On PAC learning of functions with smoothness properties using feedforward sigmoidal networks

Proceedings of the IEEE

Volumn 84, Issue 10, 1996, Pages 1562-1568

  Rao, Nageswara S V ^a   Protopopescu, Vladimir A ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; FUNCTIONS; LEARNING SYSTEMS; PROBABILITY;

FEEDFORWARD SIGMOIDAL NETWORKS; PROBABILITY AND APPROXIMATELY CORRECT;

FEEDFORWARD NEURAL NETWORKS;

EID: 0030270407     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/5.537119     Document Type: Article

References (23)

1. M. Anthony and P. Bartlett, "Function learning from interpolation," NeuroCOLT Tech. Rep. Series NC-TR-94-013, Royal Holloway, Univ. London, 1994.
2. P. L. Bartlett, P. M. Long, and R. C. Williamson, "Fat-shattering and the learnability of real-values fucntions," in Proc. 7th Annu. ACM Conf on Computational Learning Theory, 1994.
3. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth, "Learnability and the Vapnik-Chervonenkis dimension," J. Assoc. Computing Machinery, vol. 36, no. 4, pp. 929-965, 1989.
4. L. Brieman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and Regression Trees. Belmont, CA: Wadsworth, 1984.
5. B. Cheng and D. M. Titterington, "Neural networks: A review from a statistical perspective," Statistical Sci., vol. 9, no. 1, pp. 2-54, 1994.
6. Z. Ciesielski, "Haar system and nonparametric density estimation in several variables," Probability and Mathematical Statistics, vol. 9, pp. 1-11, 1988.
7. G. Cybenko, "Approximation by superpositions of a sigmoidal function," Mathematics of Contr., Signals, and Syst., vol. 2, pp. 303-314, 1989.
8. J. Engel, "A simple wavelet approach to nonparametric regression from recursive partitioning schemes," J. Multivariate Anal., vol. 49, pp. 242-254, 1994.
9. A. Macintyre and E. D. Sontag, "Finiteness results for sigmoidal neural networks," in Proc. 25th Annu. ACM Symp. on Theory of Computing, 1993, pp. 325-334.
10. E. A. Nadaraya, "Remarks on nonparametric estimates for density functions and regression curves," Theory of Probability and Applications, vol. 15, pp. 134-137, 1970.
11. V. Nedeljkovic, "A novel multilayer neural networks training algorithm that minimizes the probability of classification error," IEEE Trans. Neur. Networks, vol. 4, pp. 650-659, Apr. 1993.
12. D. Pollard, Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.
13. F. P. Preparata and M. I. Shamos, Computational Geometry: An Introduction. New York: Springer-Verlag, 1985.
14. B. L. S. Prakasa Rao, Nonparametric Functional Estimation. New York: Academic, 1983.
15. N. S. V. Rao, "Fusion methods for multiple sensor systems with unknown error densities," J. Franklin Inst., vol. 331B, no. 5, pp. 509-530, 1995.
16. V. Roychowdhury, K. Siu, and A. Orlitsky, Eds., Theoretical Advances in Neural Computation and Learning. New York: Kluwer, 1994.
17. S. Saarinen, R. B. Bramley, and G. Cybenko, "Neural networks, backpropagation and automatic differentiation," in Automatic Differentiation of Algorithms: Theory, Implementation, and Application, A. Griewank and G. F. Corliss, Eds. Philadelphia: SIAM, 1991, pp. 31-42.
18. Y. Sakai, E. Takimoto, and A. Maruoka, "Proper learning algorithm for functions of k terms under smooth distributions," in Proc. 8th Annu. ACM Conf. on Computational Learning Theory, 1995.
19. L. G. Valiant, "A theory of the learnable," Commun. ACM, vol. 27, no. 11, pp. 1134-1142, 1984.
20. V. N. Vapnik, Estimation of Dependences Based on Empirical Data. New York: Springer Verlag, 1982.
21. _, "Inductive principles of the search for empirical dependences," in Proc. 2nd Annu. Workshop on Computational Learning Theory, 1989, pp. 3-21.
22. _, The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995.
23. H. White, "Some asymptotic results for learning in single hidden layer feedforward network models," J. Amer. Statistical Assoc., vol. 84, pp. 1008-1013, 1989.