# Bounding and Approximating Intersectional Fairness through Marginal Fairness

arXiv: https://arxiv.org/abs/2206.05828 · HTML: https://mlsanity.com/paper/2206.05828/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 38 references that are in the map.
- First posted on arXiv 12 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Fair prediction with disparate impact: A study of bias in recidivism prediction instruments](https://mlsanity.com/paper/1610.07524/) (2016)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Minimax Pareto Fairness: A Multi Objective Perspective](https://mlsanity.com/paper/2011.01821/) (2020)
- [An Intersectional Definition of Fairness](https://mlsanity.com/paper/1807.08362/) (2018)
- [An Empirical Study of Rich Subgroup Fairness for Machine Learning](https://mlsanity.com/paper/1808.08166/) (2018)
- [Achieving Equalized Odds by Resampling Sensitive Attributes](https://mlsanity.com/paper/2006.04292/) (2020)
- [Can I Trust My Fairness Metric? Assessing Fairness with Unlabeled Data and Bayesian Inference](https://mlsanity.com/paper/2010.09851/) (2020)
- [Assessing Fairness in the Presence of Missing Data](https://mlsanity.com/paper/2112.04899/) (2021)
- [Bayesian Modeling of Intersectional Fairness: The Variance of Bias](https://mlsanity.com/paper/1811.07255/) (2018)

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

- [A Survey on Intersectional Fairness in Machine Learning: Notions, Mitigation, and Challenges](https://mlsanity.com/paper/2305.06969/) (2023)
- [Factoring the Matrix of Domination: A Critical Review and Reimagination of Intersectionality in AI Fairness](https://mlsanity.com/paper/2303.17555/) (2023)
- [A structured regression approach for evaluating model performance across intersectional subgroups](https://mlsanity.com/paper/2401.14893/) (2024)
- [The Intersectionality Problem for Algorithmic Fairness](https://mlsanity.com/paper/2411.02569/) (2024)
- [Machine Learning with Multitype Protected Attributes: Intersectional Fairness through Regularisation](https://mlsanity.com/paper/2509.08163/) (2025)
- [Trading-off price for data quality to achieve fair online allocation](https://mlsanity.com/paper/2306.13440/) (2023)
- [Size-adaptive Hypothesis Testing for Fairness](https://mlsanity.com/paper/2506.10586/) (2025)
- [Doubly-Regressing Approach for Subgroup Fairness](https://mlsanity.com/paper/2510.21091/) (2025)
- [Intersectional Fairness via Mixed-Integer Optimization](https://mlsanity.com/paper/2601.19595/) (2026)
- [COVAriance-Induced Fairness Gap Penalty for Subgroup-Fair Clustering](https://mlsanity.com/paper/2607.18119/) (2026)
- [Identifying Harm in Personalized, Generative AI Systems Requires User-Centered Auditing at the Interaction Level](https://mlsanity.com/paper/2608.14692/) (2026)

## Abstract (arXiv)

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure intersectional fairness -- i.e., that no subgroup is discriminated against. It is known that ensuring marginal fairness for every dimension independently is not sufficient in general. Due to the exponential number of subgroups, however, directly measuring intersectional fairness from data is impossible. In this paper, our primary goal is to understand in detail the relationship between marginal and intersectional fairness through statistical analysis. We first identify a set of sufficient conditions under which an exact relationship can be obtained. Then, we prove bounds (easily computable through marginal fairness and other meaningful statistical quantities) in high-probability on intersectional fairness in the general case. Beyond their descriptive value, we show that these theoretical bounds can be leveraged to derive a heuristic improving the approximation and bounds of intersectional fairness by choosing, in a relevant manner, protected attributes for which we describe intersectional subgroups. Finally, we test the performance of our approximations and bounds on real and synthetic data-sets.