Machine Learning

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

A Note on Learning from Multiple-Instance Examples

  • Avrim Blum
  • Adam Kalai


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 


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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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