The Unified Framework for AUC Maximizer

The area under the curve(AUC) is commonly used as a measure of the receiver operating characteristic(ROC) curve which displays the performance of a set of binary classifiers for all feasible ratios of the costs associated with true positive rate(TPR) and false positive rate(FPR). In the bipartite ranking problem where one has to compare two different observations and decide which one is "better", the AUC measures the quantity that ranking score of a randomly chosen sample in one class is larger than that of a randomly chosen sample in the other class and hence, the function which maximizes an AUC of bipartite ranking problem is different to the function which maximizes (minimizes) accuracy (misclassification error rate) of binary classification problem. In this paper, we develop a way to construct the unified framework for AUC maximizer including support vector machines based on maximizing large margin and logistic regression based on estimating posterior probability. Moreover, we develop an efficient algorithm for the proposed unified framework. Numerical results show that the propose unified framework can treat various methodologies successfully.