Skip to main content
Log in

New approaches to statistical learning theory

  • Special Section on New Trends in Statistical Information Processing
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

We present new tools from probability theory that can be applied to the analysis of learning algorithms. These tools allow to derive new bounds on the generalization performance of learning algorithms and to propose alternative measures of the complexity of the learning task, which in turn can be used to derive new learning algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Anthony, M. and Shawe-Taylor, J. (1993). A result of Vapnik with applications,Discrete Appl. Math. 47, 207–217.

    Article  MathSciNet  Google Scholar 

  • Bartlett, P. and Mendelson, S. (2002). Rademacher and gaussian complexities: Risk bounds and structural results,Journal of Machine Learning Research,3, 463–482.

    Article  MathSciNet  Google Scholar 

  • Bartlett, P., Boucheron, S. and Lugosi, G. (2002a). Model selection and error estimation,Machin Learning,48, 85–113.

    Article  Google Scholar 

  • Bartlett, P., Bousquet, O. and Mendelson, S. (2002b). Local rademacher complexities (preprint).

  • Bartett, P., Bousquet, O. and Mendelson, S. (2002c). Localized rademacher complexity,Proceedings of the 15th Annual Conference on Computational Learning Theory, Lecture Notes in Comput. Sci., 44–58, Springer, Berlin.

    Google Scholar 

  • Boucheron, S., Lugosi, G. and Massart, P. (2002). A sharp concentration inequality with applications,Random Structures Algorithms,16(3), 277–292.

    Article  MathSciNet  Google Scholar 

  • Boucheron, S., Lugosi, G. and Massart, P. (2002). Concentration inequalities using the entropy method,Ann. Probab. (to appear).

  • Bousquet, O. (2002a). A Bennett concentration inequality and its application to suprema of empirical processes,Computes Rendus Mathématique Academie des Sciences. Paris,334, 495–500.

    MathSciNet  Google Scholar 

  • Bousquet, O. (2002b). Concentration inequalities and empirical processes theory applied to the analysis of learning algorithms, Ph.D. thesis, Centre de Mathématiques Appliquées, Ecole Polytechnique (preprint).

  • Bousquet, O. and Elisseeff, A. (2002). Stability and generalization,Journal of Machine Learning Research,2, 499–526.

    Article  MathSciNet  Google Scholar 

  • Koltchinskii, V. and Panchenko, D. (2000). Rademacher processes and bounding the risk of function learning,High Dimensional Probability II (eds. E. Gine, D. Mason and J. Wellner) 443–459.

  • Ledoux, M. and Talagrand, M. (1991).Probability in Banach Spaces, Springer, Berlin.

    MATH  Google Scholar 

  • Massart, P. (2000). Some applications of concentration inequalities to statistics,Ann. Fac. Sci. Toulouse Math. (6),9(2), 245–303.

    MathSciNet  Google Scholar 

  • McDiarmid, C. (1989). On the method of bounded differences,Surveys in Combinatorics, London Math. Soc. Lecture Note Ser.,141, 148–188, Cambridge University Press, Cambridge.

    Google Scholar 

  • Mendelson, S. (2001). On the size of convex hulls of small sets,Journal of Machine Learning Research,2, 1–18.

    Article  MathSciNet  Google Scholar 

  • van der Vaart, A. and Wellner, J. (1996).Weak Convergence and Empirical Processes with Applications to Statistics, Wiley, New York.

    MATH  Google Scholar 

  • Vapnik, V. and Chervonenkis, A. (1971). On the uniform convergence of relative frequencies of events to their probabilities,Theory Probab. Appl.,16, 264–280.

    Article  Google Scholar 

  • Vapnik, V. and Chervonenkis, A. (1991). The necessary and sufficient conditions for consistency of the method of empirical risk minimization,Pattern Recognition and Image Analysis,1(3), 284–305.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Bousquet, O. New approaches to statistical learning theory. Ann Inst Stat Math 55, 371–389 (2003). https://doi.org/10.1007/BF02530506

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02530506

Key words and phrases

Navigation