# Meta Optimality for Demographic Parity Constrained Regression via Post-Processing

arXiv: https://arxiv.org/abs/2506.13947 · HTML: https://mlsanity.com/paper/2506.13947/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 48 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 30 of 31)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [Plugin Estimation of Smooth Optimal Transport Maps](https://mlsanity.com/paper/2107.12364/) (2021)
- [Fairness via Representation Neutralization](https://mlsanity.com/paper/2106.12674/) (2021)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization](https://mlsanity.com/paper/2102.01752/) (2021)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networks](https://mlsanity.com/paper/2007.04462/) (2020)
- [Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov space](https://mlsanity.com/paper/1910.12799/) (2019)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)
- [Optimal transport map estimation in general function spaces](https://mlsanity.com/paper/2212.03722/) (2022)
- [Minimax estimation of discontinuous optimal transport maps: The semi-discrete case](https://mlsanity.com/paper/2301.11302/) (2023)
- [An improved central limit theorem and fast convergence rates for entropic transportation costs](https://mlsanity.com/paper/2204.09105/) (2022)
- [Post-hoc Bias Scoring Is Optimal For Fair Classification](https://mlsanity.com/paper/2310.05725/) (2023)
- [Fair Data Representation for Machine Learning at the Pareto Frontier](https://mlsanity.com/paper/2201.00292/) (2022)
- [Loss Balancing for Fair Supervised Learning](https://mlsanity.com/paper/2311.03714/) (2023)
- [Demographic Parity Constrained Minimax Optimal Regression under Linear Model](https://mlsanity.com/paper/2206.11546/) (2022)

## Built on by (most cited first, 2 of 2)

- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)
- [Fair Classification with Efficient and Post-hoc Controllable Fairness-Accuracy Trade-off](https://mlsanity.com/paper/2606.28097/) (2026)

## Abstract (arXiv)

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the fairness constraint. However, these analyses are tightly coupled with specific data generation models. In this paper, we provide meta-theorems that can be applied to various situations to validate the fair minimax optimality of the corresponding regression algorithms. Furthermore, we demonstrate that fair minimax optimal regression can be achieved through post-processing methods, allowing researchers and practitioners to focus on improving conventional regression techniques, which can then be efficiently adapted for fair regression.