Estimating the Arc Length of the Optimal ROC Curve and Lower Bounding the Maximal AUC. (arXiv:2110.09651v3 [math.ST] UPDATED)

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 between the optimal ROC curve and the
diagonal can be expressed via a similar variational objective. …

arxiv auc math roc