# Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metrics

arXiv: https://arxiv.org/abs/2505.06435 · HTML: https://mlsanity.com/paper/2505.06435/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 72 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 30 of 38)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Mitigating Unwanted Biases with Adversarial Learning](https://mlsanity.com/paper/1801.07593/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [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)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [The Variational Fair Autoencoder](https://mlsanity.com/paper/1511.00830/) (2015)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Censoring Representations with an Adversary](https://mlsanity.com/paper/1511.05897/) (2015)
- [FairGAN: Fairness-aware Generative Adversarial Networks](https://mlsanity.com/paper/1805.11202/) (2018)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Learning Controllable Fair Representations](https://mlsanity.com/paper/1812.04218/) (2018)
- [Fairness by Learning Orthogonal Disentangled Representations](https://mlsanity.com/paper/2003.05707/) (2020)
- [Learning Certified Individually Fair Representations](https://mlsanity.com/paper/2002.10312/) (2020)
- [Satisfying Real-world Goals with Dataset Constraints](https://mlsanity.com/paper/1606.07558/) (2016)
- [Controllable Guarantees for Fair Outcomes via Contrastive Information Estimation](https://mlsanity.com/paper/2101.04108/) (2021)
- [Learning Fair Representation via Distributional Contrastive Disentanglement](https://mlsanity.com/paper/2206.08743/) (2022)
- [Learning Fair Representations via an Adversarial Framework](https://mlsanity.com/paper/1904.13341/) (2019)
- [Fair Representation Learning for Heterogeneous Information Networks](https://mlsanity.com/paper/2104.08769/) (2021)
- [Fair Representation Learning through Implicit Path Alignment](https://mlsanity.com/paper/2205.13316/) (2022)
- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)
- [Learning fair representation with a parametric integral probability metric](https://mlsanity.com/paper/2202.02943/) (2022)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [Distributional Robustness with IPMs and links to Regularization and GANs](https://mlsanity.com/paper/2006.04349/) (2020)

## Built on by (most cited first, 7 of 7)

- [On the geometry and topology of representations: the manifolds of modular addition](https://mlsanity.com/paper/2512.25060/) (2025)
- [Doubly-Regressing Approach for Subgroup Fairness](https://mlsanity.com/paper/2510.21091/) (2025)
- [AIFS-SUBS: Extending Data-Driven Forecasting to Sub-Seasonal Timescales](https://mlsanity.com/paper/2607.05100/) (2026)
- [Kernel-based Equalized Odds: A Quantification of Accuracy-Fairness Trade-off in Fair Representation Learning](https://mlsanity.com/paper/2508.15084/) (2025)
- [Extending Fair Null-Space Projections for Continuous Attributes to Kernel Methods](https://mlsanity.com/paper/2511.03304/) (2025)
- [A nonparametric two-sample test using a parametric integral probability metric](https://mlsanity.com/paper/2606.16941/) (2026)
- [A Joint-Distribution Route to Fair Representations with Continuous Sensitive Attributes](https://mlsanity.com/paper/2608.10470/) (2026)

## Abstract (arXiv)

AI fairness, also known as algorithmic fairness, aims to ensure that algorithms operate without bias or discrimination towards any individual or group. Among various AI algorithms, the Fair Representation Learning (FRL) approach has gained significant interest in recent years. However, existing FRL algorithms have a limitation: they are primarily designed for categorical sensitive attributes and thus cannot be applied to continuous sensitive attributes, such as age or income. In this paper, we propose an FRL algorithm for continuous sensitive attributes. First, we introduce a measure called the Expectation of Integral Probability Metrics (EIPM) to assess the fairness level of representation space for continuous sensitive attributes. We demonstrate that if the distribution of the representation has a low EIPM value, then any prediction head constructed on the top of the representation become fair, regardless of the selection of the prediction head. Furthermore, EIPM possesses a distinguished advantage in that it can be accurately estimated using our proposed estimator with finite samples. Based on these properties, we propose a new FRL algorithm called Fair Representation using EIPM with MMD (FREM). Experimental evidences show that FREM outperforms other baseline methods.