# On the Impact of Output Perturbation on Fairness in Binary Linear Classification

arXiv: https://arxiv.org/abs/2402.03011 · HTML: https://mlsanity.com/paper/2402.03011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Neither Private Nor Fair: Impact of Data Imbalance on Utility and Fairness in Differential Privacy](https://mlsanity.com/paper/2009.06389/) (2020)
- [Two Simple Ways to Learn Individual Fairness Metrics from Data](https://mlsanity.com/paper/2006.11439/) (2020)
- [Differential Privacy and Fairness in Decisions and Learning Tasks: A Survey](https://mlsanity.com/paper/2202.08187/) (2022)
- [Disparate Impact in Differential Privacy from Gradient Misalignment](https://mlsanity.com/paper/2206.07737/) (2022)
- [Practical Differentially Private Hyperparameter Tuning with Subsampling](https://mlsanity.com/paper/2301.11989/) (2023)
- [Arbitrary Decisions are a Hidden Cost of Differentially Private Training](https://mlsanity.com/paper/2302.14517/) (2023)
- [Differential Privacy has Bounded Impact on Fairness in Classification](https://mlsanity.com/paper/2210.16242/) (2022)
- [Stationary Behavior of Constant Stepsize SGD Type Algorithms: An Asymptotic Characterization](https://mlsanity.com/paper/2111.06328/) (2021)
- [FairGrad: Fairness Aware Gradient Descent](https://mlsanity.com/paper/2206.10923/) (2022)

## Abstract (arXiv)

We theoretically study how differential privacy interacts with both individual and group fairness in binary linear classification. More precisely, we focus on the output perturbation mechanism, a classic approach in privacy-preserving machine learning. We derive high-probability bounds on the level of individual and group fairness that the perturbed models can achieve compared to the original model. Hence, for individual fairness, we prove that the impact of output perturbation on the level of fairness is bounded but grows with the dimension of the model. For group fairness, we show that this impact is determined by the distribution of so-called angular margins, that is signed margins of the non-private model re-scaled by the norm of each example.