# Fair Community Detection and Structure Learning in Heterogeneous Graphical Models

arXiv: https://arxiv.org/abs/2112.05128 · HTML: https://mlsanity.com/paper/2112.05128/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2021.

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

- [Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior](https://mlsanity.com/paper/2406.09513/) (2024)
- [Query-Aware Flow Diffusion for Graph-Based RAG with Retrieval Guarantees](https://mlsanity.com/paper/2605.18775/) (2026)
- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [A Unified Framework for Fair Spectral Clustering With Effective Graph Learning](https://mlsanity.com/paper/2311.13766/) (2023)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)

## Abstract (arXiv)

Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and under-represented in others. This paper defines a novel ℓ1-regularized pseudo-likelihood approach for fair graphical model selection. In particular, we assume there is some community or clustering structure in the true underlying graph, and we seek to learn a sparse undirected graph and its communities from the data such that demographic groups are fairly represented within the communities. In the case when the graph is known a priori, we provide a convex semidefinite programming approach for fair community detection. We establish the statistical consistency of the proposed method for both a Gaussian graphical model and an Ising model for, respectively, continuous and binary data, proving that our method can recover the graphs and their fair communities with high probability.