Generalization errors of the simple perceptron

Journal of Physics A: Mathematical and General

Volumn 31, Issue 17, 1998, Pages 4037-4048

  Feng, Jianfeng ^a  

^a BABRAHAM INSTITUTE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032071385     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/17/013     Document Type: Article

References (35)

1. Amari S and Murata N 1993 Statistical theory of learning curves under entropic loss criterion Neural Comput. 5 140-53
2. Amari S, Murata N and Ikeda K 1995a Statistical theory of learning curves Neural Networks: The Statistical Mechanics Perspective ed J Oh, Ch Kwon and S Chao, pp 3-17
3. Amari S, Murata N, Müller K-R, Finke M and Yang H 1995b Asymptotic statistical theory of overtraining and cross-validation METR 95-06 Department of Mathematical Engineering and Information Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan
4. Baum E B 1990 The perceptron algorithm is fast for nonmalicious distribution Neural Comput. 2 248
5. Baum E B and Haussler D 1989 What size net gives valid generalization Neural Comput. 4 151-60
6. Cohn D and Tesauro G 1992 How tight are the Vapnik-Chervonenkis bounds Neural Comput. 4 249-69
7. Balkema A A and De Haan L 1978 Limit distributions for order statistics. I Theory Prob. Appl. XXIII 77-92
8. Balkema A A and De Haan L 1978 Limit distributions for order statistics. II Theory Prob. Appl. XXIII 341-58
9. Bouchaud J-P and Mézard M 1997 Universality classes for extreme value statistics J. Phys. A: Math. Gen. 30 7997-8015
10. Engel A and den Broeck C V 1993 Statistical mechanics calculation of Vapnik Chervonenkis bounds for perceptron J. Phys. A: Math. Gen. 26 6893-914
11. Feng J 1997 Behaviours of spike output jitter in the integrate-and-fire model Phys. Rev. Lett. 79 4505-8
12. Feng J 1997 Lyapunov functions for neural nets with nondifferentiable input-output characteristics Neural Comput. 9 45-51
13. Feng, J., and Brown, D.(1998), Fixed-point attractor analysis for a class of neurodynamics Neural Comput. 10 189-213
14. Feng J and Brown D 1998 Spike output jitter, mean firing time and coefficient of variation J. Phys. A: Math. Gen. 31 1239-52
15. Feng J and Hadeler K P 1996 Qualitative behaviors of some simple neural networks J. Phys. A: Math. Gen. 29 5019-33
16. Feng J, Pan H and Roychowdhury V P 1996 On neurodynamics with limiter function and Linsker's developmental model Neural Comput. 8 1003-19
17. Feng J and Tirozzi B 1995 The SLLN for the free-energy of the Hopfield and spin glass model Helv. Phys. Acta 68 365-79
18. Feng J and Tirozzi B 1997 Capacity of the Hopfield model J. Phys. A: Math. Gen. 30 3383-91
19. Galambos J 1984 Introductory Probability Theory (New York: Marcel Dekker) pp 164-8
20. Gray M S, Lawrence DT, Golomb B A and Sejnowski T J 1995 A perceptron reveals the face of sex Neural Comput. 7 1160-4
21. Haussler D, Kearns M and Shapire R 1991 Bounds on the sample complexity of Bayesian learning using information theory and the VC dimension Proc. 4th Annu. Workshop on computational Learning Theory (San Mateo, CA: Morgan Kaufmann) pp 61-74
22. Haussler D, Littlestone N and Warmuth K 1988 Predicting {0, 1} functions on randomly drawn points Proc. COLT'88 (San Mateo, CA: Morgan Kaufmann) pp 280-95
23. Hertz J, Krogh A and Palmer R 1991 Introduction to the Theory of Neural Computation (Reading, MA: Addison-Wesley)
24. Leadbetter M R, Lindgren G and Rootzén H 1983 Extremes and Related Properties of Random Sequences and Processes (New York: Springer)
25. Levin E, Tishby N and Solla S A 1990 A statistical approach to learning and generalization in layered neural networks Proc. IEEE 78 1568-74
26. Murata N, Yoshizawa S and Amari S 1994 Network information criterion-determinate the number of hidden units for an artificial neural network model IEEE Trans. NN 6 865-72
27. Opper M and Haussler D 1991 Calculation of the learning curve of Bayes optimal classification algorithm for learning perceptron with noise Proc. 4th Annu. Workshop on Computer Learning Theory pp 75-87
28. Opper M and Haussler D 1995 Bounds for predictive errors in the statistical mechanics of supervised learning Phys. Rev. Lett. 75 3772-5
29. Romeo A 1993 Generalization transitions in hidden-layer neural networks for 3rd-order feature discrimination Phys. Rev. E 47 2162-71
30. Seung H S, Sompolinsky H and Tishbby N 1992 Statistical mechanics of learning from examples Phys. Rev. A 45 6056-91
31. Sompolinsky H and Tishby N 1990 Learning in a 2-layer neural network of edge detectors Europhys. Lett. 13 567-72
32. Vapnik V N and Chervonenkis A Y 1971 On the uniform convergence of relative frequencies of events to their probabilities Theory Prob. Appl. 16 264-80
33. Vapnik E, Levin E and LeCun Y 1994 Measuring the VC dimension of a learning machine Neural Comput. 5 851-76
34. Watkin T L H, Rau A and Biehl M 1993 The statistical mechanics of learning a rule Rev. Mod. Phys. 65 499-556
35. Yamanishi K 1991 A loss bound model for on-line stochastic prediction strategies Proc. 4th Annu. Workshop on Computer Learning Theory pp 290-302