Some theoretical results concerning the convergence of compositions of regularized linear functions

Advances in Neural Information Processing Systems

Volumn , Issue , 2000, Pages 370-378

  Zhang, Tong ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COVERING NUMBERS; LINEAR CLASSIFIERS; LINEAR FUNCTIONS; SAMPLE COMPLEXITY BOUNDS;

SUPPORT VECTOR MACHINES;

EID: 0006557529     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. N. Alon, S. Ben-David, N. Cesa-Bianchi, and D. Haussier. Scale-sensitive dimenions, uniform convergence, and leamability. Journal of the ACM, 44(4):615-631, 1997.
2. A.R. Barron. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Transactions on Information Theory, 39(3):930-945, 1993.
3. P.L. Bartieri. The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network. IEEE Transactions on Information Theory, 44(2):525-536,1998.
4. R.M. Dudley. A course on empirical processes, volume 1097 of Lecture Notes in Mathematics. 1984.
5. G.H. Golub and C.R Van Loan. Matrix computations. Johns Hopkins University Press, Baltimore, MD, third edition, 1996.
6. D. Haussier. Generalizing the PAC model: sample size bounds from metric dimension-based uniform convergence results. In Proc. 30th IEEE Symposium on Foundations of Computer Science, pages 40-45, 1989.
7. Lee K. Jones. A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training. Ann. Statist., 20(1):608-613,1992.
8. A.N. Kolmogorov. Asymptotic characteristics of some completely bounded metric spaces. Doki. Akad. Nauk SSSR, 108:585-589, 1956.
9. A.N. Kolmogorov and V.M. Tihomirov. e-entropy and e-capacity of sets in functional spaces. Amer. Math. Soc. Transi., 17(2):277-364,1961.
10. Wee Sun Lee, P.L. Bartlett, and R.C. Williamson. Efficient agnostic learning of neural networks with bounded fan-in. IEEE Transactions on Information Theory, 42(6):2118-2132, 1996.
11. D. Pollard. Convergence of stochastic processes. Springer-Verlag, New York, 1984.
12. N. Sauer. On the density of families of sets. Journal of Combinatorial Theory (Series A), 13:145-147,1972.
13. Robert E. Schapire, Yoav Freund. Peter Bartlett, and Wee Sun Lee. Boosting the margin: a new explanation for the effectiveness of voting methods. Ann. Statist., 26(5): 1651-1686,1998.
14. J. Shawe-Taylor, P.L. Bartlett, R.C. Williamson, and M. Anthony. Structural risk minimization over data-dependent hierarchies. IEEE Trans. Inf. Theory, 44(5): 1926-1940, 1998.
15. V.N. Vapnik. Estimation of dependences based on empirical data. Springer-Verlag, New York, 1982. Translated from the Russian by Samuel Kotz.
16. V.N. Vapnik. The nature of statistical learning theory. Springer-Verlag, New York, 1995.
17. V.N. Vapnik and A.J. Chervonenkis. On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probability and Applications, 16:264-280,1971.
18. Tong Zhang. Analysis of regularized linear functions for classification problems. Technical Report RC-21572, IBM, 1999.