# Fair Regression under Demographic Parity: A Unified Framework

arXiv: https://arxiv.org/abs/2601.10623 · HTML: https://mlsanity.com/paper/2601.10623/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [Fairness in Multi-Task Learning via Wasserstein Barycenters](https://mlsanity.com/paper/2306.10155/) (2023)
- [Fair Generalized Linear Models with a Convex Penalty](https://mlsanity.com/paper/2206.09076/) (2022)
- [Demographic Parity Constrained Minimax Optimal Regression under Linear Model](https://mlsanity.com/paper/2206.11546/) (2022)
- [Regression under demographic parity constraints via unlabeled post-processing](https://mlsanity.com/paper/2407.15453/) (2024)
- [The Statistical Fairness-Accuracy Frontier](https://mlsanity.com/paper/2508.17622/) (2025)
- [Multi-Output Distributional Fairness via Post-Processing](https://mlsanity.com/paper/2409.00553/) (2024)
- [Meta Optimality for Demographic Parity Constrained Regression via Post-Processing](https://mlsanity.com/paper/2506.13947/) (2025)
- [Fair and Accurate Regression: Strong Formulations and Algorithms](https://mlsanity.com/paper/2412.17116/) (2024)

## Abstract (arXiv)

We propose a unified framework for fair regression tasks formulated as risk minimization problems subject to a demographic parity constraint. Unlike many existing approaches that are limited to specific loss functions or rely on challenging non-convex optimization, our framework is applicable to a broad spectrum of regression tasks. Examples include linear regression with squared loss, binary classification with cross-entropy loss, quantile regression with pinball loss, and robust regression with Huber loss. We derive a novel characterization of the fair risk minimizer, which yields a computationally efficient estimation procedure for general loss functions. Theoretically, we establish the asymptotic consistency of the proposed estimator and derive its convergence rates under mild assumptions. We illustrate the method's versatility through detailed discussions of several common loss functions. Numerical results demonstrate that our approach effectively minimizes risk while satisfying fairness constraints across various regression settings.