# Fair learning with Wasserstein barycenters for non-decomposable performance measures arXiv: https://arxiv.org/abs/2209.00427 ยท HTML: https://mlsanity.com/paper/2209.00427/ ## Key facts - Cited by 24 papers in the map (data through 14 Oct 2026). - Builds on 18 of its 62 references that are in the map. - First posted on arXiv 1 Sep 2022. ## Builds on (most cited first, 18 of 18) - [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016) - [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014) - [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018) - [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019) - [Classification with Fairness Constraints: A Meta-Algorithm with Provable Guarantees](https://mlsanity.com/paper/1806.06055/) (2018) - [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019) - [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020) - [Do the Machine Learning Models on a Crowd Sourced Platform Exhibit Bias? An Empirical Study on Model Fairness](https://mlsanity.com/paper/2005.12379/) (2020) - [Fair Preprocessing: Towards Understanding Compositional Fairness of Data Transformers in Machine Learning Pipeline](https://mlsanity.com/paper/2106.06054/) (2021) - [Classification with abstention but without disparities](https://mlsanity.com/paper/2102.12258/) (2021) - [Bayes-Optimal Classifiers under Group Fairness](https://mlsanity.com/paper/2202.09724/) (2022) - [General Fair Empirical Risk Minimization](https://mlsanity.com/paper/1901.10080/) (2019) - [Optimizing Non-decomposable Performance Measures: A Tale of Two Classes](https://mlsanity.com/paper/1505.06812/) (2015) - [Surrogate regret bounds for generalized classification performance metrics](https://mlsanity.com/paper/1504.07272/) (2015) - [Binary Classification with Karmic, Threshold-Quasi-Concave Metrics](https://mlsanity.com/paper/1806.00640/) (2018) - [Fairness with Continuous Optimal Transport](https://mlsanity.com/paper/2101.02084/) (2021) - [Towards A Holistic View of Bias in Machine Learning: Bridging Algorithmic Fairness and Imbalanced Learning](https://mlsanity.com/paper/2207.06084/) (2022) - [An example of prediction which complies with Demographic Parity and equalizes group-wise risks in the context of regression](https://mlsanity.com/paper/2011.07158/) (2020) ## Built on by (most cited first, 24 of 24) - [Fair and Optimal Classification via Post-Processing](https://mlsanity.com/paper/2211.01528/) (2022) - [Fairness in Multi-Task Learning via Wasserstein Barycenters](https://mlsanity.com/paper/2306.10155/) (2023) - [Post-hoc Bias Scoring Is Optimal For Fair Classification](https://mlsanity.com/paper/2310.05725/) (2023) - [A Sequentially Fair Mechanism for Multiple Sensitive Attributes](https://mlsanity.com/paper/2309.06627/) (2023) - [Fair Wasserstein Coresets](https://mlsanity.com/paper/2311.05436/) (2023) - [Regression under demographic parity constraints via unlabeled post-processing](https://mlsanity.com/paper/2407.15453/) (2024) - [Parametric Fairness with Statistical Guarantees](https://mlsanity.com/paper/2310.20508/) (2023) - [Multi-Output Distributional Fairness via Post-Processing](https://mlsanity.com/paper/2409.00553/) (2024) - [Demographic parity in regression and classification within the unawareness framework](https://mlsanity.com/paper/2409.02471/) (2024) - [Learning with Differentially Private (Sliced) Wasserstein Gradients](https://mlsanity.com/paper/2502.01701/) (2025) - [The Cost of Local and Global Fairness in Federated Learning](https://mlsanity.com/paper/2503.22762/) (2025) - [When majority rules, minority loses: bias amplification of gradient descent](https://mlsanity.com/paper/2505.13122/) (2025) - [Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decomposition](https://mlsanity.com/paper/2507.19627/) (2025) - [Randomized multi-class classification under system constraints: a unified approach via post-processing](https://mlsanity.com/paper/2512.14246/) (2025) - [AIFS-SUBS: Extending Data-Driven Forecasting to Sub-Seasonal Timescales](https://mlsanity.com/paper/2607.05100/) (2026) - [Fairness Explainability using Optimal Transport with Applications in Image Classification](https://mlsanity.com/paper/2308.11090/) (2023) - [EquiPy: Sequential Fairness using Optimal Transport in Python](https://mlsanity.com/paper/2503.09866/) (2025) - [Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learning](https://mlsanity.com/paper/2509.10132/) (2025) - [Set to Be Fair: Demographic Parity Constraints for Set-Valued Classification](https://mlsanity.com/paper/2510.04926/) (2025) - [Toward Unifying Group Fairness Evaluation from a Sparsity Perspective](https://mlsanity.com/paper/2511.00359/) (2025) - [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026) - [Demographic Parity Tails for Regression](https://mlsanity.com/paper/2604.02017/) (2026) - [Geometry of Relaxed Fair Regression: A Unified Framework for Aware and Unaware Settings](https://mlsanity.com/paper/2605.28233/) (2026) - [A Comprehensive View of Fairness through Distributional Stability](https://mlsanity.com/paper/2609.37061/) (2026) ## Abstract (arXiv) This work provides several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, akin to the classical unconstrained classification case, we show that maximizing accuracy under this fairness constraint is equivalent to solving a corresponding regression problem followed by thresholding at level 1/2. We extend this result to linear-fractional classification measures (e.g., rm F-score, AM measure, balanced accuracy, etc.), highlighting the fundamental role played by the regression problem in this framework. Our results leverage recently developed connection between the demographic parity constraint and the multi-marginal optimal transport formulation. Informally, our result shows that the transition between the unconstrained problems and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Finally, leveraging our analysis, we demonstrate an equivalence between the awareness and the unawareness setups in the case of two sensitive groups.