Skip to main content

On the Complexity of Samples for Learning

  • Conference paper
Computing and Combinatorics (COCOON 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3106))

Included in the following conference series:

  • 549 Accesses

Abstract

In machine-learning, maximizing the sample margin can reduce the learning generalization-error. Thus samples on which the target function has a large margin (γ) convey more information so we expect fewer such samples. In this paper, we estimate the complexity of a class of sets of large-margin samples for a general learning problem over a finite domain. We obtain an explicit dependence of this complexity on γ and the sample size.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anthony, M., Bartlett, P.L.: Neural Network Learning: Theoretical Foundations. Cambridge University Press, UK (1999)

    Book  MATH  Google Scholar 

  2. Antos, A., Kgl, B., Linder, T., Lugosi, G.: Data-dependent margin-based generalization bounds for classification. Journal of Machine Learning Research 3, 73–98 (2002)

    Article  Google Scholar 

  3. Bartlett, P.L., Boucheron, S., Lugosi, G.: Model selection and error estimation. Machine Learning 48, 85–113 (2002)

    Article  MATH  Google Scholar 

  4. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other Kernel-based learning methods. Cambridge University Press, UK (2000)

    Google Scholar 

  5. Haussler, D.: Decision theoretic generalizations of the PAC model for neural net and other learning applications. Information and Computation 100(1), 78–150 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Sauer, N.: On the density of families of sets. J. Combinatorial Theory (A) 13, 145–147 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ratsaby, J.: A constrained version of Sauer’s Lemma. In: Proc. of Third Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (MathInfo 2004), Vienna, Austria, September 2004. Birkhäuser, Basel (2004)

    Google Scholar 

  8. Ratsaby, J.: A Sharp Threshold Result for Finite-VC Classes of Large- Margin Functions, Department of Computer Science Technical Report RN/04/06, University College London (2004)

    Google Scholar 

  9. Shawe-Taylor, J., Bartlett, P.L., Williamson, R.C., Anthony, M.: Structural risk minimization over data-dependent hierarchies. IEEE Trans. Inf. Theory 44, 1926–1940 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Vapnik, V.N.: Statistical Learning Theory. Wiley, Chichester (1998)

    MATH  Google Scholar 

  11. Vapnik, V.N., Chervonenkis, A.: On the uniform convergence of relative frequencies of events to their probabilities. Theoret. Probl. Appl. 16, 264–280 (1971)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ratsaby, J. (2004). On the Complexity of Samples for Learning. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-27798-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22856-1

  • Online ISBN: 978-3-540-27798-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics