# How Far Can Fairness Constraints Help Recover From Biased Data?

arXiv: https://arxiv.org/abs/2312.10396 · HTML: https://mlsanity.com/paper/2312.10396/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 16 Dec 2023.

## Builds on (most cited first, 24 of 24)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [Fair Classification with Group-Dependent Label Noise](https://mlsanity.com/paper/2011.00379/) (2020)
- [Optimal strategies for reject option classifiers](https://mlsanity.com/paper/2101.12523/) (2021)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?](https://mlsanity.com/paper/1912.01094/) (2019)
- [Causal Fairness Analysis](https://mlsanity.com/paper/2207.11385/) (2022)
- [Noise-tolerant fair classification](https://mlsanity.com/paper/1901.10837/) (2019)
- [Fairness Through Causal Awareness: Learning Latent-Variable Models for Biased Data](https://mlsanity.com/paper/1809.02519/) (2018)
- [Fairness Evaluation in Presence of Biased Noisy Labels](https://mlsanity.com/paper/2003.13808/) (2020)
- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [Does enforcing fairness mitigate biases caused by subpopulation shift?](https://mlsanity.com/paper/2011.03173/) (2020)
- [Bayes-Optimal Classifiers under Group Fairness](https://mlsanity.com/paper/2202.09724/) (2022)
- [Ensuring Fairness under Prior Probability Shifts](https://mlsanity.com/paper/2005.03474/) (2020)
- [Fair Bayes-Optimal Classifiers Under Predictive Parity](https://mlsanity.com/paper/2205.07182/) (2022)
- [Through the Data Management Lens: Experimental Analysis and Evaluation of Fair Classification](https://mlsanity.com/paper/2101.07361/) (2021)
- [A Sandbox Tool to Bias(Stress)-Test Fairness Algorithms](https://mlsanity.com/paper/2204.10233/) (2022)
- [Consistent Range Approximation for Fair Predictive Modeling](https://mlsanity.com/paper/2212.10839/) (2022)
- [When Fair Classification Meets Noisy Protected Attributes](https://mlsanity.com/paper/2307.03306/) (2023)
- [On the Vulnerability of Fairness Constrained Learning to Malicious Noise](https://mlsanity.com/paper/2307.11892/) (2023)
- [Quantifying Infra-Marginality and Its Trade-off with Group Fairness](https://mlsanity.com/paper/1909.00982/) (2019)

## Built on by (most cited first, 5 of 5)

- [Overcoming Fairness Trade-offs via Pre-processing: A Causal Perspective](https://mlsanity.com/paper/2501.14710/) (2025)
- [SciPostGen: Bridging the Gap between Scientific Papers and Poster Layouts](https://mlsanity.com/paper/2511.22490/) (2025)
- [On Optimal Steering to Achieve Exact Fairness](https://mlsanity.com/paper/2509.15759/) (2025)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [Bias In, Bias Out? Finding Unbiased Subnetworks in Vanilla Models](https://mlsanity.com/paper/2603.05582/) (2026)

## Abstract (arXiv)

A general belief in fair classification is that fairness constraints incur a trade-off with accuracy, which biased data may worsen. Contrary to this belief, Blum & Stangl (2019) show that fair classification with equal opportunity constraints even on extremely biased data can recover optimally accurate and fair classifiers on the original data distribution. Their result is interesting because it demonstrates that fairness constraints can implicitly rectify data bias and simultaneously overcome a perceived fairness-accuracy trade-off. Their data bias model simulates under-representation and label bias in underprivileged population, and they show the above result on a stylized data distribution with i.i.d. label noise, under simple conditions on the data distribution and bias parameters. We propose a general approach to extend the result of Blum & Stangl (2019) to different fairness constraints, data bias models, data distributions, and hypothesis classes. We strengthen their result, and extend it to the case when their stylized distribution has labels with Massart noise instead of i.i.d. noise. We prove a similar recovery result for arbitrary data distributions using fair reject option classifiers. We further generalize it to arbitrary data distributions and arbitrary hypothesis classes, i.e., we prove that for any data distribution, if the optimally accurate classifier in a given hypothesis class is fair and robust, then it can be recovered through fair classification with equal opportunity constraints on the biased distribution whenever the bias parameters satisfy certain simple conditions. Finally, we show applications of our technique to time-varying data bias in classification and fair machine learning pipelines.