Real-valued multiple-instance learning with queries

Authors:
Daniel R. Dooly;Sally A. Goldman;Stephen S. Kwek
Affiliations:
Southern Illinois University Edwardsville, Edwardsville, IL 62026, USA;Washington University, St. Louis, MO 63130, USA;University of Texas San Antonio, San Antonio, TX 78249, USA
Venue:
Journal of Computer and System Sciences
Year:
2006

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Abstract

While there has been a significant amount of theoretical and empirical research on the multiple-instance learning model, most of this research is for concept learning. However, for the important application area of drug discovery, a real-valued classification is preferable. In this paper we initiate a theoretical study of real-valued multiple-instance learning. We prove that the problem of finding a target point consistent with a set of labeled multiple-instance examples (or bags) is NP-complete, and that the problem of learning from real-valued multiple-instance examples is as hard as learning DNF. Another contribution of our work is in defining and studying a multiple-instance membership query (MI-MQ). We give a positive result on exactly learning the target point for a multiple-instance problem in which the learner is provided with a MI-MQ oracle and a single adversarially selected bag.