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# A Structural SVM Based Approach for Optimizing Partial AUC

*Proceedings of the 30th International Conference on Machine Learning*, PMLR 28(1):516-524, 2013.

#### Abstract

The area under the ROC curve (AUC) is a widely used performance measure in machine learning. Increasingly, however, in several applications, ranging from ranking and biometric screening to medical diagnosis, performance is measured not in terms of the full area under the ROC curve, but instead, in terms of the partial area under the ROC curve between two specified false positive rates. In this paper, we develop a structural SVM framework for directly optimizing the partial AUC between any two false positive rates. Our approach makes use of a cutting plane solver along the lines of the structural SVM based approach for optimizing the full AUC developed by Joachims (2005). Unlike the full AUC, where the combinatorial optimization problem needed to find the most violated constraint in the cutting plane solver can be decomposed easily to yield an efficient algorithm, the corresponding optimization problem in the case of partial AUC is harder to decompose. One of our key technical contributions is an efficient algorithm for solving this combinatorial optimization problem that has the same computational complexity as Joachims’ algorithm for optimizing the usual AUC. This allows us to efficiently optimize the partial AUC in any desired false positive range. We demonstrate the approach on a variety of real-world tasks.