# Demographic Parity Constrained Minimax Optimal Regression under Linear Model

arXiv: https://arxiv.org/abs/2206.11546 · HTML: https://mlsanity.com/paper/2206.11546/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices](https://mlsanity.com/paper/1912.10754/) (2019)

## Built on by (most cited first, 6 of 6)

- [On the Maximal Local Disparity of Fairness-Aware Classifiers](https://mlsanity.com/paper/2406.03255/) (2024)
- [Meta Optimality for Demographic Parity Constrained Regression via Post-Processing](https://mlsanity.com/paper/2506.13947/) (2025)
- [Auditing and Enforcing Conditional Fairness via Optimal Transport](https://mlsanity.com/paper/2410.14029/) (2024)
- [Learning Pareto manifolds in high dimensions: How can regularization help?](https://mlsanity.com/paper/2503.08849/) (2025)
- [Reducing Biases in Record Matching Through Scores Calibration](https://mlsanity.com/paper/2411.01685/) (2024)
- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)

## Abstract (arXiv)

We explore the minimax optimal error associated with a demographic parity-constrained regression problem within the context of a linear model. Our proposed model encompasses a broader range of discriminatory bias sources compared to the model presented by Chzhen and Schreuder (2022). Our analysis reveals that the minimax optimal error for the demographic parity-constrained regression problem under our model is characterized by Theta(fracdMn), where n denotes the sample size, d represents the dimensionality, and M signifies the number of demographic groups arising from sensitive attributes. Moreover, we demonstrate that the minimax error increases in conjunction with a larger bias present in the model.