Optimal oracle inequality for aggregation of classifiers under low noise condition

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4005 LNAI, Issue , 2006, Pages 364-378

  Lecué, Guillaume ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC VARIABLES CONTROL; ADAPTIVE SYSTEMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; PARAMETER ESTIMATION;

LOW NOISE CONDITION; MINIMAX CLASSIFIERS; OPTIMAL ORACLE INEQUALITY;

PROBLEM SOLVING;

EID: 33746090509     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11776420_28     Document Type: Conference Paper

References (29)

1. Audibert, J.-Y. and Tsybakov, A.B,: Fast learning rates for plug-in classifiers under margin condition. (2005). Available at http://www.proba. jussieu.fr/mathdoc/preprints/index.html#2005 (Preprint PMA-998)
2. Barron, A. and Leung, G.: Information theory and mixing least-square regressions. (2004). Manuscript.
3. Barron, A. and Li, J.: Mixture density estimation, Biometrics, (1997), 53, 603-618.
4. Bartlett, P., Freund, Y., Lee, W.S. and Schapire, R.E.: Boosting the margin: a new explanantion for the effectiveness of voting methods, (1998), Annals of Statistics, 28, 1651-1686.
5. Bartlett, P. and Jordan, M. and McAuliffe, J.: Convexity, Classification and Risk Bounds, Technical Report 638, Department of Statistics, U.C. Berkeley, (2003). Available at http://stat-www.berkeley.edu/tech-reports/638.pdf.
6. Blanchard, G., Bousquet, O. and Massart, P.: Statistical Performance of Support Vector Machines, (2004), Available at http//mahery.math.u-psud.it/ ~blanchard/publi/.
7. Boucheron, S., Bousquet, O. and Lugosi, G.: Theory of classification: A survey of some recent advances, (2005), ESAIM: Probability and statistics, 9:325-375.
8. Blanchard, G., Lugosi, G. and Vayatis, N.: On the rate of convergence of regularized boosting classifiers, JMLR, (2003), 4, 861-894.
9. Bühlmann, P. and Yu, B.: Analyzing bagging, Ann. Statist., (2002), 30, 4, 927-961.
10. Cristianini, N. and Shawe-Taylor, J.: An introduction to Support Vector Machines, Cambridge University Press, (2002).
11. Cortes, C. and Vapnik, V.: Support-Vector Networks, Machine Learning, 20, 3, 273-297, (1995).
12. Devroye, L., Györfi, L. and Lugosi, G.: A Probabilistic Theory of Pattern Recognition, (1996), Springer, New York, Berlin, Heidelberg.
13. Catoni, O.: Statistical Learning Theory and Stochastic Optimization, (2001), Springer, N.Y., Ecole d'été de Probabilités de Saint-Flour 2001, Lecture Notes in Mathematics.
14. V. Koltchinskii and D. Panchenko: Empirical margin distributions and bounding the generalization error of combined classifiers, (2002), Ann. Statist., 30, 1-50.
15. Koltchinskii, V.: Local Rademacher Complexities and Oracle Inequalities in Risk Minimization. To appear in Ann. Statist., (2005).
16. Lugosi, G. and Vayatis, N.: On the Bayes-risk consistency of regularized boosting methods, Ann. Statist., (2004), 32, 1, 30-55.
17. Lecué, G.: Simultaneous adaptation to the margin and to complexity in classification, (2005), Available at http://hal.ccsd.cnrs.fr/ccsd-00009241/ en/.
18. Lecué, G.: Optimal rates of aggregation in classification, (2006). Available at https://hal.ccsd.cnrs.fr/ccsd-00021233.
19. Massart, P.: Some applications of concentration inequalities to Statistics, (2000), Probability Theory. Annales de la Faculté des Sciences de Toulouse, 2, 245-303, volume spécial dédié à Michel Talagrand.
20. Massart, P.: Concentration inequalities and Model Selection, (2004),Lectures notes of Saint Flour.
21. Schölkopf, B. and Smola, A.: Learning with kernels, MIT press, Cambridge University, (2002).
22. Steinwart, I. and Scovel, C.: Fast Rates for Support Vector Machines using Gaussian Kernels, (2004), Los Alamos National Laboratory Technical Report LAUR 04-8796, submitted to Annals of Statistics.
23. Steinwart, I. and Scovel, C.: Fast Rates for Support Vector Machines, (2005), COLT 2005.
24. Tsybakov, A.B.: Optimal rates of aggregation, (2003), Computational Learning Theory and Kernel Machines. B.Schölkopf and M.Warmuth, eds. Lecture Notes in Artificial Intelligence, 2777, 303-313, Springer, Heidelberg.
25. Tsybakov, A.B.: Optimal aggregation of classifiers in statistical learning, (2004), Ann. Statist., 32, 1, 135-166.
26. Tsybakov, A.B.: Introduction à l'estimation non- paramétrique, Springer, (2004).
27. Vovk, V.G.: Aggregating strategies. In Proceedings of the Third Annual Workshop on Computational Learning Theory, pages 371-383, 1990.
28. Yang, Y.: Mixing strategies for density estimation, (2000), Ann. Statist., 28, 1, 75-87.
29. Zhang, T.: Statistical behavior and consistency of classification methods based on convex risk minimization, (2004), Ann. Statist., 32, 1, 56-85.