# Fair Group-Shared Representations with Normalizing Flows

arXiv: https://arxiv.org/abs/2201.06336 · HTML: https://mlsanity.com/paper/2201.06336/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 15 of 15)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Controllable Invariance through Adversarial Feature Learning](https://mlsanity.com/paper/1705.11122/) (2017)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Measuring Fairness in Ranked Outputs](https://mlsanity.com/paper/1610.08559/) (2016)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows](https://mlsanity.com/paper/1905.12892/) (2019)
- [Provably Fair Representations](https://mlsanity.com/paper/1710.04394/) (2017)
- [FairSearch: A Tool For Fairness in Ranked Search Results](https://mlsanity.com/paper/1905.13134/) (2019)

## Built on by (most cited first, 5 of 5)

- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)
- [10 Years of Fair Representations: Challenges and Opportunities](https://mlsanity.com/paper/2407.03834/) (2024)
- [Mutatis Mutandis: Revisiting the Comparator in Discrimination Testing](https://mlsanity.com/paper/2405.13693/) (2024)
- [Learning Fair Representations with High-Confidence Guarantees](https://mlsanity.com/paper/2310.15358/) (2023)
- [Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inference](https://mlsanity.com/paper/2510.21017/) (2025)

## Abstract (arXiv)

The issue of fairness in machine learning stems from the fact that historical data often displays biases against specific groups of people which have been underprivileged in the recent past, or still are. In this context, one of the possible approaches is to employ fair representation learning algorithms which are able to remove biases from data, making groups statistically indistinguishable. In this paper, we instead develop a fair representation learning algorithm which is able to map individuals belonging to different groups in a single group. This is made possible by training a pair of Normalizing Flow models and constraining them to not remove information about the ground truth by training a ranking or classification model on top of them. The overall, ``chained'' model is invertible and has a tractable Jacobian, which allows to relate together the probability densities for different groups and ``translate'' individuals from one group to another. We show experimentally that our methodology is competitive with other fair representation learning algorithms. Furthermore, our algorithm achieves stronger invariance w.r.t. the sensitive attribute.