# Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior

arXiv: https://arxiv.org/abs/2406.09513 · HTML: https://mlsanity.com/paper/2406.09513/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 73 references that are in the map.
- First posted on arXiv 13 Jun 2024.

## Builds on (most cited first, 30 of 34)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Information](https://mlsanity.com/paper/2009.01454/) (2020)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Towards a Unified Framework for Fair and Stable Graph Representation Learning](https://mlsanity.com/paper/2102.13186/) (2021)
- [Compositional Fairness Constraints for Graph Embeddings](https://mlsanity.com/paper/1905.10674/) (2019)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [EDITS: Modeling and Mitigating Data Bias for Graph Neural Networks](https://mlsanity.com/paper/2108.05233/) (2021)
- [FairDrop: Biased Edge Dropout for Enhancing Fairness in Graph Representation Learning](https://mlsanity.com/paper/2104.14210/) (2021)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [DeBayes: a Bayesian Method for Debiasing Network Embeddings](https://mlsanity.com/paper/2002.11442/) (2020)
- [Learning Fair Representations for Recommendation: A Graph-based Perspective](https://mlsanity.com/paper/2102.09140/) (2021)
- [Uncovering the Structural Fairness in Graph Contrastive Learning](https://mlsanity.com/paper/2210.03011/) (2022)
- [Fair Node Representation Learning via Adaptive Data Augmentation](https://mlsanity.com/paper/2201.08549/) (2022)
- [Structured Graph Learning Via Laplacian Spectral Constraints](https://mlsanity.com/paper/1909.11594/) (2019)
- [Contact patterns among high school students](https://mlsanity.com/paper/1409.5318/) (2014)
- [Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting](https://mlsanity.com/paper/1711.00950/) (2017)
- [Joint Network Topology Inference in the Presence of Hidden Nodes](https://mlsanity.com/paper/2306.17364/) (2023)
- [Enhanced graph-learning schemes driven by similar distributions of motifs](https://mlsanity.com/paper/2207.04747/) (2022)
- [FairSNA: Algorithmic Fairness in Social Network Analysis](https://mlsanity.com/paper/2209.01678/) (2022)
- [Polynomial Graphical Lasso: Learning Edges from Gaussian Graph-Stationary Signals](https://mlsanity.com/paper/2404.02621/) (2024)
- [Optimization Methods for Sparse Pseudo-Likelihood Graphical Model Selection](https://mlsanity.com/paper/1409.3768/) (2014)
- [Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity](https://mlsanity.com/paper/1512.08643/) (2015)
- [FairWire: Fair Graph Generation](https://mlsanity.com/paper/2402.04383/) (2024)
- [Fair Community Detection and Structure Learning in Heterogeneous Graphical Models](https://mlsanity.com/paper/2112.05128/) (2021)
- [Learning Large-Scale MTP2 Gaussian Graphical Models via Bridge-Block Decomposition](https://mlsanity.com/paper/2309.13405/) (2023)
- [Mitigating Subpopulation Bias for Fair Network Topology Inference](https://mlsanity.com/paper/2403.15591/) (2024)
- [Joint graph learning from Gaussian observations in the presence of hidden nodes](https://mlsanity.com/paper/2212.01816/) (2022)
- [A Unified Framework for Fair Spectral Clustering With Effective Graph Learning](https://mlsanity.com/paper/2311.13766/) (2023)

## Built on by (most cited first, 10 of 10)

- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [Graph Guided Diffusion: Unified Guidance for Conditional Graph Generation](https://mlsanity.com/paper/2505.19685/) (2025)
- [Online Learning Of Expanding Graphs](https://mlsanity.com/paper/2409.08660/) (2024)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)
- [FAROS: Fair Graph Generation via Attribute Switching Mechanisms](https://mlsanity.com/paper/2507.03728/) (2025)
- [Adaptive Node Feature Selection For Graph Neural Networks](https://mlsanity.com/paper/2510.03096/) (2025)
- [Fair Minimum Labeling: Efficient Temporal Network Activations for Reachability and Equity](https://mlsanity.com/paper/2510.03899/) (2025)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes. Many real-world models exhibit unfair discriminatory behavior due to biases in data. Such discrimination is known to be exacerbated when data is equipped with pairwise relationships encoded in a graph. Additionally, the effect of biased data on graphical models is largely underexplored. We thus introduce fairness for graphical models in the form of two bias metrics to promote balance in statistical similarities across nodal groups with different sensitive attributes. Leveraging these metrics, we present Fair GLASSO, a regularized graphical lasso approach to obtain sparse Gaussian precision matrices with unbiased statistical dependencies across groups. We also propose an efficient proximal gradient algorithm to obtain the estimates. Theoretically, we express the tradeoff between fair and accurate estimated precision matrices. Critically, this includes demonstrating when accuracy can be preserved in the presence of a fairness regularizer. On top of this, we study the complexity of Fair GLASSO and demonstrate that our algorithm enjoys a fast convergence rate. Our empirical validation includes synthetic and real-world simulations that illustrate the value and effectiveness of our proposed optimization problem and iterative algorithm.