# Differentially Private Post-Processing for Fair Regression

arXiv: https://arxiv.org/abs/2405.04034 · HTML: https://mlsanity.com/paper/2405.04034/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 63 references that are in the map.
- First posted on arXiv 7 May 2024.

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

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [On Fairness and Calibration](https://mlsanity.com/paper/1709.02012/) (2017)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Hyperparameter Tuning with Renyi Differential Privacy](https://mlsanity.com/paper/2110.03620/) (2021)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Differentially Private Fair Learning](https://mlsanity.com/paper/1812.02696/) (2018)
- [Private Selection from Private Candidates](https://mlsanity.com/paper/1811.07971/) (2018)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Private Hypothesis Selection](https://mlsanity.com/paper/1905.13229/) (2019)
- [Differentially Private and Fair Deep Learning: A Lagrangian Dual Approach](https://mlsanity.com/paper/2009.12562/) (2020)
- [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022)
- [Fair Learning with Private Demographic Data](https://mlsanity.com/paper/2002.11651/) (2020)
- [On the Sample Complexity of Privately Learning Unbounded High-Dimensional Gaussians](https://mlsanity.com/paper/2010.09929/) (2020)
- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [The Role of Adaptive Optimizers for Honest Private Hyperparameter Selection](https://mlsanity.com/paper/2111.04906/) (2021)
- [Wasserstein barycenters can be computed in polynomial time in fixed dimension](https://mlsanity.com/paper/2006.08012/) (2020)
- [Discrete Wasserstein Barycenters: Optimal Transport for Discrete Data](https://mlsanity.com/paper/1507.07218/) (2015)
- [Decision Tree Classification with Differential Privacy: A Survey](https://mlsanity.com/paper/1611.01919/) (2016)
- [Understanding and Mitigating Accuracy Disparity in Regression](https://mlsanity.com/paper/2102.12013/) (2021)

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

- [Differentially Private Random Feature Model](https://mlsanity.com/paper/2412.04785/) (2024)
- [The Pitfalls of "Security by Obscurity" And What They Mean for Transparent AI](https://mlsanity.com/paper/2501.18669/) (2025)
- [Learning with Differentially Private (Sliced) Wasserstein Gradients](https://mlsanity.com/paper/2502.01701/) (2025)
- [Wasserstein projection distance for fairness testing of regression models](https://mlsanity.com/paper/2510.04114/) (2025)
- [Toward Unifying Group Fairness Evaluation from a Sparsity Perspective](https://mlsanity.com/paper/2511.00359/) (2025)

## Abstract (arXiv)

This paper describes a differentially private post-processing algorithm for learning fair regressors satisfying statistical parity, addressing privacy concerns of machine learning models trained on sensitive data, as well as fairness concerns of their potential to propagate historical biases. Our algorithm can be applied to post-process any given regressor to improve fairness by remapping its outputs. It consists of three steps: first, the output distributions are estimated privately via histogram density estimation and the Laplace mechanism, then their Wasserstein barycenter is computed, and the optimal transports to the barycenter are used for post-processing to satisfy fairness. We analyze the sample complexity of our algorithm and provide fairness guarantee, revealing a trade-off between the statistical bias and variance induced from the choice of the number of bins in the histogram, in which using less bins always favors fairness at the expense of error.