mlsanityData to 14 Oct 2026

Costs and Benefits of Fair Regression

arXiv 2106.08812 ↗First posted 16 Jun 2021cs.LG cs.AI cs.CYcited by 8

Not on the map. Why?

Abstract (arXiv)

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy with a real-valued target is not entirely clear. In this paper, we characterize the inherent tradeoff between statistical parity and accuracy in the regression setting by providing a lower bound on the error of any fair regressor. Our lower bound is sharp, algorithm-independent, and admits a simple interpretation: when the moments of the target differ between groups, any fair algorithm has to make an error on at least one of the groups. We further extend this result to give a lower bound on the joint error of any (approximately) fair algorithm, using the Wasserstein distance to measure the quality of the approximation. With our novel lower bound, we also show that the price paid by a fair regressor that does not take the protected attribute as input is less than that of a fair regressor with explicit access to the protected attribute. On the upside, we establish the first connection between individual fairness, accuracy parity, and the Wasserstein distance by showing that if a regressor is individually fair, it also approximately verifies the accuracy parity, where the gap is given by the Wasserstein distance between the two groups. Inspired by our theoretical results, we develop a practical algorithm for fair regression through the lens of representation learning, and conduct experiments on a real-world dataset to corroborate our findings.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 27 of its 58 references that are in the map. First posted on arXiv 16 Jun 2021.

Builds on

27 of 58 references.

References · 27

  1. 2015Domain-Adversarial Training of Neural Networkscited by 3,044
  2. 2016Equality of Opportunity in Supervised Learningcited by 2,007
  3. 2014Certifying and removing disparate impactcited by 715
  4. 2018Mitigating Unwanted Biases with Adversarial Learningcited by 663
  5. 2017Wasserstein GANcited by 639
  6. 2017Algorithmic decision making and the cost of fairnesscited by 403
  7. 2018Learning Adversarially Fair and Transferable Representationscited by 353
  8. 2016Learning Representations for Counterfactual Inferencecited by 329
  9. 2019Differential Privacy Has Disparate Impact on Model Accuracycited by 316
  10. 2017Joint Distribution Optimal Transportation for Domain Adaptationcited by 282
  11. 2015The Variational Fair Autoencodercited by 223
  12. 2013Fast Computation of Wasserstein Barycenterscited by 216
15 more
  1. 2020Fairness in Machine Learningcited by 194
  2. 2015Censoring Representations with an Adversarycited by 192
  3. 2019Fair Regression: Quantitative Definitions and Reduction-based Algorithmscited by 168
  4. 2017Data Decisions and Theoretical Implications when Adversarially Learning Fair Representationscited by 165
  5. 2017A Convex Framework for Fair Regressioncited by 148
  6. 2019Inherent Tradeoffs in Learning Fair Representationscited by 144
  7. 2020Fair Regression with Wasserstein Barycenterscited by 100
  8. 2019Conditional Learning of Fair Representationscited by 78
  9. 2020Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effectscited by 72
  10. 2019Pairwise Fairness for Ranking and Regressioncited by 58
  11. 2019Recovering from Biased Data: Can Fairness Constraints Improve Accuracy?cited by 50
  12. 2015On the relation between accuracy and fairness in binary classificationcited by 48
  13. 2018Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spacescited by 41
  14. 2016A statistical framework for fair predictive algorithmscited by 38
  15. 2021Understanding and Mitigating Accuracy Disparity in Regressioncited by 17

Built on by

Cited by year

Citing papers per year: 2023: 4; 2024: 2; 2025: 2.

8 papers.

  1. 2024Regression under demographic parity constraints via unlabeled post-processingcited by 5
  2. 2023A Theoretical Approach to Characterize the Accuracy-Fairness Trade-off Pareto Frontiercited by 4
  3. 2023Standardized Interpretable Fairness Measures for Continuous Risk Scorescited by 3
  4. 2025The Statistical Fairness-Accuracy Frontiercited by 3
  5. 2023Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samplescited by 2
  6. 2024Towards Harmless Rawlsian Fairness Regardless of Demographic Priorcited by 1
  7. 2023An Empirical Study of Self-supervised Learning with Wasserstein Distancecited by 0
  8. 2025Group Fairness Meets the Black Box: Enabling Fair Algorithms on Closed LLMs via Post-Processingcited by 0