A Long-Tail Perspective on Group Fairness: Fair Logit Adjustment via Prior Correction

Machine learning classifiers often exhibit unequal predictive performance across demographic groups. Post-processing offers a practical way to reduce these disparities without retraining, typically by adjusting decision thresholds or prediction distributions. To connect these interventions to the origins of disparity, we examine how the data distribution shapes predictions across groups. A class that is common overall can still be rare within a particular group, exposing a long tail at the group-class level. Under standard risk minimization, errors on these rare combinations receive less weight, while group-conditional priors absorbed into decision scores favor prevalent classes, contributing to unequal recognition across groups. These observations motivate giving each group's recognition performance on each class equal importance. We express this objective through Group-Balanced Error Rate (GBER) and derive its Bayes-optimal rule, which removes the group-conditional prior from posterior scores. This leads to Fair Logit Adjustment (FLA), a deterministic, metric-agnostic post-processing method that directly corrects learned logits. This simple score adjustment requires no constrained solver and naturally supports multi-class and multi-group settings. Across multiple benchmarks and model families, FLA achieves highly competitive fairness-utility trade-offs compared with state-of-the-art post-processing methods, with substantially lower construction cost. The same prior-correction principle also extends to an in-processing formulation. By identifying a distributional source of disparity and the score component to correct, FLA offers an interpretable and computationally lightweight approach to post-processing fairness.