language: en

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A Note on Learning from Multiple-Instance Examples

AVRIM BLUM
avrim+@cs.cmu.edu
ADAM KALAI
akalai+@cs.cmu.edu
School of Computer Science, Carnegie Mellon University,
Pittsburgh, PA 15213

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 ~ O(d 2 r=* 2 ), saving roughly a factor of r over the results of Auer et al. (1997).

Keywords: Multiple-instance examples, classification noise, statistical queries

1. Introduction and Definitions