The VOROS: Lifting ROC curves to 3D
Christopher Ratigan, Lenore Cowen
TL;DR
This work introduces VOROS, the Volume over the ROC Surface, a 3D generalization of the AUROC that accounts for misclassification costs and class imbalance by lifting the traditional ROC curve to a ROC surface. The authors formalize the ROC surface and a cost-based area function, derive a computable VOROS measure, and show it accordingly aligns with minimum expected cost while handling ranges of costs via a measure over t. They demonstrate substantial value across benchmark datasets (Wisconsin Breast Cancer, BUSI) and a credit fraud dataset, illustrating that VOROS can yield cost-aware classifier rankings when costs are uncertain or imbalanced, beyond what AUROC provides. The approach is efficient (O(n log n)) and adaptable to bounded cost scenarios, with discussion of limitations to binary tasks and avenues for generalization to multi-class settings and instance-level costs.
Abstract
While the area under the ROC curve is perhaps the most common measure that is used to rank the relative performance of different binary classifiers, longstanding field folklore has noted that it can be a measure that ill-captures the benefits of different classifiers when either the actual class values or misclassification costs are highly unbalanced between the two classes. We introduce a new ROC surface, and the VOROS, a volume over this ROC surface, as a natural way to capture these costs, by lifting the ROC curve to 3D. Compared to previous attempts to generalize the ROC curve, our formulation also provides a simple and intuitive way to model the scenario when only ranges, rather than exact values, are known for possible class imbalance and misclassification costs.