FROC: Building Fair ROC from a Trained Classifier

TL;DR

This work tackles fair probabilistic binary classification with binary protected groups by introducing $\varepsilon_1$-Equalized ROC, a fairness criterion requiring ROC curves of both groups to stay within $\mathcal{L}_1$-distance $\varepsilon$ across all thresholds. It proposes FROC, a post-processing algorithm that samples, linearly approximates (PLA), and geometrically transports the ROC curves to align them while minimizing the resultant AUC loss; the final classifier is obtained via randomized convex combinations of ROC-points. Theoretical analysis bounds the PLA and AUC losses and proves optimality under certain continuity and spacing assumptions, with an emphasis on norm-boundary geometry. Empirically, FROC reduces cross-group disparities by about 7–8% with at most ~2% AUC loss across multiple datasets (ADULT, COMPAS, CelebA), and scales to multiple protected groups, offering practical, model-agnostic fairness without retraining.

Abstract

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 $\mathcal{L}_p$ 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 $\varepsilon_p$-Equalized ROC. Given a classifier not satisfying $\varepsilon_1$-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 $\varepsilon_1$-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 $\varepsilon_1$-Equalized ROC. To achieve this, we design a linear time algorithm, namely \texttt{FROC}, to transform a given classifier's output to a probabilistic classifier that satisfies $\varepsilon_1$-Equalized ROC. We prove that under certain theoretical conditions, \texttt{FROC}\ achieves the theoretical optimal guarantees. We also study the performance of our \texttt{FROC}\ on multiple real-world datasets with many trained classifiers.

Figures (53)

• Figure 1: ROCs and convex hull
• Figure 2: Shaded Area indicates $\mathcal{L}_{PLA}$
• Figure 3: Norm Boundary
• Figure 4: C1 vs. C1-FROC
• Figure 5: C3-Fair Fair vs. C3-FROC

Theorems & Definitions (26)

• Definition 2.1: ROC-Curve
• Definition 2.2: $\varepsilon_p$-Equalized ROC
• Definition 3.1: Norm Boundary
• Definition 3.2: Boundary Cut
• Definition 3.3: UpShift
• Definition 3.4: LeftShift
• Definition 3.5: CutShift
• Theorem 4.1
• Theorem 4.2
• Theorem 4.3