# Fairness Transferability Subject to Bounded Distribution Shift

arXiv: https://arxiv.org/abs/2206.00129 · HTML: https://mlsanity.com/paper/2206.00129/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 23 of 23)

- [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)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Robust Fairness under Covariate Shift](https://mlsanity.com/paper/2010.05166/) (2020)
- [Sample Selection for Fair and Robust Training](https://mlsanity.com/paper/2110.14222/) (2021)
- [Causal Modeling for Fairness in Dynamical Systems](https://mlsanity.com/paper/1909.09141/) (2019)
- [A Short-term Intervention for Long-term Fairness in the Labor Market](https://mlsanity.com/paper/1712.00064/) (2017)
- [The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally](https://mlsanity.com/paper/1910.04123/) (2019)
- [From Fair Decision Making to Social Equality](https://mlsanity.com/paper/1812.02952/) (2018)
- [Transfer of Machine Learning Fairness across Domains](https://mlsanity.com/paper/1906.09688/) (2019)
- [Ensuring Fairness Beyond the Training Data](https://mlsanity.com/paper/2007.06029/) (2020)
- [Feature Shift Detection: Localizing Which Features Have Shifted via Conditional Distribution Tests](https://mlsanity.com/paper/2107.06929/) (2021)
- [Unintended Selection: Persistent Qualification Rate Disparities and Interventions](https://mlsanity.com/paper/2111.01201/) (2021)
- [On Fairness, Diversity and Randomness in Algorithmic Decision Making](https://mlsanity.com/paper/1706.10208/) (2017)
- [Ensuring Fairness under Prior Probability Shifts](https://mlsanity.com/paper/2005.03474/) (2020)
- [Linear Classifiers that Encourage Constructive Adaptation](https://mlsanity.com/paper/2011.00355/) (2020)
- [Model Transferability With Responsive Decision Subjects](https://mlsanity.com/paper/2107.05911/) (2021)

## Built on by (most cited first, 28 of 28)

- [Long-Term Fairness with Unknown Dynamics](https://mlsanity.com/paper/2304.09362/) (2023)
- [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)
- [Transferring Fairness under Distribution Shifts via Fair Consistency Regularization](https://mlsanity.com/paper/2206.12796/) (2022)
- [What-is and How-to for Fairness in Machine Learning: A Survey, Reflection, and Perspective](https://mlsanity.com/paper/2206.04101/) (2022)
- [Weak Proxies are Sufficient and Preferable for Fairness with Missing Sensitive Attributes](https://mlsanity.com/paper/2210.03175/) (2022)
- [Uncertainty-based Fairness Measures](https://mlsanity.com/paper/2312.11299/) (2023)
- [Improving Fair Training under Correlation Shifts](https://mlsanity.com/paper/2302.02323/) (2023)
- [Fairness Without Harm: An Influence-Guided Active Sampling Approach](https://mlsanity.com/paper/2402.12789/) (2024)
- [The Importance of Human-Labeled Data in the Era of LLMs](https://mlsanity.com/paper/2306.14910/) (2023)
- [Consistent Range Approximation for Fair Predictive Modeling](https://mlsanity.com/paper/2212.10839/) (2022)
- [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)
- [The Limits of Fair Medical Imaging AI In The Wild](https://mlsanity.com/paper/2312.10083/) (2023)
- [Procedural Fairness Through Decoupling Objectionable Data Generating Components](https://mlsanity.com/paper/2311.14688/) (2023)
- [Is it Still Fair? A Comparative Evaluation of Fairness Algorithms through the Lens of Covariate Drift](https://mlsanity.com/paper/2409.12428/) (2024)
- [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)
- [Adapting Machine Learning Diagnostic Models to New Populations Using a Small Amount of Data: Results from Clinical Neuroscience](https://mlsanity.com/paper/2308.03175/) (2023)
- [Long-term Fairness For Real-time Decision Making: A Constrained Online Optimization Approach](https://mlsanity.com/paper/2401.02552/) (2024)
- [Trustworthy Representation Learning Across Domains](https://mlsanity.com/paper/2308.12315/) (2023)
- [A Note on Bias to Complete](https://mlsanity.com/paper/2402.11710/) (2024)
- [A Theoretical Survey on Foundation Models](https://mlsanity.com/paper/2410.11444/) (2024)
- [Fair Domain Generalization: An Information-Theoretic View](https://mlsanity.com/paper/2507.05823/) (2025)
- [Fairness Under Group-Conditional Prior Probability Shift: Invariance, Drift, and Target-Aware Post-Processing](https://mlsanity.com/paper/2602.05144/) (2026)
- [Transferring Fairness using Multi-Task Learning with Limited Demographic Information](https://mlsanity.com/paper/2305.12671/) (2023)
- [On the Cause of Unfairness: A Training Sample Perspective](https://mlsanity.com/paper/2306.17828/) (2023)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)

## Abstract (arXiv)

Given an algorithmic predictor that is "fair" on some source distribution, will it still be fair on an unknown target distribution that differs from the source within some bound? In this paper, we study the transferability of statistical group fairness for machine learning predictors (i.e., classifiers or regressors) subject to bounded distribution shifts. Such shifts may be introduced by initial training data uncertainties, user adaptation to a deployed predictor, dynamic environments, or the use of pre-trained models in new settings. Herein, we develop a bound that characterizes such transferability, flagging potentially inappropriate deployments of machine learning for socially consequential tasks. We first develop a framework for bounding violations of statistical fairness subject to distribution shift, formulating a generic upper bound for transferred fairness violations as our primary result. We then develop bounds for specific worked examples, focusing on two commonly used fairness definitions (i.e., demographic parity and equalized odds) and two classes of distribution shift (i.e., covariate shift and label shift). Finally, we compare our theoretical bounds to deterministic models of distribution shift and against real-world data, finding that we are able to estimate fairness violation bounds in practice, even when simplifying assumptions are only approximately satisfied.