no. 6
Bounds on margin distributions in learning problems
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 6, pp. 943-978. 
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     author = {Koltchinskii, Vladimir},
     title = {Bounds on margin distributions in learning problems},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {943--978},
     publisher = {Elsevier},
     volume = {39},
     number = {6},
     year = {2003},
     doi = {10.1016/S0246-0203(03)00023-2},
     mrnumber = {2010392},
     zbl = {1031.60017},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0246-0203(03)00023-2/}
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Koltchinskii, Vladimir. Bounds on margin distributions in learning problems. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 6, pp. 943-978. doi : 10.1016/S0246-0203(03)00023-2. http://www.numdam.org/articles/10.1016/S0246-0203(03)00023-2/

[1] M. Anthony, P. Bartlett, Neural Network Learning: Theoretical Foundations, Cambridge University Press, 1999. | MR | Zbl

[2] P. Bartlett, 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. | MR | Zbl

[3] C. Cortes, V. Vapnik, Support vector networks, Machine Learning 20 (1995) 273-297. | Zbl

[4] L. Devroye, L. Györfi, G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York, 1996. | MR | Zbl

[5] R.M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, 1999. | MR | Zbl

[6] E. Giné, V. Koltchinskii, J. Wellner, Ratio limit theorems for empirical processes, Preprint, 2003. | MR

[7] B. Kégl, T. Linder, G. Lugosi, 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, Springer, New York, 2001, pp. 368-384. | MR | Zbl

[8] V. Koltchinskii, D. Panchenko, Rademacher processes and bounding the risk of function learning, in: Giné E., Mason D., Wellner J. (Eds.), High Dimensional Probability II, Birkhäuser, Boston, 2000, pp. 444-459. | MR | Zbl

[9] V. Koltchinskii, D. Panchenko, Empirical margin distributions and bounding the generalization error of combined classifiers, Ann. Statist. 30 (2002) 1-50. | MR | Zbl

[10] V. Koltchinskii, D. Panchenko, F. Lozano, Some new bounds on the generalization error of combined classifiers, in: Leen T.K., Dietterich T.G., Tresp V. (Eds.), Proc. of NIPS'2000, Advances in Neural Information Processing Systems, 13, MIT Press, 2001, pp. 245-251, URL: , http://www.boosting.org/.

[11] V. Koltchinskii, D. Panchenko, F. Lozano, 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, Lecture Notes in Artif. Intell., Springer, New York, 2001, pp. 241-255. | MR | Zbl

[12] V. Koltchinskii, D. Panchenko, F. Lozano, Bounding the generalization error of convex combinations of classifiers: balancing the dimensionality and the margins, Ann. Appl. Probab. 13 (1) (2003) 213-252. | MR | Zbl

[13] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer-Verlag, New York, 1991. | MR | Zbl

[14] P. Massart, About the constants in Talagrand's concentration inequalities for empirical processes, Ann. Probab. 28 (2000) 863-885. | MR | Zbl

[15] P. Massart, Some applications of concentration inequalities to statistics, Ann. Fac. Sci. Tolouse (IX) (2000) 245-303. | Numdam | MR | Zbl

[16] R. Schapire, Y. Freund, P. Bartlett, W.S. Lee, Boosting the margin: a new explanation of effectiveness of voting methods, Ann. Statist. 26 (1998) 1651-1687. | MR | Zbl

[17] M. Talagrand, A new look at independence, Ann. Probab. 24 (1996) 1-34. | MR | Zbl

[18] M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505-563. | MR | Zbl

[19] A. Tsybakov, Optimal aggregation of classifiers in statistical learning, Preprint, 2002. | MR

[20] A.W. Van Der Vaart, J.A. Wellner, Weak Convergence and Empirical Processes. With Applications to Statistics, Springer-Verlag, New York, 1996. | MR | Zbl

[21] V. Vapnik, Statistical Learning Theory, Wiley, New York, 1998. | MR | Zbl

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