Functional classification with margin conditions

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

Volumn 4005 LNAI, Issue , 2006, Pages 94-108

  Fromont, Magalie ^a   Tuleau, Christine ^b,c  

^a UNIVERSITÉ RENNES 2   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSIFICATION (OF INFORMATION); FUNCTION EVALUATION; PERFORMANCE; THEOREM PROVING;

FUNCTIONAL CLASSIFICATION;

LEARNING SYSTEMS;

EID: 33746031419     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11776420_10     Document Type: Conference Paper

References (37)

1. Biau, G., Bunea, F., Wegkamp, M.: Functional classification in Hubert spaces. IEEE Trans. Inf. Theory 51 (2005) 2163-2172
2. Devroye, L., Györfi, L., Lugosi, G.: A probabilistic theory of pattern recognition. Applications of Mathematics. Springer, New York (1996)
3. Boucheron, S., Bousquet, O., Lugosi, G.: Theory of classification: some recent advances. ESAIM Probability and Statistics 9 (2005) 323-375
4. Stone, C.: Consistent nonparametric regression. Ann. Statist. 5 (1977) 595-645
5. 1 convergence of the kernel regression estimate. Journal of the Statistical Planning and Inference 23 (1989) 71-82
6. Dabo-Niang, S., Rhomari, N.: Nonparametric regression estimation when the regressor takes its values in a metric space. Technical report, Université Paris VI (2001) http://www.ccr.jussieu.fr/lsta.
7. Abraham, C., Biau, G., Cadre, B.: On the kernel rule for function classification. Technical report (2003) Université de Montpellier, http://www.math.univmontp2.fr/~biau/publications.html.
8. Kulkarni, S., Posner, S.: Rates of convergence of nearest neighbor estimation under arbitrary sampling. IEEE Trans. Inf. Theory 41 (1995) 1028-1039
9. Cerou, F., Guyader, A.: Nearest neighbor classification in infinite dimension. Technical report, IRISA, Rennes, France (2005)
10. Ramsay, J., Silverman, B.: Functional data analysis. Springer Series in Statistics. Springer-Verlag, New York (1997)
11. Ramsay, J., Silverman, B.: Applied functional data analysis. Springer Series in Statistics. Springer-Verlag, New York (2002) Methods and case studies.
12. Hastie, T., Buja, A., Tibshirani, R.: Penalized discriminant analysis. Ann. Statist. 23 (1995) 73-102
13. Hall, P., Poskitt, D., Presnell, B.: A functional data-analytic approach to signal discrimination. Technometrics 43 (2001) 1-9
14. Ferraty, F., Vieu, P.: Curves discrimination: a nonparametric functional approach. Comput. Statist. Data Anal. 44 (2003) 161-173
15. Hastie, T., Tibshirani, R.: Discriminant adaptive nearest neighbor classification. IEEE Trans. Pattern Anal. Mach. Intell. 18 (1996) 607-616
16. Rossi, F., Villa, N.: Classification in Hubert spaces with support vector machines. In: Proceedings of ASMDA 2005, Brest, France (2005) 635-642
17. Hengartner, N., Matzner-Lober, E., Wegkamp, M.: Bandwidth selection for local linear regression. Journal of the Royal Statistical Society, Series B 64 (2002) 1-14
18. Stone, C.: Consistent nonparametric regression. Ann. Statist. 5 (1977) 595-645
19. Vapnik, V., Chervonenkis, A.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16 (1971) 264-280
20. Lugosi, G.: Pattern classification and learning theory. In Györfi, L., ed.: Principles of Nonparametric Learning. Springer, Wien, New York (2002) 1-56
21. Vapnik, V., Chervonenkis, A.: Teoriya raspoznavaniya obrazov. Statisticheskie problemy obucheniya (Theory of pattern recognition. Statistical problems of learning). Nauka, Moscow (1974)
22. Devroye, L., Wagner, T.: Nonparametric discrimination and density estimation. Technical Report 183, Electronics Research Center, University of Texas (1976)
23. Vapnik, V.: Estimation of dependences based on empirical data. Springer-Verlag, New York (1982)
24. Blumer, A., Ehrenfeucht, A., Haussler, D., Warmuth, M.: Learnability and the Vapnik-Chervonenkis dimension. J. Assoc. Comput. Mach. 36 (1989) 929-965
25. Haussler, D., Littlestone, N., Warmuth, M.: Predicting {0, l}-functions on randomly drawn points. Inf. Comput. 115 (1994) 248-292
26. Devroye, L., Lugosi, G.: Lower bounds in pattern recognition and learning. Pattern Recognition 28 (1995) 1011-1018
27. Mammen, E., Tsybakov, A.: Smooth discrimination analysis. Ann. Statist. 27 (1999) 1808-1829
28. Tsybakov, A.; Optimal aggregation of classifiers in statistical learning. Ann. Statist. 32 (2004) 135-166
29. Massart, P., Nédélec, E.: Risk bounds for statistical learning. Ann. Statist. (2005) To appear.
30. Bartlett, P., Jordan, M., McAuliffe, J.: Convexity, classification, and risk bounds. Journal of the American Statistical Association 101 (2006) 138-156
31. Audibert, J.Y., Tsybakov, A.: Fast learning rates for plug-in estimators under margin condition. Preprint (2005)
32. Massart, P.: Concentration inequalities and model selection. Lectures given at the Saint-Flour summer school of probability theory. To appear in Lect. Notes Math. (2003)
33. Györfi, L.: On the rate of convergence of k-nearest-neighbor classification rule. Preprint (2005)
34. Birgé, L., Massart, P.: Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 (1998) 329-375
35. Yang, Y.: Can the strengths of AIC and BIC be shared? a conflict between model identification and regression estimation. Biometrika 92 (2005) 937-950
36. Berlinet, A., Biau, G., Rouvière, L.: Functional learning with wavelets. To appear in IEEE Trans. Inf. Theory (2005)
37. Tuleau, C.: Sélection de variables pour la discrimination en grande dimension et classification de données fonctionnelles. PhD thesis, Université Paris Sud (2005)