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Efficient distribution-free population learning of simple concepts

  • Atsuyoshi Nakamura
  • Naoki Abe
  • Jun-ichi Takeuchi
Selected Papers Algorithmic Learning Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 872)

Abstract

We consider a variant of the ‘population learning model’ proposed by Kearns and Seung, in which the learner is required to be ‘distribution-free’ as well as computationally efficient. A population learner receives as input hypotheses from a large population of agents and produces as output its final hypothesis. Each agent is assumed to independently obtain labeled sample for the target concept and outputs a hypothesis. A polynomial time population learner is said to ‘PAC learn’ a concept class, if its hypothesis is probably approximately correct whenever the population size exceeds a certain bound which is polynomial, even if the sample size for each agent is fixed at some constant. We exhibit some general population learning strategies, and some simple concept classes that can be learned by them. These strategies include the ‘supremum hypothesis finder,’ the ‘minimum superset finder’ (a special case of the ‘supremum hypothesis finder’), and various voting schemes. When coupled with appropriate agent algorithms, these strategies can learn a variety of simple concept classes, such as the ‘high-low game,’ conjunctions, axis-parallel rectangles and others. We give upper bounds on the required population size for each of these cases, and show that these systems can be used to obtain a speed up from the ordinary PAC-learning model, with appropriate choices of sample and population sizes. With the population learner restricted to be a voting scheme, what we have is effectively a model of ‘population prediction,’ in which the learner is to predict the value of the target concept at an arbitrarily drawn point, as a threshold function of the predictions made by its agents on the same point. We show that the population learning model is strictly more powerful than the population prediction model. Finally we consider a variant of this model with classification noise, and exhibit a population learner for the class of conjunctions in this model.

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References

  1. [1]
    D. Angluin and P. Laird. Learning from noisy examples. Machine Learning, 2:343–370, 1988.Google Scholar
  2. [2]
    W. Feller. An Introduction to Probability and its Applications, volume 2. John Wiley and Sons, second edition, 1971.Google Scholar
  3. [3]
    P. Fischer and H. U. Simon. On learning ring-sum-expansions. SIAM J. Comput., 21(1):181–192, 1992.Google Scholar
  4. [4]
    S. Goldman, M. Kearns, and R. Schapire. On the sample complexity of weak learning. In Proceedings of the 1990 Workshop on Computational Learning Theory. Morgan Kaufmann, San Mateo, California, August 1990.Google Scholar
  5. [5]
    D. Helmbold, R. Sloan, and M. K. Warmuth. Learning nested differences of intersection closed concept classes. Machine Learning, 5 (1), June 1990.Google Scholar
  6. [6]
    M. Kearns and S. Seung. Learning from a population of hypotheses. In Proceedings of the Sixth Annual ACM Workshop on Computational Learning Theory. Morgan Kaufmann, San Mateo, California, August 1993.Google Scholar
  7. [7]
    B. K. Natarajan. On learning boolean functions. In Proc. 19th ACM Symp. on Theory of Computing, pages 296–304, 1987.Google Scholar
  8. [8]
    L. G. Valiant. A theory of the learnable. Communications of A.C.M., 27:1134–1142, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Atsuyoshi Nakamura
    • 1
  • Naoki Abe
    • 1
  • Jun-ichi Takeuchi
    • 1
  1. 1.C&C Research LaboratoriesTheory NEC Laboratory, RWCP 1Miyamae-ku KawasakiJapan

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