# Regression under demographic parity constraints via unlabeled post-processing

arXiv: https://arxiv.org/abs/2407.15453 · HTML: https://mlsanity.com/paper/2407.15453/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 22 Jul 2024.

## Builds on (most cited first, 18 of 18)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [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)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Lower Bounds for Non-Convex Stochastic Optimization](https://mlsanity.com/paper/1912.02365/) (2019)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning](https://mlsanity.com/paper/1704.00805/) (2017)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [How To Make the Gradients Small Stochastically: Even Faster Convex and Nonconvex SGD](https://mlsanity.com/paper/1801.02982/) (2018)
- [A statistical framework for fair predictive algorithms](https://mlsanity.com/paper/1610.08077/) (2016)
- [The Complexity of Making the Gradient Small in Stochastic Convex Optimization](https://mlsanity.com/paper/1902.04686/) (2019)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Costs and Benefits of Fair Regression](https://mlsanity.com/paper/2106.08812/) (2021)
- [FairGrad: Fairness Aware Gradient Descent](https://mlsanity.com/paper/2206.10923/) (2022)
- [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)

## Built on by (most cited first, 5 of 5)

- [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024)
- [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025)
- [Happiness as a Measure of Fairness](https://mlsanity.com/paper/2511.01069/) (2025)
- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)
- [Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings](https://mlsanity.com/paper/2605.28233/) (2026)

## Abstract (arXiv)

We address the problem of performing regression while ensuring demographic parity, even without access to sensitive attributes during inference. We present a general-purpose post-processing algorithm that, using accurate estimates of the regression function and a sensitive attribute predictor, generates predictions that meet the demographic parity constraint. Our method involves discretization and stochastic minimization of a smooth convex function. It is suitable for online post-processing and multi-class classification tasks only involving unlabeled data for the post-processing. Unlike prior methods, our approach is fully theory-driven. We require precise control over the gradient norm of the convex function, and thus, we rely on more advanced techniques than standard stochastic gradient descent. Our algorithm is backed by finite-sample analysis and post-processing bounds, with experimental results validating our theoretical findings.