Bounds on margin distributions in learning problems

Vladimir Koltchinskii

Annales de l'I.H.P. Probabilités et statistiques (2003)

  • Volume: 39, Issue: 6, page 943-978
  • ISSN: 0246-0203

How to cite

top

Koltchinskii, Vladimir. "Bounds on margin distributions in learning problems." Annales de l'I.H.P. Probabilités et statistiques 39.6 (2003): 943-978. <http://eudml.org/doc/77791>.

@article{Koltchinskii2003,
author = {Koltchinskii, Vladimir},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {machine learning; error of learning algorithms},
language = {eng},
number = {6},
pages = {943-978},
publisher = {Elsevier},
title = {Bounds on margin distributions in learning problems},
url = {http://eudml.org/doc/77791},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Koltchinskii, Vladimir
TI - Bounds on margin distributions in learning problems
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2003
PB - Elsevier
VL - 39
IS - 6
SP - 943
EP - 978
LA - eng
KW - machine learning; error of learning algorithms
UR - http://eudml.org/doc/77791
ER -

References

top
  1. [1] M. Anthony, P. Bartlett, Neural Network Learning: Theoretical Foundations, Cambridge University Press, 1999. Zbl0968.68126MR1741038
  2. [2] 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 Trans. Inform. Theory44 (1998) 525-536. Zbl0901.68177MR1607706
  3. [3] C. Cortes, V. Vapnik, Support vector networks, Machine Learning20 (1995) 273-297. Zbl0831.68098
  4. [4] L. Devroye, L. Györfi, G. Lugosi, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York, 1996. Zbl0853.68150MR1383093
  5. [5] R.M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, 1999. Zbl0951.60033MR1720712
  6. [6] E. Giné, V. Koltchinskii, J. Wellner, Ratio limit theorems for empirical processes, Preprint, 2003. Zbl1055.60019MR2073436
  7. [7] B. Kégl, T. Linder, G. Lugosi, Data-dependent margin-based generalization bounds for classification, in: Helmbold D., Williamson B. (Eds.), Proc. of 14th Annual Conference on Computational Learning Theory, COLT2001, Lecture Notes in Artificial Intelligence, Springer, New York, 2001, pp. 368-384. Zbl0992.68091MR2042047
  8. [8] V. Koltchinskii, D. Panchenko, Rademacher processes and bounding the risk of function learning, in: Giné E., Mason D., Wellner J. (Eds.), High Dimensional Probability II, Birkhäuser, Boston, 2000, pp. 444-459. Zbl1106.68385MR1857339
  9. [9] V. Koltchinskii, D. Panchenko, Empirical margin distributions and bounding the generalization error of combined classifiers, Ann. Statist.30 (2002) 1-50. Zbl1012.62004MR1892654
  10. [10] V. Koltchinskii, D. Panchenko, F. Lozano, Some new bounds on the generalization error of combined classifiers, in: Leen T.K., Dietterich T.G., Tresp V. (Eds.), Proc. of NIPS'2000, Advances in Neural Information Processing Systems, 13, MIT Press, 2001, pp. 245-251, URL: , http://www.boosting.org/. 
  11. [11] V. Koltchinskii, D. Panchenko, F. Lozano, Further explanation of the effectiveness of voting methods: the game between margins and weights, in: Helmbold D., Williamson B. (Eds.), Proc. of 14th Annual Conference on Computational Learning Theory, COLT2001, Lecture Notes in Artif. Intell., Springer, New York, 2001, pp. 241-255. Zbl0992.68511MR2042039
  12. [12] V. Koltchinskii, D. Panchenko, F. Lozano, Bounding the generalization error of convex combinations of classifiers: balancing the dimensionality and the margins, Ann. Appl. Probab.13 (1) (2003) 213-252. Zbl1073.62535MR1951998
  13. [13] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer-Verlag, New York, 1991. Zbl0748.60004MR1102015
  14. [14] P. Massart, About the constants in Talagrand's concentration inequalities for empirical processes, Ann. Probab.28 (2000) 863-885. Zbl1140.60310MR1782276
  15. [15] P. Massart, Some applications of concentration inequalities to statistics, Ann. Fac. Sci. Tolouse (IX) (2000) 245-303. Zbl0986.62002MR1813803
  16. [16] R. Schapire, Y. Freund, P. Bartlett, W.S. Lee, Boosting the margin: a new explanation of effectiveness of voting methods, Ann. Statist.26 (1998) 1651-1687. Zbl0929.62069MR1673273
  17. [17] M. Talagrand, A new look at independence, Ann. Probab.24 (1996) 1-34. Zbl0858.60019MR1387624
  18. [18] M. Talagrand, New concentration inequalities in product spaces, Invent. Math.126 (1996) 505-563. Zbl0893.60001MR1419006
  19. [19] A. Tsybakov, Optimal aggregation of classifiers in statistical learning, Preprint, 2002. MR2051002
  20. [20] A.W. van der Vaart, J.A. Wellner, Weak Convergence and Empirical Processes. With Applications to Statistics, Springer-Verlag, New York, 1996. Zbl0862.60002MR1385671
  21. [21] V. Vapnik, Statistical Learning Theory, Wiley, New York, 1998. Zbl0935.62007MR1641250

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.