# Everything is Relative: Understanding Fairness with Optimal Transport

arXiv: https://arxiv.org/abs/2102.10349 · HTML: https://mlsanity.com/paper/2102.10349/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [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)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [The Frontiers of Fairness in Machine Learning](https://mlsanity.com/paper/1810.08810/) (2018)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Towards a Critical Race Methodology in Algorithmic Fairness](https://mlsanity.com/paper/1912.03593/) (2019)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [Equalizing Recourse across Groups](https://mlsanity.com/paper/1909.03166/) (2019)
- [FlipTest: Fairness Testing via Optimal Transport](https://mlsanity.com/paper/1906.09218/) (2019)
- [Fair Classification and Social Welfare](https://mlsanity.com/paper/1905.00147/) (2019)
- [A Statistical Test for Probabilistic Fairness](https://mlsanity.com/paper/2012.04800/) (2020)
- [Auditing ML Models for Individual Bias and Unfairness](https://mlsanity.com/paper/2003.05048/) (2020)
- [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021)
- [Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses](https://mlsanity.com/paper/2009.07165/) (2020)

## Built on by (most cited first, 2 of 2)

- [How Gender Debiasing Affects Internal Model Representations, and Why It Matters](https://mlsanity.com/paper/2204.06827/) (2022)
- [Standardized Interpretable Fairness Measures for Continuous Risk Scores](https://mlsanity.com/paper/2308.11375/) (2023)

## Abstract (arXiv)

To study discrimination in automated decision-making systems, scholars have proposed several definitions of fairness, each expressing a different fair ideal. These definitions require practitioners to make complex decisions regarding which notion to employ and are often difficult to use in practice since they make a binary judgement a system is fair or unfair instead of explaining the structure of the detected unfairness. We present an optimal transport-based approach to fairness that offers an interpretable and quantifiable exploration of bias and its structure by comparing a pair of outcomes to one another. In this work, we use the optimal transport map to examine individual, subgroup, and group fairness. Our framework is able to recover well known examples of algorithmic discrimination, detect unfairness when other metrics fail, and explore recourse opportunities.