Have you ever wondered how to demonstrate that one machine learning model's test set performance differs significantly from the test set performance of an alternative model? This post will describe how to use DeLong's test to obtain a p-value for whether one model has a significantly different AUC than another model, where AUC refers to the area under the receiver operating characteristic. This post includes a hand-calculated example to illustrate all the steps in DeLong's test for a small data set. It also includes an example R implementation of DeLong's test to enable efficient calculation on large data sets. An example use case for DeLong's test: Model A predicts heart disease risk with AUC of 0.92, and Model B predicts heart disease risk with AUC of 0.87, and we use DeLong's test to demonstrate that Model A has a significantly different AUC from Model B with p 0.05.

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem. We study large deviation properties of the AUC; in particular, we derive a distribution-free large deviation bound for the AUC which serves to bound the expected accuracy of a ranking function in terms of its empirical AUC on an independent test sequence. A comparison of our result with a corresponding large deviation result for the classification error rate suggests that the test sample size required to obtain an ɛ-accurate estimate of the expected accuracy of a ranking function with δ-confidence is larger than that required to obtain an ɛ-accurate estimate of the expected error rate of a classification function with the same confidence. A simple application of the union bound allows the large deviation bound to be extended to learned ranking functions chosen from finite function classes.

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem. We study large deviation properties of the AUC; in particular, we derive a distribution-free large deviation bound for the AUC which serves to bound the expected accuracy of a ranking function in terms of its empirical AUC on an independent test sequence. A comparison of our result with a corresponding large deviation result for the classification error rate suggests that the test sample size required to obtain an ɛ-accurate estimate of the expected accuracy of a ranking function with δ-confidence is larger than that required to obtain an ɛ-accurate estimate of the expected error rate of a classification function with the same confidence. A simple application of the union bound allows the large deviation bound to be extended to learned ranking functions chosen from finite function classes.

The area under the ROC curve (AUC) has been advocated as an evaluation criterion for the bipartite ranking problem.