# Fair regression under localized demographic parity constraints

arXiv: https://arxiv.org/abs/2603.25224 · HTML: https://mlsanity.com/paper/2603.25224/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 26 Mar 2026.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Fair Data Adaptation with Quantile Preservation](https://mlsanity.com/paper/1911.06685/) (2019)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [Equal Opportunity of Coverage in Fair Regression](https://mlsanity.com/paper/2311.02243/) (2023)
- [Fairness in Multi-Task Learning via Wasserstein Barycenters](https://mlsanity.com/paper/2306.10155/) (2023)
- [A Sequentially Fair Mechanism for Multiple Sensitive Attributes](https://mlsanity.com/paper/2309.06627/) (2023)
- [Fair quantile regression](https://mlsanity.com/paper/1907.08646/) (2019)
- [Parametric Fairness with Statistical Guarantees](https://mlsanity.com/paper/2310.20508/) (2023)
- [Enforcing Fair Predicted Scores on Intervals of Percentiles by Difference-of-Convex Constraints](https://mlsanity.com/paper/2505.12530/) (2025)
- [Testing Fairness with Utility Tradeoffs: A Wasserstein Projection Approach](https://mlsanity.com/paper/2505.11678/) (2025)

## Abstract (arXiv)

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression and can lead to substantial accuracy loss. We propose a relaxation of DP tailored to regression, enforcing parity only at a finite set of quantile levels and/or score thresholds. Concretely, we introduce a novel (ℓ, Z)-fair predictor, which imposes groupwise CDF constraints of the form F f |S=s (z m ) = ℓ m for prescribed pairs (ℓ m , z m ). For this setting, we derive closed-form characterizations of the optimal fair discretized predictor via a Lagrangian dual formulation and quantify the discretization cost, showing that the risk gap to the continuous optimum vanishes as the grid is refined. We further develop a model-agnostic post-processing algorithm based on two samples (labeled for learning a base regressor and unlabeled for calibration), and establish finite-sample guarantees on constraint violation and excess penalized risk. In addition, we introduce two alternative frameworks where we match group and marginal CDF values at selected score thresholds. In both settings, we provide closed-form solutions for the optimal fair discretized predictor. Experiments on synthetic and real datasets illustrate an interpretable fairness-accuracy trade-off, enabling targeted corrections at decision-relevant quantiles or thresholds while preserving predictive performance.