ROC convex hull and nonparametric maximum likelihood estimation

摘要

The ROC convex hull (ROCCH) is the least convex majorant of the empirical ROC curve, and represents the optimal ROC curve of a set of classifiers. This paper provides a probabilistic view to the ROCCH. We show that the ROCCH can be characterized as a nonparametric maximum likelihood estimator (NPMLE) of a convex ROC curve. We provide two NPMLE formulations, one unconditional and the other conditional, both of which yield the ROOCH as the solution. The solution technique relates the NPMLEs to convex optimization and classifier calibration. The connection between the NPMLEs and the ROCCH also suggests efficient algorithms to compute NPMLEs of a convex ROC curve, and a conditional bootstrap procedure for assessing uncertainties in the ROCCH.