# Fair Regression: Quantitative Definitions and Reduction-based Algorithms

arXiv: https://arxiv.org/abs/1905.12843 · HTML: https://mlsanity.com/paper/1905.12843/

## Key facts

- Cited by 168 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 30 of 168)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [A Clarification of the Nuances in the Fairness Metrics Landscape](https://mlsanity.com/paper/2106.00467/) (2021)
- [Trustworthy AI: A Computational Perspective](https://mlsanity.com/paper/2107.06641/) (2021)
- [Fairlearn: Assessing and Improving Fairness of AI Systems](https://mlsanity.com/paper/2303.16626/) (2023)
- [FairCLIP: Harnessing Fairness in Vision-Language Learning](https://mlsanity.com/paper/2403.19949/) (2024)
- [Characterizing Fairness Over the Set of Good Models Under Selective Labels](https://mlsanity.com/paper/2101.00352/) (2021)
- [Socially Responsible AI Algorithms: Issues, Purposes, and Challenges](https://mlsanity.com/paper/2101.02032/) (2021)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Hatemoji: A Test Suite and Adversarially-Generated Dataset for Benchmarking and Detecting Emoji-based Hate](https://mlsanity.com/paper/2108.05921/) (2021)
- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [A Trip Towards Fairness: Bias and De-Biasing in Large Language Models](https://mlsanity.com/paper/2305.13862/) (2023)
- [Minimax Regret Optimization for Robust Machine Learning under Distribution Shift](https://mlsanity.com/paper/2202.05436/) (2022)
- [Harvard Glaucoma Fairness: A Retinal Nerve Disease Dataset for Fairness Learning and Fair Identity Normalization](https://mlsanity.com/paper/2306.09264/) (2023)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [FairGBM: Gradient Boosting with Fairness Constraints](https://mlsanity.com/paper/2209.07850/) (2022)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Assessing Fairness in the Presence of Missing Data](https://mlsanity.com/paper/2112.04899/) (2021)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [FairTune: Optimizing Parameter Efficient Fine Tuning for Fairness in Medical Image Analysis](https://mlsanity.com/paper/2310.05055/) (2023)
- [When Fair Ranking Meets Uncertain Inference](https://mlsanity.com/paper/2105.02091/) (2021)
- [Fair Representation Learning through Implicit Path Alignment](https://mlsanity.com/paper/2205.13316/) (2022)
- [Reliable and Trustworthy Machine Learning for Health Using Dataset Shift Detection](https://mlsanity.com/paper/2110.14019/) (2021)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [The Authors Matter: Understanding and Mitigating Implicit Bias in Deep Text Classification](https://mlsanity.com/paper/2105.02778/) (2021)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)
- [Modeling Techniques for Machine Learning Fairness: A Survey](https://mlsanity.com/paper/2111.03015/) (2021)
- [Adaptive Fairness Improvement Based on Causality Analysis](https://mlsanity.com/paper/2209.07190/) (2022)
- [Improving Fairness in AI Models on Electronic Health Records: The Case for Federated Learning Methods](https://mlsanity.com/paper/2305.11386/) (2023)
- [Scalable Spectral Clustering with Group Fairness Constraints](https://mlsanity.com/paper/2210.16435/) (2022)
- [Equal Opportunity of Coverage in Fair Regression](https://mlsanity.com/paper/2311.02243/) (2023)

## Abstract (arXiv)

In this paper, we study the prediction of a real-valued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems fair regression. We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined level. While we only study these two notions of fairness, our schemes are applicable to arbitrary Lipschitz-continuous losses, and so they encompass least-squares regression, logistic regression, quantile regression, and many other tasks. Our schemes only require access to standard risk minimization algorithms (such as standard classification or least-squares regression) while providing theoretical guarantees on the optimality and fairness of the obtained solutions. In addition to analyzing theoretical properties of our schemes, we empirically demonstrate their ability to uncover fairness--accuracy frontiers on several standard datasets.