Skip to main content
SpringerLink
Log in

Teaching Classes with High Teaching Dimension Using Few Examples

  • 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 consider the Boolean concept classes of 2-term DNF and 1-decision lists which both have a teaching dimension exponential in the number n of variables. It is shown that both classes have an average teaching dimension linear in n. We also consider learners that always choose a simplest consistent hypothesis instead of an arbitrary consistent one. Both classes can be taught to these learners by efficient teaching algorithms using only a linear number of examples.

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. Angluin, D.: Queries and concept learning. Machine Learning 2(4), 319–342 (1988)

    Google Scholar 

  2. Angluin, D.: Queries revisited. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 12–31. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Angluin, D., Kriķis, M.: Teachers, learners and black boxes. In: Proceedings COLT 1997, pp. 285–297. ACM Press, New York (1997)

    Chapter  Google Scholar 

  4. Angluin, D., Kriķis, M.: Learning from different teachers. Machine Learning 51(2), 137–163 (2003)

    Article  MATH  Google Scholar 

  5. Anthony, M., Brightwell, G., Shawe-Taylor, J.: On specifying boolean functions by labelled examples. Discrete Applied Mathematics 61(1), 1–25 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  6. Eiter, T., Ibaraki, T., Makino, K.: Decision lists and related Boolean functions. Theoretical Computer Science 270(1–2), 493–524 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  7. Freivalds, R., Kinber, E.B., Wiehagen, R.: On the power of inductive inference from good examples. Theoretical Computer Science 110(1), 131–144 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Goldman, S.: Learning Binary Relations, Total Orders, and Read-Once Formulas. PhD thesis, MIT Dept. of Electr. Engineering and Computer Science (September 1990)

    Google Scholar 

  9. Goldman, S.A., Kearns, M.J.: On the complexity of teaching. J. of Comput. Syst. Sci. 50(1), 20–31 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  10. Goldman, S.A., Mathias, H.D.: Teaching a smarter learner. J. of Comput. Syst. Sci. 52(2), 255–267 (1996)

    Article  MathSciNet  Google Scholar 

  11. Goldman, S.A., Rivest, R.L., Schapire, R.E.: Learning binary relations and total orders. SIAM J. Comput. 22(5), 1006–1034 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hancock, T., Jiang, T., Li, M., Tromp, J.: Lower bound on learning decision lists and trees. Inform. Comput. 126(2), 114–122 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hegedüs, T.: Generalized teaching dimensions and the query complexity of learning. In: Proceedings COLT 1995, pp. 108–117. ACM Press, New York (1995)

    Chapter  Google Scholar 

  14. Jackson, J., Tomkins, A.: A computational model of teaching. In: Proceedings COLT 1992, pp. 319–326. ACM Press, New York (1992)

    Chapter  Google Scholar 

  15. Jain, S., Lange, S., Nessel, J.: Learning of r.e. languages from good examples. In: Li, M. (ed.) ALT 1997. LNCS, vol. 1316, Springer, Heidelberg (1997)

    Google Scholar 

  16. Kuhlmann, C.: On teaching and learning intersection-closed concept classes. In: Fischer, P., Simon, H.U. (eds.) EuroCOLT 1999. LNCS (LNAI), vol. 1572, pp. 168–182. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  17. Mathias, H.D.: A model of interactive teaching. J. of Comput. Syst. Sci. 54(3), 487–501 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pitt, L., Valiant, L.G.: Computational limitations on learning from examples. J. ACM 35(4), 965–984 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  19. Rivest, R.L.: Learning decision lists. Machine Learning 2, 229–246 (1987)

    MathSciNet  Google Scholar 

  20. Shinohara, A., Miyano, S.: Teachability in computational learning. New Generation Computing 8(4), 337–348 (1991)

    Article  MATH  Google Scholar 

  21. Simon, H.U.: Learning decision lists and trees with equivalence-queries. In: Proceedings EuroCOLT 1995. LNCS (LNAI), vol. 904, pp. 322–336. Springer, Heidelberg (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Frank J. Balbach

Authors
  1. Frank J. Balbach
    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

Balbach, F.J. (2005). Teaching Classes with High Teaching Dimension Using Few Examples. 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_45

Download citation

  • DOI: https://doi.org/10.1007/11503415_45

  • 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