# Ensuring Fairness under Prior Probability Shifts

arXiv: https://arxiv.org/abs/2005.03474 · HTML: https://mlsanity.com/paper/2005.03474/

## Key facts

- Cited by 16 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 6 May 2020.

## Built on by (most cited first, 16 of 16)

- [Fairness Transferability Subject to Bounded Distribution Shift](https://mlsanity.com/paper/2206.00129/) (2022)
- [Fairness and Accuracy under Domain Generalization](https://mlsanity.com/paper/2301.13323/) (2023)
- [Supervised Algorithmic Fairness in Distribution Shifts: A Survey](https://mlsanity.com/paper/2402.01327/) (2024)
- [Measuring Fairness Under Unawareness of Sensitive Attributes: A Quantification-Based Approach](https://mlsanity.com/paper/2109.08549/) (2021)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Algorithmic Fairness Generalization under Covariate and Dependence Shifts Simultaneously](https://mlsanity.com/paper/2311.13816/) (2023)
- [Secure and Confidential Certificates of Online Fairness](https://mlsanity.com/paper/2410.02777/) (2024)
- [How does promoting the minority fraction affect generalization? A theoretical study of the one-hidden-layer neural network on group imbalance](https://mlsanity.com/paper/2403.07310/) (2024)
- [How Far Can Fairness Constraints Help Recover From Biased Data?](https://mlsanity.com/paper/2312.10396/) (2023)
- [FEAMOE: Fair, Explainable and Adaptive Mixture of Experts](https://mlsanity.com/paper/2210.04995/) (2022)
- [Context matters for fairness -- a case study on the effect of spatial distribution shifts](https://mlsanity.com/paper/2206.11436/) (2022)
- [Fairness Overfitting in Machine Learning: An Information-Theoretic Perspective](https://mlsanity.com/paper/2506.07861/) (2025)
- [A Survey on Preserving Fairness Guarantees in Changing Environments](https://mlsanity.com/paper/2211.07530/) (2022)
- [On Comparing Fair Classifiers under Data Bias](https://mlsanity.com/paper/2302.05906/) (2023)
- [Fairness Under Group-Conditional Prior Probability Shift: Invariance, Drift, and Target-Aware Post-Processing](https://mlsanity.com/paper/2602.05144/) (2026)
- [Levels of Autonomous Radiology](https://mlsanity.com/paper/2112.07286/) (2021)

## Abstract (arXiv)

In this paper, we study the problem of fair classification in the presence of prior probability shifts, where the training set distribution differs from the test set. This phenomenon can be observed in the yearly records of several real-world datasets, such as recidivism records and medical expenditure surveys. If unaccounted for, such shifts can cause the predictions of a classifier to become unfair towards specific population subgroups. While the fairness notion called Proportional Equality (PE) accounts for such shifts, a procedure to ensure PE-fairness was unknown. In this work, we propose a method, called CAPE, which provides a comprehensive solution to the aforementioned problem. CAPE makes novel use of prevalence estimation techniques, sampling and an ensemble of classifiers to ensure fair predictions under prior probability shifts. We introduce a metric, called prevalence difference (PD), which CAPE attempts to minimize in order to ensure PE-fairness. We theoretically establish that this metric exhibits several desirable properties. We evaluate the efficacy of CAPE via a thorough empirical evaluation on synthetic datasets. We also compare the performance of CAPE with several popular fair classifiers on real-world datasets like COMPAS (criminal risk assessment) and MEPS (medical expenditure panel survey). The results indicate that CAPE ensures PE-fair predictions, while performing well on other performance metrics.