The Link between Multiple-Instance Learning and Learning from Only Positive and Unlabelled Examples

This paper establishes a link between two supervised learning frameworks, namely multiple-instance learning (MIL) and learning from only positive and unlabelled examples (LOPU). MIL represents an object as a bag of instances. It is studied under the assumption that its instances are drawn from a mixture distribution of the concept and the non-concept. Based on this assumption, the classification of bags can be formulated as a classifier combining problem and the Bayes classifier for instances is shown to be closely related to the classification in LOPU. This relationship provides a possibility to adopt methods from LOPU to MIL or vice versa. In particular, we examine a parameter estimator in LOPU being applied to MIL. Experiments demonstrate the effectiveness of the instance classifier and the parameter estimator.