approximation by neural networks is not continuous
6. Geometry and topology of continuous best and near best approximations
7. Constructive approximation
8. Compression of wavelet decompositions
9. Nonlinear approximation by trigonometric sums
10. Bounds on rates of variable-basis and neural network approximation
11. A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
12. Hinging hyperplanes for regression, classification, and function approximation
13. Neural net approximation
14. Estimates of the number of hidden units and variation with respect to half-spaces
15. Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse
16. Dimension-independent rates of approximation by neural networks
17. Representations and rates of approximation of real-valued Boolean functions by neural networks
18. Remarques sur un resultat non publié de B. Maurey
19. Incremental approximation by neural networks
20. Dimension-independent bounds on the degree of approximation by neural networks
21. Rate of approximation results motivated by robust neural network learning
22. Approximation error bounds that use VC-bounds
23. Approximation and learning of convex superpositions
24. Uniform approximation by neural networks
25. Random approximants and neural networks
26. Tightness of upper bounds on rates of neural-network approximation
27. There exists a neural network that does not make avoidable mistakes
28. Utilizing geometric anomalies of high dimension: When complexity makes computation easier