skip to main content
10.1145/130385.130402acmconferencesArticle/Chapter ViewAbstractPublication PagescoltConference Proceedingsconference-collections
Article
Free Access

The learning complexity of smooth functions of a single variable

Authors Info & Claims
Published:01 July 1992Publication History

ABSTRACT

We study the on-line learning of classes of functions of a single real variable formed through bounds on various norms of functions' derivatives. We determine the best bounds obtainable on the worst-case sum of squared errors (also “absolute” errors) for several such classes.

References

  1. Bar91.A. Barron. Approximation and estimation bounds for artificial neural networks. The 1991 Workshop on Computational Learning Theory, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. FM91.V. Faber and J. Mycielski. Applications of learning theorems. Fundamenia Informaticae, 15(2):145-167, 1991.Google ScholarGoogle Scholar
  3. Har91.W. Hardle. Smoothing Techniques. Springer Verlag, 1991.Google ScholarGoogle Scholar
  4. Hau89.D. Haussler. Generalizing the PAC model: sample size bounds from metric dimensionbased uniform convergence results. Proceedings of the 30th Annual Symposium on the Foundations of Computer Science, 1989.Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Lei81.G. Leitmann. The Calculus of Variations and Optimal Control. Plenum Press, 1981.Google ScholarGoogle ScholarCross RefCross Ref
  6. Lit89.N. Littlestone. Mistake Bounds and Logarithmic Linear-threshold Learning Algorithms. PhD thesis, UC Santa Cruz, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. LLW91.N. Littlestone, P.M. Long, and M.K. Warmuth. On-line learning of linear functions. Proceedings of the ~3rd ACM Symposium on the Theory of Computation, pages 465-475, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. LW89.N. Littlestone and M.K. Warmuth. The weighted majority algorithm. Proceedings of the 30th Annual Symposium on the Foundations of Computer Science, 1989.Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. MT89.W. Maass and G. Turan. On the complexity of learning from counterexamples. Proceedings of the 30th Annual Symposium on the Foundations of Computer Science, 1989.Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Myc88.J. Mycielski. A learning algorithm for linear operators. Proceedings of the American Mathematical Society, 103(2):547-550, 1988.Google ScholarGoogle ScholarCross RefCross Ref
  11. WH60.B. Widrow and M.E. Hoff. Adaptive switching circuits. 1960 IRE WESCON Cony. Record, pages 96-104, 1960.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. The learning complexity of smooth functions of a single variable

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Conferences
      COLT '92: Proceedings of the fifth annual workshop on Computational learning theory
      July 1992
      452 pages
      ISBN:089791497X
      DOI:10.1145/130385

      Copyright © 1992 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 July 1992

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • Article

      Acceptance Rates

      Overall Acceptance Rate35of71submissions,49%

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader