# A Note on Learning from Multiple-Instance Examples

Article

DOI: 10.1023/A:1007402410823

- Cite this article as:
- Blum, A. & Kalai, A. Machine Learning (1998) 30: 23. doi:10.1023/A:1007402410823

- 34 Citations
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## 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(d^{2}r/ε^{2}) , 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