# Achieving Fairness with a Simple Ridge Penalty

arXiv: https://arxiv.org/abs/2105.13817 · HTML: https://mlsanity.com/paper/2105.13817/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 58 references that are in the map.
- First posted on arXiv 18 May 2021.

## Builds on (most cited first, 13 of 13)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fairness in Criminal Justice Risk Assessments: The State of the Art](https://mlsanity.com/paper/1703.09207/) (2017)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Mitigating Bias in Algorithmic Hiring: Evaluating Claims and Practices](https://mlsanity.com/paper/1906.09208/) (2019)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [A Convex Framework for Fair Regression](https://mlsanity.com/paper/1706.02409/) (2017)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Fair Kernel Learning](https://mlsanity.com/paper/1710.05578/) (2017)
- [Review of Mathematical frameworks for Fairness in Machine Learning](https://mlsanity.com/paper/2005.13755/) (2020)
- [Lecture notes on ridge regression](https://mlsanity.com/paper/1509.09169/) (2015)
- [Fast Fair Regression via Efficient Approximations of Mutual Information](https://mlsanity.com/paper/2002.06200/) (2020)

## Built on by (most cited first, 13 of 13)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Fair and Green Hyperparameter Optimization via Multi-objective and Multiple Information Source Bayesian Optimization](https://mlsanity.com/paper/2205.08835/) (2022)
- [Counterfactual Fairness by Combining Factual and Counterfactual Predictions](https://mlsanity.com/paper/2409.01977/) (2024)
- [SimFair: A Unified Framework for Fairness-Aware Multi-Label Classification](https://mlsanity.com/paper/2302.09683/) (2023)
- [Uncertainty-aware predictive modeling for fair data-driven decisions](https://mlsanity.com/paper/2211.02730/) (2022)
- [Mean Parity Fair Regression in RKHS](https://mlsanity.com/paper/2302.10409/) (2023)
- [fairml: A Statistician's Take on Fair Machine Learning Modelling](https://mlsanity.com/paper/2305.02009/) (2023)
- [A Novel Regularization Approach to Fair ML](https://mlsanity.com/paper/2208.06557/) (2022)
- [Fair Supervised Learning with A Simple Random Sampler of Sensitive Attributes](https://mlsanity.com/paper/2311.05866/) (2023)
- [Generalizing Orthogonalization for Models with Non-Linearities](https://mlsanity.com/paper/2405.02475/) (2024)
- [Penalized Fair Regression for Multiple Groups in Chronic Kidney Disease](https://mlsanity.com/paper/2512.17340/) (2025)
- [Variable Selection in the Context of AI Fairness](https://mlsanity.com/paper/2608.11251/) (2026)
- [The Role of Uncertainty in Assessing the Fairness of Machine Learning Models](https://mlsanity.com/paper/2609.07959/) (2026)

## Abstract (arXiv)

In this paper we present a general framework for estimating regression models subject to a user-defined level of fairness. We enforce fairness as a model selection step in which we choose the value of a ridge penalty to control the effect of sensitive attributes. We then estimate the parameters of the model conditional on the chosen penalty value. Our proposal is mathematically simple, with a solution that is partly in closed form, and produces estimates of the regression coefficients that are intuitive to interpret as a function of the level of fairness. Furthermore, it is easily extended to generalised linear models, kernelised regression models and other penalties; and it can accommodate multiple definitions of fairness. We compare our approach with the regression model from Komiyama et al. (2018), which implements a provably-optimal linear regression model; and with the fair models from Zafar et al. (2019). We evaluate these approaches empirically on six different data sets, and we find that our proposal provides better goodness of fit and better predictive accuracy for the same level of fairness. In addition, we highlight a source of bias in the original experimental evaluation in Komiyama et al. (2018).