Radial basis function networks and complexity regularization in function learning

IEEE Transactions on Neural Networks

Volumn 9, Issue 2, 1998, Pages 247-256

  Krzyzak, Adam ^a,b   Linder, Tamás ^a,c,d  

^a IEEE   (Canada)

^b Gina Cody School of Engineering and Computer Science   (Canada)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

Complexity regularization; Convergence rates; Function estimation; Radial basis functions; Random covering numbers

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; LEARNING SYSTEMS; NUMBER THEORY; PARAMETER ESTIMATION; RANDOM PROCESSES;

COMPLEXITY REGULARIZATION; FUNCTION LEARNING; RANDOM COVERING NUMBERS;

NEURAL NETWORKS;

EID: 0032022221     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.661120     Document Type: Article

References (31)

1. G. Cybenko, "Approximations by superpositions of sigmoidal functions," Math. Contr., Signals, Syst., vol. 2, pp. 303-314, 1989.
2. K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Networks, vol. 2, pp. 359-366, 1989.
3. A. R. Barron, "Universal approximation bounds for superpositions of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, pp. 930-944, 1993.
4. n ) by multilayer feedforward networks and related problems," IEEE Trans. Neural Networks, vol. 6, pp. 25-30, Jan. 1995.
5. L. K. Jones, "A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural networks," Ann. Statist., vol. 20, pp. 608-613, 1992.
6. F. Girosi and G. Anzellotti, "Rates of convergence for radial basis functions and neural networks," in Artificial Neural Networks for Speech and Vision, R. J. Mammone, Ed. London: Chapman and Hall, 1993, pp. 97-113.
7. H. White, "Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings," Neural Networks, vol. 3, pp. 535-549, 1990.
8. A. R. Barron, "Complexity regularization with application to artificial neural networks," in Nonparametric Functional Estimation and Related Topics, G. Roussas, Ed., NATO ASI Series. Dordrecht, The Netherlands: Kluwer, 1991, pp. 561-576.
9. D. Haussler, "Decision theoretic generalizations of the PAC model for neural net and other learning applications," Inform. Computa., vol. 100, pp. 78-150, 1992.
10. A. Faragó and G. Lugosi, "Strong universal consistency of neural-network classifiers," IEEE Trans. Inform. Theory, vol. 39, pp. 1146-1151, 1993.
11. A. R. Barron, "Approximation and estimation bounds for artificial neural networks," Machine Learning, vol. 14, pp. 115-133, 1994.
12. D. F. McCaffrey and A. R. Gallant, "Convergence rates for single hiddden layer feedforward networks," Neural Networks, vol. 7, no. 1, pp. 147-158, 1994.
13. W. S. Lee, P. L. Bartlett, and R. C. Williamson, "Efficient agnostic learning of neural networks with bounded fan-in," IEEE Trans. Inform. Theory, vol. 42, pp. 2118-2132, Nov. 1996.
14. F. Girosi, "Regularization theory, radial basis functions and networks," in From Statistics to Neural Networks: Theory and Pattern Recognition Applications, V. Cherkassky, J. H. Friedman, and H. Wechsler, Eds. Berlin: Springer-Verlag, 1992, pp. 166-187.
15. F. Girosi, M. Jones, and T. Poggio, "Regularization theory and neural-network architectures," Neural Computa. vol. 7, pp. 219-267, 1995.
16. A. Krzyżak, T. Linder, and G. Lugosi, "Nonparametric estimation and classification using radial basis function nets and empirical risk minimization," IEEE Trans. Neural Networks, vol. 7, pp. 475-487, Mar. 1996.
17. P. Niyogi and F. Girosi, "On the relationship between generalization error, hypothesis complexity, and sample complexity for radial basis functions," Neural Computa., vol. 8, pp. 819-842, 1996.
18. U. Grenander, Abstract Inference. New York: Wiley, 1981.
19. G. Lugosi and K. Zeger, "Nonparametric estimation via empirical risk minimization," IEEE Trans. Inform. Theory, vol. 41, pp. 677-678, 1995.
20. V. N. Vapnik, Estimation of Dependencies Based on Empirical Data, New York: Springer-Verlag, 1982.
21. L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition. New York: Springer, 1996.
22. J. Rissanen, "A universal prior for integers and estimation by minimum description length," Ann. Statist., vol. 11, pp. 416-431, 1983.
23. G. Lugosi and A. Nobel, "Adaptive model selection using empirical complexities," Dept. Statist., Univ. North Carolina, Chapel Hill, Tech. Rep. 2346, 1996.
24. C. Darken, M. Donahue, L. Gurvits, and E. Sontag, "Rate of approximation results motivated by robust neural-network learning," in Proc. 6th Annu. Wkshp. Computa. Learning Theory, 1993, pp. 303-309.
25. W. J. Rey, Introduction to Robust and Quasi-Robust Statistical Methods. Berlin: Springer-Verlag, 1983.
26. H. L. Royden, Real Analysis. New York: Macmillan, 1968.
27. E. M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton, NJ: Princeton Univ. Press, 1970.
28. D. Pollard, Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.
29. _, Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics. Hayward, CA: Inst. Math. Statist., 1990.
30. D. Nolan and D. Pollard, "U-processes: Rates of convergence," Ann. Statist., vol. 15, pp. 780-799, 1987.
31. D. Haussler, "Sphere packing numbers for subsets of the Boolean n-cube with bounded Vapnik-Chervonenkis dimension," J. Combinatorial Theory Series A, vol. 69, pp. 217-232, 1995.