# Demographic parity in regression and classification within the unawareness framework

arXiv: https://arxiv.org/abs/2409.02471 · HTML: https://mlsanity.com/paper/2409.02471/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 19 of 19)

- [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)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [Bayes-Optimal Classifiers under Group Fairness](https://mlsanity.com/paper/2202.09724/) (2022)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019)
- [Review of Mathematical frameworks for Fairness in Machine Learning](https://mlsanity.com/paper/2005.13755/) (2020)
- [Deontological Ethics By Monotonicity Shape Constraints](https://mlsanity.com/paper/2001.11990/) (2020)
- [Fair Bayes-Optimal Classifiers Under Predictive Parity](https://mlsanity.com/paper/2205.07182/) (2022)
- [Optimal transportation between unequal dimensions](https://mlsanity.com/paper/1805.11187/) (2018)
- [Regression under demographic parity constraints via unlabeled post-processing](https://mlsanity.com/paper/2407.15453/) (2024)
- [An example of prediction which complies with Demographic Parity and equalizes group-wise risks in the context of regression](https://mlsanity.com/paper/2011.07158/) (2020)
- [Group-blind optimal transport to group parity and its constrained variants](https://mlsanity.com/paper/2310.11407/) (2023)
- [Multidimensional matching](https://mlsanity.com/paper/1604.05771/) (2016)

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

- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)
- [Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings](https://mlsanity.com/paper/2605.28233/) (2026)

## Abstract (arXiv)

This paper explores the theoretical foundations of fair regression under the constraint of demographic parity within the unawareness framework, where disparate treatment is prohibited, extending existing results where such treatment is permitted. Specifically, we aim to characterize the optimal fair regression function when minimizing the quadratic loss. Our results reveal that this function is given by the solution to a barycenter problem with optimal transport costs. Additionally, we study the connection between optimal fair cost-sensitive classification, and optimal fair regression. We demonstrate that nestedness of the decision sets of the classifiers is both necessary and sufficient to establish a form of equivalence between classification and regression. Under this nestedness assumption, the optimal classifiers can be derived by applying thresholds to the optimal fair regression function; conversely, the optimal fair regression function is characterized by the family of cost-sensitive classifiers.