Skip to main content
SpringerLink
Log in

Unlabeled Compression Schemes for Maximum Classes

  • Conference paper
Learning Theory (COLT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3559))

Included in the following conference series:

Abstract

We give a compression scheme for any maximum class of VC dimension d that compresses any sample consistent with a concept in the class to at most d unlabeled points from the domain of the sample.

Supported by NSF grant CCR CCR 9821087.

Some work on this paper was done while authors were visiting National ICT Australia.

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

Access this chapter

Log in via an institution
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 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

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. Floyd, S.: Space-bounded learning and the Vapnik-Chervonenkis Dimension (Ph.D). PhD thesis, U.C. Berkeley, ICSI Tech Report TR-89-061 (December 1989)

    Google Scholar 

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

    Google Scholar 

  3. Gurvits, L.: Linear algebraic proofs of VC-dimension based inequalities. In: Ben-David, S. (ed.) EuroCOLT 1997. LNCS, vol. 1208, pp. 238–250. Springer, Heidelberg (1997)

    Google Scholar 

  4. Haussler, D., Littlestone, N., Warmuth, M.K.: Predicting {0,1} functions on randomly drawn points. Information and Computation 115(2), 284–293 (1994); Was in FOCS 1988, COLT 1988, and Univ. of California at Santa Cruz TR UCSC-CRL-90-54

    Article  MathSciNet  Google Scholar 

  5. Langford, J.: Tutorial on practical prediction theory for classification. In: ICML 2003 (2003)

    Google Scholar 

  6. Li, Y., Long, P.M., Srinivasan, A.: The one-inclusion graph algorithm is near optimal for the prediction model of learning. Transaction on Information Theory 47(3), 1257–1261 (2002)

    Article  MathSciNet  Google Scholar 

  7. Littlestone, N., Warmuth, M.K.: Relating data compression and learnability. Unpublished manuscript, June 10 (1986), obtainable at http://www.cse.ucsc.edu/~manfred

  8. Marchand, M., Shawe-Taylor, J.: The Set Covering Machine. Journal of Machine Learning Research 3, 723–746 (2002)

    Article  MathSciNet  Google Scholar 

  9. Marchand, M., Shawe-Taylor, J.: The Decision List Machine. In: Advances in Neural Information Processing Systems 15, pp. 921–928. MIT-Press, Cambridge (2003)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  11. Vapnik, V.N.: Estimation of Dependences Based on Empirical Data. Springer, New York (1982)

    MATH  Google Scholar 

  12. Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Theory of Probab. and its Applications 16(2), 264–280 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  13. von Luxburg, U., Bousquet, O., Schölkopf, B.: A compression approach to support vector model selection. Journal of Machine Learning Research 5, 293–323 (2004)

    Google Scholar 

  14. Warmuth, M.K.: Compressing to VC dimension many points. In: COLT open problems (2003)

    Google Scholar 

  15. Warmuth, M.K.: The optimal PAC algorithm. In: COLT open problems (2004)

    Google Scholar 

  16. Welzl, E.: Complete range spaces. Unpublished notes (1987)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, University of California, Santa Cruz

    Dima Kuzmin & Manfred K. Warmuth

Authors
  1. Dima Kuzmin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manfred K. Warmuth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Leoben, A-8700, Leoben, Austria

    Peter Auer

  2. Department of Electrical Engineering, Technion, P.O. Box, 3200, Haifa, Israel

    Ron Meir

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kuzmin, D., Warmuth, M.K. (2005). Unlabeled Compression Schemes for Maximum Classes . In: Auer, P., Meir, R. (eds) Learning Theory. COLT 2005. Lecture Notes in Computer Science(), vol 3559. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11503415_40

Download citation

  • DOI: https://doi.org/10.1007/11503415_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26556-6

  • Online ISBN: 978-3-540-31892-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation