Recent Results In On-line Prediction and Boosting

  • Nicolò Cesa-Bianchi
  • Sandra Panizza
Conference paper
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)

Abstract

The successful design of practical algorithms for solving a class of problems very often depends on the existence of a formal model where algorithmical ideas can be developed, analyzed, and compared. In the case of machine learning, a number of such formal models have been proposed in the past. Some of them have been successful in generating elegant mathematical results but, on the other hand, they have had a rather limited impact on the practical side. In this paper, we suggest that the on-line prediction model is a good source of interesting algorithmic ideas with a great potential for new applications. To this end, we will describe a simple algorithm based on “multiplicative weights,” we will analyze this algorithm within the on-line prediction model, and finally we will show some of its variants and applications.

Keywords

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References

  1. [1]
    P. Auer, N. Cesa-Bianchi, Y. Freund, and R. E. Schapire. Gambling in a rigged casino: The adversarial multi-armed bandit problem. In Proceedings of the 36th Annual Symposium on the Foundations of Computer Science pages 322–331. IEEE press, 1995.Google Scholar
  2. [2]
    N. Cesa-Bianchi, Y. Freund, D. P. Helmbold, D. Haussler, R. Schapire, and M. K. Warmuth. How to use expert advice. Technical Report UCSC-CRL-95–19, University of California at Santa Cruz, 1995. An extended abstract appeared in the Proceedings of the 25th ACM Symposium on the Theory of Computation.Google Scholar
  3. [3]
    N. Cesa-Bianchi, Y. Freund, D. P. Helmbold, and M. K. Warmuth. On-line prediction and conversion strategies Machine Learning To appear. An extended abstract appeared in the Proceedings of the First EuroCOLT Workshop.Google Scholar
  4. [4]
    N. Cesa-Bianchi, D. P. Helmbold, and S. Panizza. On Bayes methods for on-line boolean prediction. In Proceedings of the 9ih Annual Conference on Computational Learning Theory pages 314–324. ACM Press, 1996.Google Scholar
  5. [5]
    C. Cortes and H. Drucker. Boosting decision trees. In Advances in Neural Information Processing Systems SMIT Press, 1996. To appear.Google Scholar
  6. [6]
    T. Dietterich, M. Kearns, and Y. Mansour. Applying the weak learning framework to understand and improve C4.5. In Proceedings of the 13th International Conference on Machine Learning pages 96–104. Morgan Kaufmann, 1996.Google Scholar
  7. [7]
    Y. Freund and R. Schapire. A decision-theoretic generalization of on-line learning, and an application to boosting. In Proceedings of the 2nd Euro-COLT Workshop pages 23–37. Lecture Notes on Artificial Intelligence, Vol. 904, Springer-Verlag, 1995.Google Scholar
  8. [8]
    Y. Freund and R. Schapire. Experiments with a new boosting algorithm. In Proceedings of the 13th International Conference on Machine Learning, pages 148–156. Morgan Kaufmann, 1996.Google Scholar
  9. [9]
    Y. Freund and R. Schapire. Game theory, on-line prediction and boosting. In Proceedings of the 9th Annual Conference on Computational Learning TheoryACM Press, 1996.Google Scholar
  10. [10]
    D. Haussler and A. Barron. How well does the Bayes method work in on-line predictions of {+1,-1} values? In Proceedings of 3rd NEC Symposiumpages 74–100. SIAM, 1993.Google Scholar
  11. [11]
    D. Haussler, J. Kivinen, and M. K. Warmuth. Tight worst-case loss bounds for predicting with expert advice. In Proceedings of the 2nd European Conference on Computational Learning Theory, pages 69–83. Lecture Notes on Artificial Intelligence, Vol. 904, 1995.Google Scholar
  12. [12]
    D. P. Helmbold, J. Kivinen, and M. K. Warmuth. Worst-case loss bounds for sigmoided neurons. In Advances in Neural Information Processing Systems 8MIT Press, 1996. In press.Google Scholar
  13. [13]
    M. Kearns and Y. Mansour. On the boosting ability of top-down decision tree learning algorithms. In Proceedings of the 28th ACM Symposium on the Theory of Computing, pages 459–468. ACM Press, 1996.Google Scholar
  14. [14]
    J. Kivinen and M. K. Warmut h. Exponentiated gradient versus gradient descent for linear predictors. Technical Report UCSC-CRL-94–16, University of California at Santa Cruz, 1994. To appear in Information and Computation. Google Scholar
  15. [15]
    N. Littlestone and M. K. Warmuth. The weighted majority algorithm. Information and Computation, 108:212–261, 1994.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    H. Robbins. Some aspects of the sequential design of experiments. Bullettin of the American Mathematical Society, 55:527–535, 1952.MathSciNetCrossRefGoogle Scholar
  17. [17]
    V. G. Vovk. Aggregating strategies. In Proceedings of the 3rd Annual Workshop on Computational Learning Theory, pages 372–383, 1990.Google Scholar
  18. [18]
    V.G. Vovk. A game of prediction with expert advice. In Proceedings of the 8th Annual Conference on Computational Learning Theory, pages 51–60, 1995. An extended version is to appear in Journal of Computer and Systems Sciences.Google Scholar
  19. K. Yamanishi. On-line maximum likelihood prediction with respect to general loss functions. In Proceedings of the 2nd European Conference on Computational Learning Theory, pages 84–98. Lecture Notes on Artificial Intelligence, Vol. 904, 1995.Google Scholar

Copyright information

© Springer-Verlag London Limited 1997

Authors and Affiliations

  • Nicolò Cesa-Bianchi
    • 1
  • Sandra Panizza
    • 1
  1. 1.DSIUniversità di MilanoMilanoItaly

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