On multiple-instance learning of halfspaces

Authors:
D. I. Diochnos;R. H. Sloan;Gy. TuráN
Affiliations:
University of Illinois at Chicago, United States;University of Illinois at Chicago, United States;University of Illinois at Chicago, United States and Research Group on AI, Hungarian Academy of Sciences & University of Szeged, Hungary
Venue:
Information Processing Letters
Year:
2012

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Abstract

In multiple-instance learning the learner receives bags, i.e., sets of instances. A bag is labeled positive if it contains a positive example of the target. An @W(dlogr) lower bound is given for the VC-dimension of bags of size r for d-dimensional halfspaces and it is shown that the same lower bound holds for halfspaces over any large point set in general position. This lower bound improves an @W(logr) lower bound of Sabato and Tishby, and it is sharp in order of magnitude. We also show that the hypothesis finding problem is NP-complete and formulate several open problems.