Bounds on margin distributions in learning problems

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 39, Issue 6, 2003, Pages 943-978

  Koltchinskii, Vladimir ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0141425582     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(03)00023-2     Document Type: Article

References (21)

1. Anthony M. Bartlett P. Neural Network Learning: Theoretical Foundations 1999 Cambridge University Press
2. Bartlett P. The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network IEEE Trans. Inform. Theory 44 1998 525-536
3. Cortes C. Vapnik V. Support vector networks Machine Learning 20 1995 273-297
4. Devroye L. Györfi L. Lugosi G. A Probabilistic Theory of Pattern Recognition 1996 Springer-Verlag New York
5. Dudley R.M. Uniform Central Limit Theorems 1999 Cambridge University Press
6. E. Giné, V. Koltchinskii, J. Wellner, Ratio limit theorems for empirical processes, Preprint, 2003
7. Kégl B. Linder T. Lugosi G. Data-dependent margin-based generalization bounds for classification, in: Helmbold D. Williamson B. (Eds.), Proc. of 14th Annual Conference on Computational Learning Theory, COLT2001, Lecture Notes in Artificial Intelligence 2001 368-384 Springer New York
8. Koltchinskii V. Panchenko D. Rademacher processes and bounding the risk of function learning, in: Giné E. Mason D. Wellner J. (Eds.), High Dimensional Probability II 2000 444-459 Birkhäuser Boston
9. Koltchinskii V. Panchenko D. Empirical margin distributions and bounding the generalization error of combined classifiers Ann. Statist. 30 2002 1-50
10. Koltchinskii V. Panchenko D. Lozano F. Some new bounds on the generalization error of combined classifiers, in: Leen T.K. Dietterich T.G. Tresp V. (Eds.), Proc. of NIPS'2000, in: Advances in Neural Information Processing Systems 13 2001 245-251 MIT Press URL: http://www.boosting.org/
11. Koltchinskii V. Panchenko D. Lozano F. Further explanation of the effectiveness of voting methods: the game between margins and weights, in: Helmbold D. Williamson B. (Eds.), Proc. of 14th Annual Conference on Computational Learning Theory, COLT2001, in: Lecture Notes in Artif. Intell. 2001 241-255 Springer New York
12. Koltchinskii V. Panchenko D. Lozano F. Bounding the generalization error of convex combinations of classifiers: balancing the dimensionality and the margins Ann. Appl. Probab. 13 1 2003 213-252
13. Ledoux M. Talagrand M. Probability in Banach Spaces 1991 Springer-Verlag New York
14. Massart P. About the constants in Talagrand's concentration inequalities for empirical processes Ann. Probab. 28 2000 863-885
15. Massart P. Some applications of concentration inequalities to statistics Ann. Fac. Sci. Tolouse (IX) 2000 245-303
16. Schapire R. Freund Y. Bartlett P. Lee W.S. Boosting the margin: a new explanation of effectiveness of voting methods Ann. Statist. 26 1998 1651-1687
17. Talagrand M. A new look at independence Ann. Probab. 24 1996 1-34
18. Talagrand M. New concentration inequalities in product spaces Invent. Math. 126 1996 505-563
19. A. Tsybakov, Optimal aggregation of classifiers in statistical learning, Preprint, 2002
20. van der Vaart A.W. Wellner J.A. Weak Convergence and Empirical Processes. With Applications to Statistics 1996 Springer-Verlag New York
21. Vapnik V. Statistical Learning Theory 1998 Wiley New York