Simplified and Unified Analysis of Various Learning Problems by Reduction to Multiple-Instance Learning

In statistical learning, many problem formulations have been proposed so far, such as multi-class learning, complementarily labeled learning, multi-label learning, multi-task learning, which provide theoretical models for various real-world tasks. Although they have been extensively studied, the relationship among them has not been fully investigated. In this work, we focus on a particular problem formulation called Multiple-Instance Learning (MIL), and show that various learning problems including all the problems mentioned above with some of new problems can be reduced to MIL with theoretically guaranteed generalization bounds, where the reductions are established under a new reduction scheme we provide as a byproduct. The results imply that the MIL-reduction gives a simplified and unified framework for designing and analyzing algorithms for various learning problems. Moreover, we show that the MIL-reduction framework can be kernelized.