Convex formulation of multiple instance learning from positive and unlabeled bags

Multiple instance learning (MIL) is a variation of traditional supervised learning problems where data (referred to as bags) are composed of sub-elements (referred to as instances) and only bag labels are available. MIL has a variety of applications such as content-based image retrieval, text categorization, and medical diagnosis. Most of the previous work for MIL assume that training bags are fully labeled. However, it is often difficult to obtain an enough number of labeled bags in practical situations, while many unlabeled bags are available. A learning framework called PU classification (positive and unlabeled classification) can address this problem. In this paper, we propose a convex PU classification method to solve an MIL problem. We experimentally show that the proposed method achieves better performance with significantly lower computation costs than an existing method for PU-MIL.