Fairness Under Group-Conditional Prior Probability Shift: Invariance, Drift, and Target-Aware Post-Processing
Amir Asiaee, Kaveh Aryan
TL;DR
This work analyzes fairness under group-conditional prior probability shift (GPPS), where within-group feature-label relationships remain stable but group-specific label prevalences change across domains. It proves a clean dichotomy: equalized odds (and other separation-based criteria) are invariant under GPPS, while demographic parity and predictive parity can drift with prevalence; it also establishes shift-robust impossibility results for DP and PPV. The authors show that target risk and fairness gaps are identifiable without target labels, leveraging ROC invariance to estimate target performance from source data and unlabeled target data. They propose TAP-GPPS, a label-free post-processing pipeline that estimates target prevalences, corrects posteriors, and selects group-specific thresholds to meet target-domain DP with minimal utility loss, and validate it on synthetic and semi-synthetic benchmarks. The results provide actionable guidance for criterion selection and deployment monitoring in non-stationary environments with demographic heterogeneity.
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.