A Review of the Receiver Operating Characteristic Curve and a Proof About the Area Beneath It

TL;DR

This paper reviews the ROC curve, formalizes the probabilistic interpretation of its area, provides bounds on its accuracy, and summarizes related literature.

Contribution

It formalizes the ROC area interpretation, derives bounds on its accuracy, and offers a concise literature review.

Findings

The ROC area has a probabilistic interpretation as ranking probability.

Bounds are established on the deviation from the true probability.

A literature review of ROC curve studies is provided.

Abstract

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.