# Multi-Output Distributional Fairness via Post-Processing

arXiv: https://arxiv.org/abs/2409.00553 · HTML: https://mlsanity.com/paper/2409.00553/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 79 references that are in the map.
- First posted on arXiv 31 Aug 2024.

## Builds on (most cited first, 30 of 52)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Learning Not to Learn: Training Deep Neural Networks with Biased Data](https://mlsanity.com/paper/1812.10352/) (2018)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Data Decisions and Theoretical Implications when Adversarially Learning Fair Representations](https://mlsanity.com/paper/1707.00075/) (2017)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Fair Attribute Classification through Latent Space De-biasing](https://mlsanity.com/paper/2012.01469/) (2020)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Automated Experiments on Ad Privacy Settings: A Tale of Opacity, Choice, and Discrimination](https://mlsanity.com/paper/1408.6491/) (2014)
- [Fairness by Learning Orthogonal Disentangled Representations](https://mlsanity.com/paper/2003.05707/) (2020)
- [Bias Mitigation Post-processing for Individual and Group Fairness](https://mlsanity.com/paper/1812.06135/) (2018)
- [Fair Contrastive Learning for Facial Attribute Classification](https://mlsanity.com/paper/2203.16209/) (2022)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [Fairness via Representation Neutralization](https://mlsanity.com/paper/2106.12674/) (2021)
- [Post-processing for Individual Fairness](https://mlsanity.com/paper/2110.13796/) (2021)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)

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

- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)
- [Demystifying the Optimal Fair Classifier in Multi-Class Classification](https://mlsanity.com/paper/2606.00656/) (2026)

## Abstract (arXiv)

The post-processing approaches are becoming prominent techniques to enhance machine learning models' fairness because of their intuitiveness, low computational cost, and excellent scalability. However, most existing post-processing methods are designed for task-specific fairness measures and are limited to single-output models. In this paper, we introduce a post-processing method for multi-output models, such as the ones used for multi-task/multi-class classification and representation learning, to enhance a model's distributional parity, a task-agnostic fairness measure. Existing methods for achieving distributional parity rely on the (inverse) cumulative density function of a model's output, restricting their applicability to single-output models. Extending previous works, we propose to employ optimal transport mappings to move a model's outputs across different groups towards their empirical Wasserstein barycenter. An approximation technique is applied to reduce the complexity of computing the exact barycenter and a kernel regression method is proposed to extend this process to out-of-sample data. Our empirical studies evaluate the proposed approach against various baselines on multi-task/multi-class classification and representation learning tasks, demonstrating the effectiveness of the proposed approach.