mlsanityData to 13 Oct 2026

Fair Regression with Wasserstein Barycenters

arXiv 2006.07286 ↗First posted 12 Jun 2020stat.ML cs.LG math.STcited by 99

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Abstract (arXiv)

We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the sensitive attribute is available for prediction. We establish a connection between fair regression and optimal transport theory, based on which we derive a close form expression for the optimal fair predictor. Specifically, we show that the distribution of this optimum is the Wasserstein barycenter of the distributions induced by the standard regression function on the sensitive groups. This result offers an intuitive interpretation of the optimal fair prediction and suggests a simple post-processing algorithm to achieve fairness. We establish risk and distribution-free fairness guarantees for this procedure. Numerical experiments indicate that our method is very effective in learning fair models, with a relative increase in error rate that is inferior to the relative gain in fairness.

Key facts. Cited by 99 papers in the map (data through 13 Oct 2026). First posted on arXiv 12 Jun 2020.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 9; 2022: 17; 2023: 17; 2024: 17; 2025: 28; 2026: 11.

99 papers.

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  1. 2022Bias Mitigation for Machine Learning Classifiers: A Comprehensive Surveycited by 125
  2. 2022Fair and Optimal Classification via Post-Processingcited by 50
  3. 2021Transport-based Counterfactual Modelscited by 27
  4. 2021A Sociotechnical View of Algorithmic Fairnesscited by 24
  5. 2022Fair learning with Wasserstein barycenters for non-decomposable performance measurescited by 24
  6. 2022Fair Representation Learning through Implicit Path Alignmentcited by 22
  7. 2022Conformalized Fairness via Quantile Regressioncited by 19
  8. 2021Understanding and Mitigating Accuracy Disparity in Regressioncited by 17
  9. 2023Fairness in Multi-Task Learning via Wasserstein Barycenterscited by 14
  10. 2021Towards Return Parity in Markov Decision Processescited by 12
  11. 2022Fair Data Representation for Machine Learning at the Pareto Frontiercited by 12
  12. 2022Optimal Transport of Classifiers to Fairnesscited by 12
38 more
  1. 2022Input-agnostic Certified Group Fairness via Gaussian Parameter Smoothingcited by 11
  2. 2021Fairness with Continuous Optimal Transportcited by 9
  3. 2021Costs and Benefits of Fair Regressioncited by 8
  4. 2022Repairing Regressors for Fair Binary Classification at Any Decision Thresholdcited by 8
  5. 2023Scalable Infomin Learningcited by 8
  6. 2023Counterfactual Situation Testing: Uncovering Discrimination under Fairness given the Differencecited by 8
  7. 2023A Sequentially Fair Mechanism for Multiple Sensitive Attributescited by 8
  8. 2024OTClean: Data Cleaning for Conditional Independence Violations using Optimal Transportcited by 8
  9. 2024Counterfactual Fairness by Combining Factual and Counterfactual Predictionscited by 8
  10. 2023Mitigating Discrimination in Insurance with Wasserstein Barycenterscited by 7
  11. 2022Obtaining Dyadic Fairness by Optimal Transportcited by 6
  12. 2022Metrizing Fairnesscited by 6
  13. 2022Demographic Parity Constrained Minimax Optimal Regression under Linear Modelcited by 6
  14. 2023Mean Parity Fair Regression in RKHScited by 6
  15. 2023Positivity-free Policy Learning with Observational Datacited by 6
  16. 2023Strong statistical parity through fair synthetic datacited by 6
  17. 2021Fair Sparse Regression with Clustering: An Invex Relaxation for a Combinatorial Problemcited by 5
  18. 2022Error Parity Fairness: Testing for Group Fairness in Regression Taskscited by 5
  19. 2023FairWASP: Fast and Optimal Fair Wasserstein Pre-processingcited by 5
  20. 2024Differentially Private Post-Processing for Fair Regressioncited by 5
  21. 2024Regression under demographic parity constraints via unlabeled post-processingcited by 5
  22. 2022Fairness-aware Regression Robust to Adversarial Attackscited by 4
  23. 2023Retiring DeltaDP: New Distribution-Level Metrics for Demographic Paritycited by 4
  24. 2023Group-blind optimal transport to group parity and its constrained variantscited by 4
  25. 2024Threshold-Independent Fair Matching through Score Calibrationcited by 4
  26. 2021Fair Regression under Sample Selection Biascited by 3
  27. 2023Standardized Interpretable Fairness Measures for Continuous Risk Scorescited by 3
  28. 2024Benchmarking the Fairness of Image Upsampling Methodscited by 3
  29. 2024Optimal Transport for Fairness: Archival Data Repair using Small Research Data Setscited by 3
  30. 2025The Statistical Fairness-Accuracy Frontiercited by 3
  31. 2023Fairness under Covariate Shift: Improving Fairness-Accuracy tradeoff with few Unlabeled Test Samplescited by 2
  32. 2023Parametric Fairness with Statistical Guaranteescited by 2
  33. 2024On the Consistency of Fairness Measurement Methods for Regression Taskscited by 2
  34. 2024Multi-Output Distributional Fairness via Post-Processingcited by 2
  35. 2024Demographic parity in regression and classification within the unawareness frameworkcited by 2
  36. 2025Counterfactual Situation Testing: From Single to Multidimensional Discriminationcited by 2
  37. 2025Learning with Differentially Private (Sliced) Wasserstein Gradientscited by 2
  38. 2025Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraintscited by 2

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