Fairness Under Group-Conditional Prior Probability Shift: Invariance, Drift, and Target-Aware Post-Processing

TL;DR

This paper analyzes how fairness criteria behave under group-conditional prior probability shifts, showing invariance for error-based metrics, identifying drift for acceptance-rate metrics, and proposing a label-free post-processing method to achieve target fairness.

Contribution

It provides a theoretical analysis of fairness under GPPS, proves invariance and drift properties, and introduces TAP-GPPS, a novel method for target fairness without labeled target data.

Findings

Equalized odds are invariant under GPPS.

Demographic parity can drift and is shift-robust impossible.

TAP-GPPS effectively achieves target fairness with minimal utility loss.

Abstract

Machine learning systems are often trained and evaluated for fairness on historical data, yet deployed in environments where conditions have shifted. A particularly common form of shift occurs when the prevalence of positive outcomes changes differently across demographic groups--for example, when disease rates rise faster in one population than another, or when economic conditions affect loan default rates unequally. We study group-conditional prior probability shift (GPPS), where the label prevalence $P(Y=1\mid A=a)$ may change between training and deployment while the feature-generation process $P(X\mid Y,A)$ remains stable. Our analysis yields three main contributions. First, we prove a fundamental dichotomy: fairness criteria based on error rates (equalized odds) are structurally invariant under GPPS, while acceptance-rate criteria (demographic parity) can drift--and we prove this drift is unavoidable for non-trivial classifiers (shift-robust impossibility). Second, we show that target-domain risk and fairness metrics are identifiable without target labels: the invariance of ROC quantities under GPPS enables consistent estimation from source labels and unlabeled target data alone, with finite-sample guarantees. Third, we propose TAP-GPPS, a label-free post-processing algorithm that estimates prevalences from unlabeled data, corrects posteriors, and selects thresholds to satisfy demographic parity in the target domain. Experiments validate our theoretical predictions and demonstrate that TAP-GPPS achieves target fairness with minimal utility loss.