# Learning fair representation with a parametric integral probability metric

arXiv: https://arxiv.org/abs/2202.02943 · HTML: https://mlsanity.com/paper/2202.02943/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 7 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [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)
- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [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)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Learning Adversarially Fair and Transferable Representations](https://mlsanity.com/paper/1802.06309/) (2018)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [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)
- [Path-Specific Counterfactual Fairness](https://mlsanity.com/paper/1802.08139/) (2018)
- [FairGAN: Fairness-aware Generative Adversarial Networks](https://mlsanity.com/paper/1805.11202/) (2018)
- [Counterfactual Fairness in Text Classification through Robustness](https://mlsanity.com/paper/1809.10610/) (2018)
- [Algorithmic Fairness](https://mlsanity.com/paper/2001.09784/) (2020)
- [Fair Mixup: Fairness via Interpolation](https://mlsanity.com/paper/2103.06503/) (2021)
- [Learning Certified Individually Fair Representations](https://mlsanity.com/paper/2002.10312/) (2020)
- [Two Simple Ways to Learn Individual Fairness Metrics from Data](https://mlsanity.com/paper/2006.11439/) (2020)
- [Average Individual Fairness: Algorithms, Generalization and Experiments](https://mlsanity.com/paper/1905.10607/) (2019)
- [Probably Approximately Metric-Fair Learning](https://mlsanity.com/paper/1803.03242/) (2018)
- [Fair Representation Learning for Heterogeneous Information Networks](https://mlsanity.com/paper/2104.08769/) (2021)
- [A Characteristic Function Approach to Deep Implicit Generative Modeling](https://mlsanity.com/paper/1909.07425/) (2019)
- [Algorithmic Decision Making with Conditional Fairness](https://mlsanity.com/paper/2006.10483/) (2020)
- [Learning Smooth and Fair Representations](https://mlsanity.com/paper/2006.08788/) (2020)

## Built on by (most cited first, 20 of 20)

- [FARE: Provably Fair Representation Learning with Practical Certificates](https://mlsanity.com/paper/2210.07213/) (2022)
- [MMD-B-Fair: Learning Fair Representations with Statistical Testing](https://mlsanity.com/paper/2211.07907/) (2022)
- [Covariate balancing using the integral probability metric for causal inference](https://mlsanity.com/paper/2305.13715/) (2023)
- [The Representation Jensen-Shannon Divergence](https://mlsanity.com/paper/2305.16446/) (2023)
- [SF-PATE: Scalable, Fair, and Private Aggregation of Teacher Ensembles](https://mlsanity.com/paper/2204.05157/) (2022)
- [Toward Operationalizing Pipeline-aware ML Fairness: A Research Agenda for Developing Practical Guidelines and Tools](https://mlsanity.com/paper/2309.17337/) (2023)
- [Fair Representation Learning for Continuous Sensitive Attributes using Expectation of Integral Probability Metrics](https://mlsanity.com/paper/2505.06435/) (2025)
- [Achieving Group Fairness through Independence in Predictive Process Monitoring](https://mlsanity.com/paper/2412.04914/) (2024)
- [Hoeffding's Inequality for Markov Chains under Generalized Concentrability Condition](https://mlsanity.com/paper/2310.02941/) (2023)
- [Efficient Fairness-Performance Pareto Front Computation](https://mlsanity.com/paper/2409.17643/) (2024)
- [Learning Fair Representations with High-Confidence Guarantees](https://mlsanity.com/paper/2310.15358/) (2023)
- [ReLU integral probability metric and its applications](https://mlsanity.com/paper/2504.18897/) (2025)
- [SoK: Data Minimization in Machine Learning](https://mlsanity.com/paper/2508.10836/) (2025)
- [Doubly-Regressing Approach for Subgroup Fairness](https://mlsanity.com/paper/2510.21091/) (2025)
- [Back to the Drawing Board for Fair Representation Learning](https://mlsanity.com/paper/2405.18161/) (2024)
- [FedFACT: A Provable Framework for Controllable Group-Fairness Calibration in Federated Learning](https://mlsanity.com/paper/2506.03777/) (2025)
- [Kernel-based Equalized Odds: A Quantification of Accuracy-Fairness Trade-off in Fair Representation Learning](https://mlsanity.com/paper/2508.15084/) (2025)
- [Fair Representation Learning with Controllable High Confidence Guarantees via Adversarial Inference](https://mlsanity.com/paper/2510.21017/) (2025)
- [Demystifying the Optimal Fair Classifier in Multi-Class Classification](https://mlsanity.com/paper/2606.00656/) (2026)
- [A nonparametric two-sample test using a parametric integral probability metric](https://mlsanity.com/paper/2606.16941/) (2026)

## Abstract (arXiv)

As they have a vital effect on social decision-making, AI algorithms should be not only accurate but also fair. Among various algorithms for fairness AI, learning fair representation (LFR), whose goal is to find a fair representation with respect to sensitive variables such as gender and race, has received much attention. For LFR, the adversarial training scheme is popularly employed as is done in the generative adversarial network type algorithms. The choice of a discriminator, however, is done heuristically without justification. In this paper, we propose a new adversarial training scheme for LFR, where the integral probability metric (IPM) with a specific parametric family of discriminators is used. The most notable result of the proposed LFR algorithm is its theoretical guarantee about the fairness of the final prediction model, which has not been considered yet. That is, we derive theoretical relations between the fairness of representation and the fairness of the prediction model built on the top of the representation (i.e., using the representation as the input). Moreover, by numerical experiments, we show that our proposed LFR algorithm is computationally lighter and more stable, and the final prediction model is competitive or superior to other LFR algorithms using more complex discriminators.