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. © 2005 Elsevier Inc. All rights reserved.
Dooly, D. R., Goldman, S. A., & Kwek, S. S. (2006). Real-valued multiple-instance learning with queries. Journal of Computer and System Sciences, 72(1), 1–15. https://doi.org/10.1016/j.jcss.2005.06.002