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

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