A few notes on statistical learning theory

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

Volumn 2600, Issue , 2003, Pages 1-40

  Mendelson, Shahar ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35248851077     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36434-x_1     Document Type: Article

References (36)

1. M. Anthony, P.L. Bartlett: Neural Network Learning: Theoretical Foundations, Cambridge University Press, 1999.
2. N. Alon, S. Ben-David, N. Cesa-Bianchi, D. Haussler: Scale sensitive dimensions, uniform convergence and learnability, J. of ACM 44 (4), 615-631, 1997.
3. O. Bousquet: A Bennett concentration inequality and its application to suprema of empirical processes, preprint.
4. L. Devroye, L. Györfi, G. Lugosi: A Probabilistic Theory of Pattern Recognition, Springer, 1996.
5. R.M. Dudley: Real Analysis and Probability, Chapman and Hall, 1993.
6. R.M. Dudley: The sizes of compact subsets of Hilbert space and continuity of Gaussian processes, J. of Functional Analysis 1, 290-330, 1967.
7. R.M. Dudley: Central limit theorems for empirical measures, Annals of Probability 6(6), 899-929, 1978.
8. R.M. Dudley: Uniform Central Limit Theorems, Cambridge Studies in Advanced Mathematics 63, Cambridge University Press, 1999.
9. E. Giné, J. Zinn: Some limit theorems for empirical processes, Annals of Probability, 12(4), 929-989, 1984.
10. D. Haussler: Sphere packing numbers for subsets of Boolean n-cube with bounded Vapnik-Chervonenkis dimension, J. of Combinatorial Theory (A) 69, 217-232, 1995.
11. W. Hoeffding: Probability inequalities for sums of bounded random variables, J. of the American Statistical Association, 58, 13-30, 1963.
12. V. Koltchinskii, D. Panchenko: Rademacher processes and bounding the risk of function learning, High Dimensional Probability, II (Seattle, WA, 1999), 443-457, Progr. Probab., 47, Birkhauser.
13. R. Latala, K. Oleszkiewicz: On the best constant in the Khintchine-Kahane inequality, Studia Math. 109(1), 101-104, 1994.
14. M. Ledoux: The Concentration of Measure Phenomenon, Mathematical Surveys an Monographs, Vol 89, AMS, 2001.
15. M. Ledoux, M. Talagrand: Probability in Danach Spaces: Isoperimetry and Processes, Springer, 1991.
16. W.S. Lee, P.L. Bartlett, R.C. Williamson: The Importance of Convexity in Learning with Squared Loss, IEEE Transactions on Information Theory 44 (5), 1974-1980, 1998.
17. P. Massart: About the constants in Talagrand's concentration inequality for empirical processes, Annals of Probability, 28(2), 863-884, 2000.
18. S. Mendelson: Rademacher averages and phase transitions in Glivenko-Cantelli class, IEEE Transactions on Information Theory, 48(1), 251-263, 2002.
19. S. Mendelson: Improving the sample complexity using global data, IEEE Transactions on Information Theory, 48(7), 1977-1991, 2002.
20. S. Mendelson: Geometric parameters of kernel machines, in Proceedings of the 15th annual conference on Computational Learning Theory COLT02, Jyrki Kivinen and Robert H. Sloan(Eds.), Lecture Notes in Computer Sciences 2375, Springer, 29-43, 2002.
21. S. Mendelson, R. Vershynin: Entropy, combinatorial dimensions and random averages, in Proceedings of the 15th annual conference on Computational Learning Theory COLT02, Jyrki Kivinen and Robert H. Sloan(Eds.), Lecture Notes in Computer Sciences 2375, Springer, 14-28, 2002.
22. S. Mendelson, R. Vershynin: Entropy and the combinatorial dimension, Inventiones Mathematicae, to appear.
23. S. Mendelson, R.C. Williamson: Agnostic learning nonconvex classes of functions, in Proceedings of the 15th annual conference on Computational Learning Theory COLT02, Jyrki Kivinen and Robert H. Sloan(Eds.), Lecture Notes in Computer Sciences 2375, Springer, 1-13, 2002.
24. V.D. Milman, G. Schechtman: Asymptotic Theory of Finite Dimensional Nor1med Spaces, Lecture Notes in Mathematics 1200, Springer 1986.
25. n des espaces de Banach, Hermann, Paris, 1985.
26. G. Pisier: The volume of convex bodies and Banach space geometry, Cambridge University Press, 1989.
27. E. Rio: Une inegalité de Bennett pour les maxima de processus empiriques, preprint.
28. N. Sauer: On the density of families of sets, J. Combinatorial Theory (A), 13, 145-147, 1972.
29. S. Shelah: A combinatorial problem: stability and orders for models and theories in infinitary languages, Pacific Journal of Mathematics, 41, 247-261, 1972.
30. V.N. Sudakov: Gaussian processes and measures of solid angles in Hubert space, Soviet Mathematics. Doklady 12, 412-415, 1971.
31. M. Talagrand: Type, infratype and the Elton-Pajor theorem, Inventiones Mathematicae, 107, 41-59, 1992.
32. M. Talagrand: Sharper bounds for Gaussian and empirical processes, Annals of Probability, 22(1), 28-76, 1994.
33. A.W. Van der Vaart, J.A. Wellner: Weak Convergence and Empirical Processes, Springer-Verlag, 1996.
34. V. Vapnik: Statistical Learning Theory, Wiley 1998.
35. A. Vidyasagar: The Theory of Learning and Generalization Springer-Verlag, 1996.
36. V. Vapnik, A. Chervonenkis: Necessary and sufficient conditions for uniform convergence of means to mathematical expectations, Theory Prob. Applic. 26(3), 532-553, 1971.