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

2021/10/18 by Liu, Song
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2110.09651

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^-β/4) (β∈ (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. These new insights lead to a novel 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.

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