Skip to main content

Comment: The Two Styles of VC Bounds

  • Chapter
  • First Online:
  • 2786 Accesses

Abstract

First of all, I would like to congratulate Léon Bottou on an excellent paper, containing a lucid discussion of the sources of looseness in the Vapnik–Chervonenkis bounds on the generalization error derived in Vapnik, Chervonenkis, Proc USSR Acad Sci 181(4): 781–783, 1968 and Vapnik, Chervonenkis, Theory Probab Appl 16(2): 264–280, (1971). I will comment only on the paper in this volume (Chap. 9), although most of the comments will also be applicable to the other papers co-authored by Léon and by Konstantin Vorontsov that are mentioned in Léon’s bibliography.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

References

  1. Balasubramanian, V.N., Ho, S.S., Vovk, V. (eds.): Conformal Prediction for Reliable Machine Learning: Theory, Adaptations, and Applications. Elsevier, Waltham (2014)

    Google Scholar 

  2. Floyd, S., Warmuth, M.: Sample compression, learnability, and the Vapnik-Chervonenkis dimension. Mach. Learn. 21(3), 269–304 (1995)

    Google Scholar 

  3. Littlestone, N., Warmuth, M.K.: Relating Data Compression and Learnability. Technical report University of California, Santa Cruz (1986)

    Google Scholar 

  4. Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)

    MATH  Google Scholar 

  5. Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Proc. USSR Acad. Sci. 181(4), 781–783 (1968). (English translation: Sov. Math. Dokl. 9, 915–918 (1968))

    Google Scholar 

  6. Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16(2), 264–280 (1971). (This volume, Chap. 3)

    Google Scholar 

  7. Vapnik, V.N., Chervonenkis, A.Y.: Теория распознавания образов: Статистические проблемы обучения (Theory of Pattern Recognition: Statistical Problems of Learning: in Russian). Nauka, Moscow (1974). German translation: Theorie der Zeichenerkennung, transl. K.G. Stöckel and B. Schneider, ed. S. Unger and B. Fritzsch, Akademie Verlag, Berlin (1979)

    Google Scholar 

  8. Vovk, V., Gammerman, A., Shafer, G.: Algorithmic Learning in a Random World. Springer, New York (2005)

    MATH  Google Scholar 

Download references

Acknowledgments

Many thanks to Léon Bottou and Konstantin Vorontsov for useful discussions. I am grateful to Ran El-Yaniv for sharing with me his thoughts about Léon Bottou’s work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vladimir Vovk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Vovk, V. (2015). Comment: The Two Styles of VC Bounds. In: Vovk, V., Papadopoulos, H., Gammerman, A. (eds) Measures of Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-21852-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21852-6_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21851-9

  • Online ISBN: 978-3-319-21852-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics