# The KL-Divergence between a Graph Model and its Fair I-Projection as a Fairness Regularizer

arXiv: https://arxiv.org/abs/2103.01846 · HTML: https://mlsanity.com/paper/2103.01846/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 14 of 14)

- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [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)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Identifying and Correcting Label Bias in Machine Learning](https://mlsanity.com/paper/1901.04966/) (2019)
- [Compositional Fairness Constraints for Graph Embeddings](https://mlsanity.com/paper/1905.10674/) (2019)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [DeBayes: a Bayesian Method for Debiasing Network Embeddings](https://mlsanity.com/paper/2002.11442/) (2020)
- [The Fairness of Risk Scores Beyond Classification: Bipartite Ranking and the xAUC Metric](https://mlsanity.com/paper/1902.05826/) (2019)
- [All of the Fairness for Edge Prediction with Optimal Transport](https://mlsanity.com/paper/2010.16326/) (2020)
- [Conditional Network Embeddings](https://mlsanity.com/paper/1805.07544/) (2018)

## Built on by (most cited first, 17 of 17)

- [Fairness in Graph Mining: A Survey](https://mlsanity.com/paper/2204.09888/) (2022)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Fair Node Representation Learning via Adaptive Data Augmentation](https://mlsanity.com/paper/2201.08549/) (2022)
- [Fairness-Aware Graph Neural Networks: A Survey](https://mlsanity.com/paper/2307.03929/) (2023)
- [Fairness Amidst Non-IID Graph Data: A Literature Review](https://mlsanity.com/paper/2202.07170/) (2022)
- [A Survey on Fairness for Machine Learning on Graphs](https://mlsanity.com/paper/2205.05396/) (2022)
- [Optimal Transport of Classifiers to Fairness](https://mlsanity.com/paper/2202.03814/) (2022)
- [FairGAT: Fairness-aware Graph Attention Networks](https://mlsanity.com/paper/2303.14591/) (2023)
- [Graph Learning with Localized Neighborhood Fairness](https://mlsanity.com/paper/2212.12040/) (2022)
- [Fairness-Aware Graph Filter Design](https://mlsanity.com/paper/2303.11459/) (2023)
- [fairret: a Framework for Differentiable Fairness Regularization Terms](https://mlsanity.com/paper/2310.17256/) (2023)
- [FairWire: Fair Graph Generation](https://mlsanity.com/paper/2402.04383/) (2024)
- [FairNorm: Fair and Fast Graph Neural Network Training](https://mlsanity.com/paper/2205.09977/) (2022)
- [On Explaining Unfairness: An Overview](https://mlsanity.com/paper/2402.10762/) (2024)
- [Fairness-aware Optimal Graph Filter Design](https://mlsanity.com/paper/2310.14432/) (2023)
- [Debiasing Graph Representation Learning based on Information Bottleneck](https://mlsanity.com/paper/2409.01367/) (2024)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)

## Abstract (arXiv)

Learning and reasoning over graphs is increasingly done by means of probabilistic models, e.g. exponential random graph models, graph embedding models, and graph neural networks. When graphs are modeling relations between people, however, they will inevitably reflect biases, prejudices, and other forms of inequity and inequality. An important challenge is thus to design accurate graph modeling approaches while guaranteeing fairness according to the specific notion of fairness that the problem requires. Yet, past work on the topic remains scarce, is limited to debiasing specific graph modeling methods, and often aims to ensure fairness in an indirect manner. We propose a generic approach applicable to most probabilistic graph modeling approaches. Specifically, we first define the class of fair graph models corresponding to a chosen set of fairness criteria. Given this, we propose a fairness regularizer defined as the KL-divergence between the graph model and its I-projection onto the set of fair models. We demonstrate that using this fairness regularizer in combination with existing graph modeling approaches efficiently trades-off fairness with accuracy, whereas the state-of-the-art models can only make this trade-off for the fairness criterion that they were specifically designed for.