Robust support vector machines for multiple instance learning

This paper presents the multiple instance classification problem that can be used for drug and molecular activity prediction, text categorization, image annotation, and object recognition. In order to model a more robust representation of outliers, hard margin loss formulations that minimize the number of misclassified instances are proposed. Although the problem is $mathcal{NP}$ -hard, computational studies show that medium sized problems can be solved to optimality in reasonable time using integer programming and constraint programming formulations. A three-phase heuristic algorithm is proposed for larger problems. Furthermore, different loss functions such as hinge loss, ramp loss, and hard margin loss are empirically compared in the context of multiple instance classification. The proposed heuristic and robust support vector machines with hard margin loss demonstrate superior generalization performance compared to other approaches for multiple instance learning.