Prequential AUC: properties of the area under the ROC curve for data streams with concept drift

Modern data-driven systems often require classifiers capable of dealing with streaming imbalanced data and concept changes. The assessment of learning algorithms in such scenarios is still a challenge, as existing online evaluation measures focus on efficiency, but are susceptible to class ratio changes over time. In case of static data, the area under the receiver operating characteristics curve, or simply AUC, is a popular measure for evaluating classifiers both on balanced and imbalanced class distributions. However, the characteristics of AUC calculated on time-changing data streams have not been studied. This paper analyzes the properties of our recent proposal, an incremental algorithm that uses a sorted tree structure with a sliding window to compute AUC with forgetting. The resulting evaluation measure, called prequential AUC, is studied in terms of: visualization over time, processing speed, differences compared to AUC calculated on blocks of examples, and consistency with AUC calculated traditionally. Simulation results show that the proposed measure is statistically consistent with AUC computed traditionally on streams without drift and comparably fast to existing evaluation procedures. Finally, experiments on real-world and synthetic data showcase characteristic properties of prequential AUC compared to classification accuracy, G-mean, Kappa, Kappa M, and recall when used to evaluate classifiers on imbalanced streams with various difficulty factors.