# Fair Generalized Linear Models with a Convex Penalty

arXiv: https://arxiv.org/abs/2206.09076 · HTML: https://mlsanity.com/paper/2206.09076/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 40 references that are in the map.
- First posted on arXiv 18 Jun 2022.

## Builds on (most cited first, 15 of 15)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [CheXclusion: Fairness gaps in deep chest X-ray classifiers](https://mlsanity.com/paper/2003.00827/) (2020)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [iFair: Learning Individually Fair Data Representations for Algorithmic Decision Making](https://mlsanity.com/paper/1806.01059/) (2018)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019)
- [Blackbox Post-Processing for Multiclass Fairness](https://mlsanity.com/paper/2201.04461/) (2022)
- [Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms](https://mlsanity.com/paper/2012.12356/) (2020)
- [Fast and Simple Optimization for Poisson Likelihood Models](https://mlsanity.com/paper/1608.01264/) (2016)

## Built on by (most cited first, 11 of 11)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Data Augmentation via Subgroup Mixup for Improving Fairness](https://mlsanity.com/paper/2309.07110/) (2023)
- [fairml: A Statistician's Take on Fair Machine Learning Modelling](https://mlsanity.com/paper/2305.02009/) (2023)
- [Fair Mixed Effects Support Vector Machine](https://mlsanity.com/paper/2405.06433/) (2024)
- [Fair and Accurate Regression: Strong Formulations and Algorithms](https://mlsanity.com/paper/2412.17116/) (2024)
- [Using Property Elicitation to Understand the Impacts of Fairness Regularizers](https://mlsanity.com/paper/2309.11343/) (2023)
- [Generalizing Orthogonalization for Models with Non-Linearities](https://mlsanity.com/paper/2405.02475/) (2024)
- [Fair Generalized Linear Mixed Models](https://mlsanity.com/paper/2405.09273/) (2024)
- [Uncovering Fairness through Data Complexity as an Early Indicator](https://mlsanity.com/paper/2504.05923/) (2025)
- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)
- [MIFair: A Mutual-Information Framework for Intersectionality and Multiclass Fairness](https://mlsanity.com/paper/2604.28030/) (2026)

## Abstract (arXiv)

Despite recent advances in algorithmic fairness, methodologies for achieving fairness with generalized linear models (GLMs) have yet to be explored in general, despite GLMs being widely used in practice. In this paper we introduce two fairness criteria for GLMs based on equalizing expected outcomes or log-likelihoods. We prove that for GLMs both criteria can be achieved via a convex penalty term based solely on the linear components of the GLM, thus permitting efficient optimization. We also derive theoretical properties for the resulting fair GLM estimator. To empirically demonstrate the efficacy of the proposed fair GLM, we compare it with other well-known fair prediction methods on an extensive set of benchmark datasets for binary classification and regression. In addition, we demonstrate that the fair GLM can generate fair predictions for a range of response variables, other than binary and continuous outcomes.