A Fast Algorithm for Unbiased Estimation of Variance of AUC Based on Dynamic Programming

Receiver operating characteristic (ROC) curve is a plot traced out by pairs of false-positive rate and true-positive rate according to various decision threshold settings. The area under the ROC curve (AUC) is widely used as a figure of merit to summarize a diagnostic system's performance, a binary classifier's overall accuracy, or an energy detector's power. Exploiting the equivalent relationship between the sample version of AUC and Mann Whitney U statistic (MWUS), in this paper, we develop an efficient algorithm of linearithmic order, based on dynamic programming, for unbiased estimation of the mean and variance of MWUS. Monte Carlo simulations verify our algorithmic findings.