What is the probabilistic interpretation of ROC-AUC?

ROC-AUC (Area Under the Receiver Operating Characteristic Curve) can be interpreted as the probability that a randomly chosen positive object will be scored higher by the model than a randomly chosen negative object.

In other words, if you take a random positive example and a random negative example, AUC is the probability that the model assigns a higher score (probability of belonging to the positive class) to the positive example than to the negative one.

This makes ROC-AUC a convenient metric for evaluating the quality of binary classifiers, especially when classes are imbalanced, as it does not depend on the chosen classification threshold.