FROC: Building Fair ROC from a Trained Classifier

This paper considers the problem of fair probabilistic binary classification with binary protected groups. The classifier assigns scores, and a practitioner predicts labels using a certain cut-off threshold based on the desired trade-off between false positives vs. false negatives. It derives these thresholds from the ROC of the classifier. The resultant classifier may be unfair to one of the two protected groups in the dataset. It is desirable that no matter what threshold the practitioner uses, the classifier should be fair to both the protected groups; that is, the Lp norm between FPRs and TPRs of both the protected groups should be at most varepsilon. We call such fairness on ROCs of both the protected attributes varepsilonp-Equalized ROC. Given a classifier not satisfying varepsilon1-Equalized ROC, we aim to design a post-processing method to transform the given (potentially unfair) classifier's output (score) to a suitable randomized yet fair classifier. That is, the resultant classifier must satisfy varepsilon1-Equalized ROC. First, we introduce a threshold query model on the ROC curves for each protected group. The resulting classifier is bound to face a reduction in AUC. With the proposed query model, we provide a rigorous theoretical analysis of the minimal AUC loss to achieve varepsilon1-Equalized ROC. To achieve this, we design a linear time algorithm, namely textttFROC, to transform a given classifier's output to a probabilistic classifier that satisfies varepsilon1-Equalized ROC. We prove that under certain theoretical conditions, textttFROC achieves the theoretical optimal guarantees. We also study the performance of our textttFROC on multiple real-world datasets with many trained classifiers.