# Fair Regression with Wasserstein Barycenters

arXiv: https://arxiv.org/abs/2006.07286 · HTML: https://mlsanity.com/paper/2006.07286/

## Key facts

- Cited by 100 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 30 of 100)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [A Sociotechnical View of Algorithmic Fairness](https://mlsanity.com/paper/2110.09253/) (2021)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Fair Representation Learning through Implicit Path Alignment](https://mlsanity.com/paper/2205.13316/) (2022)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)
- [Fairness in Multi-Task Learning via Wasserstein Barycenters](https://mlsanity.com/paper/2306.10155/) (2023)
- [Towards Return Parity in Markov Decision Processes](https://mlsanity.com/paper/2111.10476/) (2021)
- [Fair Data Representation for Machine Learning at the Pareto Frontier](https://mlsanity.com/paper/2201.00292/) (2022)
- [Optimal Transport of Classifiers to Fairness](https://mlsanity.com/paper/2202.03814/) (2022)
- [Input-agnostic Certified Group Fairness via Gaussian Parameter Smoothing](https://mlsanity.com/paper/2206.11423/) (2022)
- [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021)
- [A Sequentially Fair Mechanism for Multiple Sensitive Attributes](https://mlsanity.com/paper/2309.06627/) (2023)
- [Costs and Benefits of Fair Regression](https://mlsanity.com/paper/2106.08812/) (2021)
- [Repairing Regressors for Fair Binary Classification at Any Decision Threshold](https://mlsanity.com/paper/2203.07490/) (2022)
- [Scalable Infomin Learning](https://mlsanity.com/paper/2302.10701/) (2023)
- [Counterfactual Situation Testing: Uncovering Discrimination under Fairness given the Difference](https://mlsanity.com/paper/2302.11944/) (2023)
- [OTClean: Data Cleaning for Conditional Independence Violations using Optimal Transport](https://mlsanity.com/paper/2403.02372/) (2024)
- [Counterfactual Fairness by Combining Factual and Counterfactual Predictions](https://mlsanity.com/paper/2409.01977/) (2024)
- [Mitigating Discrimination in Insurance with Wasserstein Barycenters](https://mlsanity.com/paper/2306.12912/) (2023)
- [Obtaining Dyadic Fairness by Optimal Transport](https://mlsanity.com/paper/2202.04520/) (2022)
- [Metrizing Fairness](https://mlsanity.com/paper/2205.15049/) (2022)
- [Demographic Parity Constrained Minimax Optimal Regression under Linear Model](https://mlsanity.com/paper/2206.11546/) (2022)
- [Mean Parity Fair Regression in RKHS](https://mlsanity.com/paper/2302.10409/) (2023)
- [Positivity-free Policy Learning with Observational Data](https://mlsanity.com/paper/2310.06969/) (2023)
- [Strong statistical parity through fair synthetic data](https://mlsanity.com/paper/2311.03000/) (2023)
- [Fair Sparse Regression with Clustering: An Invex Relaxation for a Combinatorial Problem](https://mlsanity.com/paper/2102.09704/) (2021)
- [Error Parity Fairness: Testing for Group Fairness in Regression Tasks](https://mlsanity.com/paper/2208.08279/) (2022)

## 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.