A. N. Giné-e, . Ossiander-m, and . Zinn-j, « The central limit theorem and the law of iterated logarithm for empirical processes under local conditions, pp.271-305, 1988.

B. P. Williamson-r, « The Vapnik-Chervonenkis dimension and pseudodimension of two-layer neural networks with discrete inputs, Neural computation, vol.8, pp.653-656, 1996.

. 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 Transactions on Information Theory, vol.44, issue.2, pp.2-525, 1998.
DOI : 10.1109/18.661502

. A. Barron, . Birgé-l, and . Massart-p, Risk bounds for model selection via penalization, Probab. Theory Relat. Fields, pp.301-413, 1999.
DOI : 10.1007/s004400050210

. P. Bartlett and . J. Shawe-taylor, « Generalization Performance of Support Vector Machines and Other Pattern Classifiers, Advances in Kernel Methods, Support Vector Learning, pp.43-54, 1999.

. G. Bennett, Probability Inequalities for the Sum of Independent Random Variables, Journal of the American Statistical Association, vol.18, issue.297, pp.33-45, 1962.
DOI : 10.1214/aoms/1177730437

I. A. Benedek-g and . Nonuniform-learnability, Nonuniform learnability, Journal of Computer and System Sciences, vol.48, issue.2, pp.311-323, 1994.
DOI : 10.1016/S0022-0000(05)80005-4

. S. Bernstein, The Theory of Probabilities, 1946.

. J. Blum, On the Convergence of Empiric Distribution Functions, The Annals of Mathematical Statistics, vol.26, issue.3, pp.527-529, 1955.
DOI : 10.1214/aoms/1177728499

. O. Bousquet, Concentration Inequalities and Empirical Processes Theory Applied to the Analysis of Learning Algorithms, 2002.

C. Cervellera and . Muselli-m, Deterministic Design for Neural Network Learning: An Approach Based on Discrepancy, IEEE Transactions on Neural Networks, vol.15, issue.3, pp.3-533, 2004.
DOI : 10.1109/TNN.2004.824413

C. Chu, « An estimate concerning the Kolmogoroff limit distribution », Transactions of the, pp.36-50, 1949.

. J. Dehardt, Generalizations of the Glivenko-Cantelli Theorem, The Annals of Mathematical Statistics, vol.42, issue.6, pp.2050-2055, 1971.
DOI : 10.1214/aoms/1177693073

D. R. Duda-r and H. P. , « Weak convergence of measures on non separable metric spaces and empirical measures on Euclidean spaces » Pattern Classification and Scene Analysis, Illinois J. Math, vol.10, issue.73, pp.109-126, 1966.

. Gee, . Van-der, and . S. Geer, Empirical Processes in M-estimation, 2000.

K. W. Gerstner, Spiking Neuron Models, Single Neurons, Populations, Plasticity, 2002.

G. E. Zinn-j, « Some limit theorems for empirical processes, Annals of Probability, vol.12, issue.4, pp.929-989, 1984.

. E. Giné, . Zinn-j, and . Bootstrapping, Bootstrapping General Empirical Measures, The Annals of Probability, vol.18, issue.2, pp.851-869, 1990.
DOI : 10.1214/aop/1176990862

. P. Golberg, Bounding the Vapnik-Chervonenkis dimension of concept classes parametrized by real numbers, Machine Learning, pp.131-148, 1995.

. Y. Guermeur, . Maumy-m, and . Sur-f, Notes sur le " théorème de Maurey-Carl, 2005.

. L. Gurvits and . Koiran-p, Approximation and learning of convex superpositions, Proceedings of EUROCOLT'95, 1995.

. L. Gurvits and . Koiran-p, Approximation and Learning of Convex Superpositions, Journal of Computer and System Sciences, vol.55, pp.1-161, 1997.

. L. Gurvits, « A note on a scale-sensitive dimension of linear bounded functionals in Banach spaces, Theoretical Computer Science, vol.261, pp.1-81, 2001.

H. T. Tibshirani-r and . Friedman-j, The Elements of Statistical Learning - Data Mining, Inference, and Prediction, 2002.

