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

Published: 31 Oct 2022, Last Modified: 15 Jan 2023NeurIPS 2022 AcceptReaders: Everyone
Keywords: ROC Curve, f-divergence, density ratio estimation, AUC maximization
TL;DR: The arc length of the optimal ROC curve can be expressed as a novel $f$-divergence, the estimator of which enables us to lower bound the maximal AUC.
Abstract: 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.
Supplementary Material: zip
19 Replies