Maximization of AUC and Buffered AUC in Classification

This paper utilizes a new concept, called Buffered Probability of Exceedance (bPOE), to introduce an alternative to the Area Under the Receiver Operating Characteristic Curve (AUC) performance metric called Buffered AUC (bAUC). Central to the creation of bAUC is a new technique for calculation and optimization of bPOE. We show this formula to be easily integrable into optimization frameworks, often reducing bPOE minimization to convex, sometimes even linear, programming. Then, we utilize bPOE to create the bAUC performance metric, showing it to be an intuitive counterpart to AUC. In addition, we show that bAUC is much easier to handle in optimization frameworks than AUC, specifically reducing to convex and linear programming. We use these friendly optimization properties to introduce the bAUC Efficiency Frontier, a concept that serves to partially resolve the “incoherency” that arises when misclassification costs need be considered. We conclude that bAUC avoids many of the numerically troublesome issues encountered by AUC and integrates much more smoothly into the general framework of model selection and evaluation.