A Note on Learning from Multiple-Instance Examples

  • Authors:
  • Avrim Blum;Adam Kalai

  • Affiliations:
  • School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213.;School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213.

  • Venue:
  • Machine Learning - Special issue on the ninth annual conference on computational theory (COLT '96)
  • Year:
  • 1998

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Abstract

We describe a simple reduction from the problem ofPAC-learning from multiple-instance examples to that of PAC-learningwith one-sided random classification noise. Thus, all concept classeslearnable with one-sided noise, which includes all concepts learnablein the usual 2-sided random noise model plus others such as the parityfunction, are learnable from multiple-instance examples. We alsodescribe a more efficient (and somewhat technically more involved)reduction to the Statistical-Query model that results in apolynomial-time algorithm for learning axis-parallel rectangles with sample complexityÕ(d^2r/ϵ^2), saving roughly a factor of r over theresults of Auer et al. (1997).