Radial basis function networks: Generalization in over-realizable and unrealizable scenarios

Neural Networks

Volumn 9, Issue 9, 1996, Pages 1521-1529

  Freeman, Jason A S ^a   Saad, David ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b NONE

Author keywords

generalization; neural networks; over realizable; radial basis functions; regularization; stochastic learning; supervised learning; unreali zable

Indexed keywords

ERROR ANALYSIS; FUNCTION EVALUATION; KNOWLEDGE REPRESENTATION; LEARNING SYSTEMS; MATHEMATICAL MODELS; RANDOM PROCESSES;

RADIAL BASIS FUNCTIONS; STOCHASTIC LEARNING;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; LEARNING; PRIORITY JOURNAL;

EID: 0030480111     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/0893-6080(95)00122-0     Document Type: Article

References (17)

1. Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory. 39:1993;930-945.
2. Barron A.R. Approximation and estimation bounds for artificial neural networks. Machine Learning. 14:1994;115-133.
3. Bruce A.D., Saad D. Statistical mechanics of hypothesis evaluation. Journal of Physics A: Mathematical and General. 27:1994;3355-3363.
4. Dunmur A.P., Wallace D.J. Learning and generalisation in a linear perceptron stochastically trained with noisy data. Journal of Physics A: Mathematical and General. 26:1993;5767-5779.
5. Freeman, J.A.S., & Saad, D. (1995). Learning and generalisation in radial basis function networks. Neural Computation (in press).
6. Hansen L.K. Stochastic linear learning: Exact test and training error averages. Neural Networks. 6:1993;393-396.
7. Hartman E.J., Keeler J.D., Kowalski J.M. Layered neural networks with gaussian hidden units as universal approximators. Neural Computation. 2:1993;210-215.
8. Haussler, D. (1994). The probably approximately correct (pac) and other learning models. In A. Meyrowitz & S. Chipman (Eds.), Foundations of knowledge acquisition: machine learning (Chapter 9). Boston: Kluwer.
9. Levin, E., Tishby, N., & Solla, S.A. (1989). A statistical approach to learning and generalisation in layered neural networks. In Colt '89: 2nd Workshop on Computational Learning Theory (pp. 245-260).
10. Mackay D.J.C. Bayesian interpolation. Neural Computation. 4:1992;415-447.
11. Niyogi, P., & Girosi, F. (1994). On the relationship between generalization error, hypothesis complexity and sample complexity for radial basis functions. (Technical report, AI Laboratory, Massachusetts Institute of Technology).
12. Radons, G., Schuster, H.G., & Werner, D. (1990). Drift and diffusion in backpropagation learning. In R. Eckmiller et al., (Eds.), Parallel processing in neural systems and computers. Amsterdam: Elsevier Science Publishers, North Holland.
13. Rögnvaldsson T. On Langevin updating in multilayer perceptrons. Neural Computation. 6:1994;916-926.
14. Schwarze H. Learning a rule in a multilayer neural network. Journal of Physics A: Mathematical and General. 26:1993;5781-5794.
15. Vapnik V.N., Chervonenkis A.Y. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and its Applications. 17:1971;264-280.
16. Watkin T.L.H., Rau A., Biehl M. The statistical mechanics of learning a rule. Reviews of Modern Physics. 65:1993;499-556.
17. Wolpert D.H. On the connection between in-sample testing and generalisation error. Complex Systems. 6:1992;47-96.