A Review of the Receiver Operating Characteristic Curve and a Proof About the Area Beneath It
For researchers and practitioners using AUC as a performance metric, this work clarifies the theoretical foundation and limitations of the probabilistic interpretation.
This paper formalizes the probabilistic interpretation of the area under the ROC curve (AUC) as the probability that a classifier ranks a random positive above a random negative, provides a bound on the error when assumptions are violated, and includes a literature review.
The Receiver Operating Characteristic (ROC) curve of a binary classifier has often been utilized to measure the performance of the classifier. The area beneath this curve is used in particular because of its quoted probabilistic interpretation as being equal to the probability that the classifier will rank a random positive observation above a random negative observation. This paper formalizes this claim, produces a bound on how far away from the truth it is if a hypothesis is not met, and gives a small literature review of the ROC curve.