# Optimal Transport of Classifiers to Fairness

arXiv: https://arxiv.org/abs/2202.03814 · HTML: https://mlsanity.com/paper/2202.03814/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 8 Feb 2022.

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

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [A survey on datasets for fairness-aware machine learning](https://mlsanity.com/paper/2110.00530/) (2021)
- [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [FNNC: Achieving Fairness through Neural Networks](https://mlsanity.com/paper/1811.00247/) (2018)
- [A Statistical Test for Probabilistic Fairness](https://mlsanity.com/paper/2012.04800/) (2020)
- [Testing Group Fairness via Optimal Transport Projections](https://mlsanity.com/paper/2106.01070/) (2021)
- [The KL-Divergence between a Graph Model and its Fair I-Projection as a Fairness Regularizer](https://mlsanity.com/paper/2103.01846/) (2021)

## Built on by (most cited first, 12 of 12)

- [FFB: A Fair Fairness Benchmark for In-Processing Group Fairness Methods](https://mlsanity.com/paper/2306.09468/) (2023)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [fairret: a Framework for Differentiable Fairness Regularization Terms](https://mlsanity.com/paper/2310.17256/) (2023)
- [Robust ML Auditing using Prior Knowledge](https://mlsanity.com/paper/2505.04796/) (2025)
- [Group-blind optimal transport to group parity and its constrained variants](https://mlsanity.com/paper/2310.11407/) (2023)
- [Mitigating Source Bias for Fairer Weak Supervision](https://mlsanity.com/paper/2303.17713/) (2023)
- [AdapFair: Ensuring Adaptive Fairness for Machine Learning Operations](https://mlsanity.com/paper/2409.15088/) (2024)
- [Fairness-aware Anomaly Detection via Fair Projection](https://mlsanity.com/paper/2505.11132/) (2025)
- [A Critical Review of Predominant Bias in Neural Networks](https://mlsanity.com/paper/2502.11031/) (2025)
- [FairPOT: Balancing AUC Performance and Fairness with Proportional Optimal Transport](https://mlsanity.com/paper/2508.03940/) (2025)
- [New Algorithmic Directions in Optimal Transport and Applications for Product Spaces](https://mlsanity.com/paper/2509.21502/) (2025)
- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)

## Abstract (arXiv)

In past work on fairness in machine learning, the focus has been on forcing the prediction of classifiers to have similar statistical properties for people of different demographics. To reduce the violation of these properties, fairness methods usually simply rescale the classifier scores, ignoring similarities and dissimilarities between members of different groups. Yet, we hypothesize that such information is relevant in quantifying the unfairness of a given classifier. To validate this hypothesis, we introduce Optimal Transport to Fairness (OTF), a method that quantifies the violation of fairness constraints as the smallest Optimal Transport cost between a probabilistic classifier and any score function that satisfies these constraints. For a flexible class of linear fairness constraints, we construct a practical way to compute OTF as a differentiable fairness regularizer that can be added to any standard classification setting. Experiments show that OTF can be used to achieve an improved trade-off between predictive power and fairness.