Estimating the Arc Length of the Optimal ROC Curve and Lower Bounding the Maximal AUC

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Song Liu


In this paper, we show the arc length of the optimal ROC curve is an $f$-divergence. By leveraging this result, we express the arc length using a variational objective and estimate it accurately using positive and negative samples. We show this estimator has a non-parametric convergence rate $O_p(n^{-\beta/4})$ ($\beta \in (0,1]$ depends on the smoothness). Using the same technique, we show the surface area sandwiched between the optimal ROC curve and the diagonal can be expressed via a similar variational objective. These new insights lead to a novel two-step classification procedure that maximizes an approximate lower bound of the maximal AUC. Experiments on CIFAR-10 datasets show the proposed two-step procedure achieves good AUC performance in imbalanced binary classification tasks.