# General Fair Empirical Risk Minimization

arXiv: https://arxiv.org/abs/1901.10080 · HTML: https://mlsanity.com/paper/1901.10080/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2019.

## Built on by (most cited first, 23 of 23)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [Selective Regression Under Fairness Criteria](https://mlsanity.com/paper/2110.15403/) (2021)
- [Assessing Fairness in the Presence of Missing Data](https://mlsanity.com/paper/2112.04899/) (2021)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Marrying Fairness and Explainability in Supervised Learning](https://mlsanity.com/paper/2204.02947/) (2022)
- [Conformalized Fairness via Quantile Regression](https://mlsanity.com/paper/2210.02015/) (2022)
- [Fair Generalized Linear Models with a Convex Penalty](https://mlsanity.com/paper/2206.09076/) (2022)
- [Learning to Teach Fairness-aware Deep Multi-task Learning](https://mlsanity.com/paper/2206.08403/) (2022)
- [Properties of fairness measures in the context of varying class imbalance and protected group ratios](https://mlsanity.com/paper/2411.08425/) (2024)
- [Mean Parity Fair Regression in RKHS](https://mlsanity.com/paper/2302.10409/) (2023)
- [Fairness-Aware Naive Bayes Classifier for Data with Multiple Sensitive Features](https://mlsanity.com/paper/2202.11499/) (2022)
- [Benchmarking the Fairness of Image Upsampling Methods](https://mlsanity.com/paper/2401.13555/) (2024)
- [The Statistical Fairness-Accuracy Frontier](https://mlsanity.com/paper/2508.17622/) (2025)
- [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024)
- [Increasing Fairness in Predictions Using Bias Parity Score Based Loss Function Regularization](https://mlsanity.com/paper/2111.03638/) (2021)
- [Debiasing Machine Learning Models by Using Weakly Supervised Learning](https://mlsanity.com/paper/2402.15477/) (2024)
- [Evaluating Fairness and Mitigating Bias in Machine Learning: A Novel Technique using Tensor Data and Bayesian Regression](https://mlsanity.com/paper/2506.11627/) (2025)
- [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025)
- [Debiasing Credit Scoring using Evolutionary Algorithms](https://mlsanity.com/paper/2110.12838/) (2021)
- [Extending Fair Null-Space Projections for Continuous Attributes to Kernel Methods](https://mlsanity.com/paper/2511.03304/) (2025)
- [An Empirical Study of Machine Learning Robustness and Scalability for Imbalanced Tabular Clinical Data in Emergency and Critical Care](https://mlsanity.com/paper/2512.21602/) (2025)
- [The Role of Uncertainty in Assessing the Fairness of Machine Learning Models](https://mlsanity.com/paper/2609.07959/) (2026)
- [A Comprehensive View of Fairness through Distributional Stability](https://mlsanity.com/paper/2609.37061/) (2026)

## Abstract (arXiv)

We tackle the problem of algorithmic fairness, where the goal is to avoid the unfairly influence of sensitive information, in the general context of regression with possible continuous sensitive attributes. We extend the framework of fair empirical risk minimization to this general scenario, covering in this way the whole standard supervised learning setting. Our generalized fairness measure reduces to well known notions of fairness available in literature. We derive learning guarantees for our method, that imply in particular its statistical consistency, both in terms of the risk and the fairness measure. We then specialize our approach to kernel methods and propose a convex fair estimator in that setting. We test the estimator on a commonly used benchmark dataset (Communities and Crime) and on a new dataset collected at the University of Genova, containing the information of the academic career of five thousand students. The latter dataset provides a challenging real case scenario of unfair behaviour of standard regression methods that benefits from our methodology. The experimental results show that our estimator is effective at mitigating the trade-off between accuracy and fairness requirements.