# Review of Mathematical frameworks for Fairness in Machine Learning

arXiv: https://arxiv.org/abs/2005.13755 · HTML: https://mlsanity.com/paper/2005.13755/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2020.

## Built on by (most cited first, 21 of 21)

- [Improving the Fairness of Chest X-ray Classifiers](https://mlsanity.com/paper/2203.12609/) (2022)
- [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021)
- [Achieving Fairness with a Simple Ridge Penalty](https://mlsanity.com/paper/2105.13817/) (2021)
- [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021)
- [fairml: A Statistician's Take on Fair Machine Learning Modelling](https://mlsanity.com/paper/2305.02009/) (2023)
- [Debiasing Diffusion Model: Enhancing Fairness through Latent Representation Learning in Stable Diffusion Model](https://mlsanity.com/paper/2503.12536/) (2025)
- [Fairness Uncertainty Quantification: How certain are you that the model is fair?](https://mlsanity.com/paper/2304.13950/) (2023)
- [Fairness-Aware Grouping for Continuous Sensitive Variables: Application for Debiasing Face Analysis with respect to Skin Tone](https://mlsanity.com/paper/2507.11247/) (2025)
- [Quantum Fair Machine Learning](https://mlsanity.com/paper/2102.00753/) (2021)
- [Subgroup Fairness in Two-Sided Markets](https://mlsanity.com/paper/2106.02702/) (2021)
- [A survey of Identification and mitigation of Machine Learning algorithmic biases in Image Analysis](https://mlsanity.com/paper/2210.04491/) (2022)
- [Practical Approaches for Fair Learning with Multitype and Multivariate Sensitive Attributes](https://mlsanity.com/paper/2211.06138/) (2022)
- [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024)
- [When mitigating bias is unfair: multiplicity and arbitrariness in algorithmic group fairness](https://mlsanity.com/paper/2302.07185/) (2023)
- [Measuring and Mitigating Biases in Motor Insurance Pricing](https://mlsanity.com/paper/2311.11900/) (2023)
- [Debiasing Machine Learning Models by Using Weakly Supervised Learning](https://mlsanity.com/paper/2402.15477/) (2024)
- [When majority rules, minority loses: bias amplification of gradient descent](https://mlsanity.com/paper/2505.13122/) (2025)
- [Computability, Complexity, Consistency and Controllability: A Four C's Framework for cross-disciplinary Ethical Algorithm Research](https://mlsanity.com/paper/2102.04234/) (2021)
- [Assessing Perceived Fairness from Machine Learning Developer's Perspective](https://mlsanity.com/paper/2304.03745/) (2023)
- [Model-Agnostic Fairness Regularization for GNNs with Incomplete Sensitive Information](https://mlsanity.com/paper/2512.03074/) (2025)
- [FairBED: A Bayesian Experimental Design Approach to Gathering Fairer Data](https://mlsanity.com/paper/2606.23515/) (2026)

## Abstract (arXiv)

A review of the main fairness definitions and fair learning methodologies proposed in the literature over the last years is presented from a mathematical point of view. Following our independence-based approach, we consider how to build fair algorithms and the consequences on the degradation of their performance compared to the possibly unfair case. This corresponds to the price for fairness given by the criteria textitstatistical parity or textitequality of odds. Novel results giving the expressions of the optimal fair classifier and the optimal fair predictor (under a linear regression gaussian model) in the sense of textitequality of odds are presented.