Machine Learning

, Volume 30, Issue 1, pp 23–29 | Cite as

A Note on Learning from Multiple-Instance Examples

  • Avrim Blum
  • Adam Kalai

Abstract

We describe a simple reduction from the problem of PAC-learning from multiple-instance examples to that of PAC-learning with one-sided random classification noise. Thus, all concept classes learnable with one-sided noise, which includes all concepts learnable in the usual 2-sided random noise model plus others such as the parity function, are learnable from multiple-instance examples. We also describe a more efficient (and somewhat technically more involved) reduction to the Statistical-Query model that results in a polynomial-time algorithm for learning axis-parallel rectangles with sample complexity Õ(d2r/ε2) , saving roughly a factor of r over the results of Auer et al. (1997).

Multiple-instance examples classification noise statistical queries 

References

  1. Auer, P. (1997). On learning from multi-instance examples: Empirical evaluation of a theoretical approach. In Proceedings of the Fourteenth International Conference on Machine Learning.Google Scholar
  2. Auer, P., Long, P., and Srinivasan, A. (1997). Approximating hyper-rectangles: Learning and pseudo-random sets. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing. To appear.Google Scholar
  3. Dietterich, T. G., Lanthrop, R. H., and Lozano-Perez, T. (1997). Solving the multiple-instance problem with axis-parallel rectangles. Artifical Intelligence, 89(1-2):31–71.Google Scholar
  4. Kearns, M. (1993). Efficient noise-tolerant learning from statistical queries. In Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing, pages 392–401.Google Scholar
  5. Long, P. and Tan, L. (1996). PAC learning axis-aligned rectangles with respect to product distributions from multiple-instance examples. In Proceedings of the 9th Annual Conference on Computational Learning Theory, pages 228–234.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Avrim Blum
    • 1
    • 1
  • Adam Kalai
    • 1
    • 1
  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburgh

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