H. and ]. D. Haussler, « Sphere packing numbers for subsets of the boolean n-cube with bounded Vapnik-Chervonenkis dimension, Journal of Combinatorial Theory A, vol.69, pp.217-232, 1995.

H. , ]. D. Haussler, and L. P. , « A Generalization of Sauer's Lemma. », Journal of Combinatorial Theory, Series A, vol.71, pp.219-240, 1995.

. K. Hor-89-]-hornik, . Stinchcombe-m, and . White-h, Multilayer feedforward networks are universal approximators, Multilayer feedforward networks are universal approximators, pp.359-366, 1989.
DOI : 10.1016/0893-6080(89)90020-8

. M. Karpinski and . Macintyre-a, Polynomial bounds for VC dimension of sigmoidal neural networks, Proceedings of the twenty-seventh annual ACM symposium on Theory of computing , STOC '95, pp.200-208, 1995.
DOI : 10.1145/225058.225118

. M. Karpinski and . Macintyre-a, Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks, Journal of Computer and System Sciences, vol.54, issue.1, pp.169-176, 1997.
DOI : 10.1006/jcss.1997.1477

. Kea, . Kearns-m, and . Schapire-r, « Efficient distribution-free learning of probabilistic concepts, Proceedings of the 31st Annual Symposium on Foundations of Computer Science, pp.382-391, 1990.

. Kea, . Kearns-m, and . Schapire-r, « Efficient Distribution-free Learning of Probabilistic Concepts, Journal of Computer and System Sciences, vol.48, issue.3, pp.464-497, 1994.

. J. Kiefer, On Large Deviations of the Empiric D.F. of Vector Chance Variables and a Law of the Iterated Logarithm, Pacific journal of mathematics, vol.11, pp.649-660, 1961.
DOI : 10.1007/978-1-4613-8505-9_28

. T. Kohonen, Self-Organization and Associative Memory, 1989.

. A. Kolmogorov and . Tihomirov-v, « ?-entropy and ?-capacity of sets in functional spaces », Amer, Math. Soc. Translations, vol.17, issue.2, pp.277-364, 1961.

. V. Kolcinski, « On the central limit theorem for empirical measures, Theory of Probability and Mathematical Statistics, pp.71-82, 1981.

L. G. Zeger-k, Nonparametric estimation via empirical risk minimization, IEEE Transactions on Information Theory, vol.41, pp.677-687, 1995.

L. G. Zeger-k, « Concept learning using complexity regularization, IEEE Transactions on Information Theor, vol.42, pp.48-54, 1996.

M. A. Sontag-e, « Finiteness results for sigmoidal " neural " networks, Proceedings of 25th Annual ACM Symposium on the Theory of Computing, pp.325-334, 1993.

. B. Natarajan, On learning sets and functions, Machine Learning, pp.67-97, 1989.
DOI : 10.1007/BF00114804

. H. Nie-92-]-niederreiter, Random Number Generation and Quasi-Monte-Carlo Methodes, Society of Industrial and Applied Mathematics, 1992.

. Sauer-n, On the density of families of sets, Journal of Combinatorial Theory, Series A, vol.13, issue.1, pp.145-147, 1972.
DOI : 10.1016/0097-3165(72)90019-2

S. R. Freund-y, B. P. , and L. W. , Boosting the Margin : A New Explanation for the Effectiveness of Voting Methods », The Annals of Statistics, pp.1651-1686, 1998.

S. B. Smola-a, Learning with Kernels, Support Vector Machines, Regularization , Optimization and Beyond, 2002.

. Van-der and W. A. Vaart, Weak Convergence and Empirical Processes, With Applications to Statistics, 1996.

. Van-der and . A. Vaart, Asymptotic Statistics, Cambridge Series in Statistical and Probabilistic Mathematics, 1998.
DOI : 10.1017/CBO9780511802256

. Williamson-r, . Smola-a, and . Schölkopf-b, Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators, IEEE Transactions on Information Theory, vol.47, issue.6, pp.6-2516, 2001.
DOI : 10.1109/18.945262