Generalizing the AUC-ROC for unbalanced data, early retrieval and link prediction evaluation

The AUC-ROC is a widespread measure to assess the performance of a binary classification model across various discrimination thresholds. Yet, it is not apt for unbalanced class problems and is misleading for early retrieval. For instance, link prediction in complex networks is an unbalanced early retrieval problem, whose goal is to offer a ranking of the nonobserved network links, prioritizing a small cohort of positive links (for which we are sure the labels are reliable) on top of a list largely populated by unlabeled links (for which the labels are uncertain). Differently from binary classification, here the evaluation focuses on how the predictor prioritizes the positive class, because the negative class does not exist and is replaced by an unlabeled class. For decades, scholars have been investigating the necessity to correct and to generalize the AUC-ROC to work for both unbalanced classification and early retrieval evaluation, this is requested in many applied domains of computational science. Here we propose the area under the magnified ROC (AUC-mROC), a new measure that adjusts the standard AUC-ROC to work for unbalanced early retrieval problems such as link prediction. Finally, we introduce the area under the generalized ROC (AUC-gROC), which unifies both AUC-mROC and AUC-ROC to provide a universal and reliable evaluation measure that can work for both classification and early retrieval problems, regardless of class proportion.This discovery represents a critical achievement, culminating in success after decades of contentious research. Its solution promises to significantly impact various domains within applied computational science.