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

arXiv: https://arxiv.org/abs/2602.05144 · HTML: https://mlsanity.com/paper/2602.05144/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Robust Fairness under Covariate Shift](https://mlsanity.com/paper/2010.05166/) (2020)
- [Fairness Transferability Subject to Bounded Distribution Shift](https://mlsanity.com/paper/2206.00129/) (2022)
- [Does enforcing fairness mitigate biases caused by subpopulation shift?](https://mlsanity.com/paper/2011.03173/) (2020)
- [Ensuring Fairness under Prior Probability Shifts](https://mlsanity.com/paper/2005.03474/) (2020)
- [Quantification under prior probability shift: the ratio estimator and its extensions](https://mlsanity.com/paper/1807.03929/) (2018)

## Built on by (most cited first, 1 of 1)

- [Is invariance all you need for algorithmic fairness? Removing demographic information can create new bias](https://mlsanity.com/paper/2609.32004/) (2026)

## Abstract (arXiv)

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=1mid A=a) may change between training and deployment while the feature-generation process P(Xmid 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.