SVM_pAUC^tight: a new support vector method for optimizing partial AUC based on a tight convex upper bound

The area under the ROC curve (AUC) is a well known performance measure in machine learning and data mining. In an increasing number of applications, however, ranging from ranking applications to a variety of important bioinformatics applications, performance is measured in terms of the partial area under the ROC curve between two specified false positive rates. In recent work, we proposed a structural SVM based approach for optimizing this performance measure (Narasimhan and Agarwal, 2013). In this paper, we develop a new support vector method, SVM_pAUC^tight, that optimizes a tighter convex upper bound on the partial AUC loss, which leads to both improved accuracy and reduced computational complexity. In particular, by rewriting the empirical partial AUC risk as a maximum over subsets of negative instances, we derive a new formulation, where a modified form of the earlier optimization objective is evaluated on each of these subsets, leading to a tighter hinge relaxation on the partial AUC loss. As with our previous method, the resulting optimization problem can be solved using a cutting-plane algorithm, but the new method has better run time guarantees. We also discuss a projected subgradient method for solving this problem, which offers additional computational savings in certain settings. We demonstrate on a wide variety of bioinformatics tasks, ranging from protein-protein interaction prediction to drug discovery tasks, that the proposed method does, in many cases, perform significantly better on the partial AUC measure than the previous structural SVM approach. In addition, we also develop extensions of our method to learn sparse and group sparse models, often of interest in biological applications.