Some extensions of an inequality of vapnik and chervonenkis

Electronic Communications in Probability

Volumn 7, Issue , 2002, Pages 55-65

  Panchenko, Dmitriy ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Concentration of measure; Empirical processes

Indexed keywords

EID: 0347349284     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v7-1047     Document Type: Article

References (18)

1. Boucheron, S., Lugosi, G., Massart, P., A sharp concentration inequality with applications, Random Structures Algorithms, 16 (2000), 277-292.
2. Dembo, A., Information inequalities and concentration of measure, Ann. Probab., 25 (1997), 527-539.
3. Dudley, R.M., Uniform Central Limit Theorems, Cambridge University Press, (1999).
4. Haussler, D., Sphere packing numbers for subsets of the boolean n—cube with bounded Vapnik-Chervonenkis dimension, J. Combin. Theory Ser. A, 69 (1995), 217-232.
5. Kohler, M., Inequalities for uniform deviations of averages from expectations with applications to nonparametric regression. J. Statist. Plann. Inference, 89 (2000), no. 1-2, 1-23.
6. Ledoux, M., On Talagrand’s deviation inequalities for product measures, ESAIM: Probab. Statist., 1(1996), 63-87.
7. Li, Y., Long, P.M., Srinivasan, A., Improved bounds on the sample complexity of learning, Journal of Computer and System Sciences, 62 (2001), 516-527.
8. Massart, P., About the constants in Talagrand’s concentration inequalities for empirical processes, Ann. Probab., 28 (2000), 863-885.
9. Panchenko, D., A note on Talagrand’s concentration inequality, Elect. Comm. in Probab., 6 (2001), 55-65.
10. Panchenko, D., New zero-error bounds for voting algorithms, (2001), preprint.
11. Rio E., Inégalités exponentielles pour les processus empiriques, C.R. Acad. Sci. Paris, t.330, Série I (2000), 597-600.
12. Rio E., Inégalités de concentration pour les processus empiriques de classes de parties, Probab. Theory Relat. Fields, 119 (2001), 163-175.
13. Talagrand, M., Concentration of measure and isoperimetric inequalities in product spaces, Publications Mathématiques de l’I.H.E.S. 81 (1995), 73-205.
14. Talagrand, M., New concentration inequalities in product spaces. Invent. Math., 126 (1996), 505-563.
15. van der Vaart, A., Wellner, J., Weak Convergence and Empirical Processes: With Applications to Statistics, John Wiley & Sons, New York, (1996).
16. Vapnik, V.N., Chervonenkis, A. Ya., On the uniform convergence of relative frequencies of events to their probabilities, Soviet Math. Dokl.,9, (1968), 915-918.
17. Vapnik, V., Chervonenkis, A., Theory of Pattern Recognition. Nauka, Moscow (1974).
18. Vapnik, V.N., Statistical Learning Theory, Wiley, New York (1998).