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Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior
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Proposes Fair GLASSO, a graphical lasso variant with convex group-fairness penalties (group-level H and node-level H_node) on precision matrix entries, solved by accelerated proximal gradient (FISTA), with error bounds and convergence analysis.
Problem
Estimating sparse Gaussian graphical models whose conditional dependence structure is free of bias with respect to sensitive node groups, when observations and underlying graphs may be biased.
Approach
Defines dyadic demographic parity for graphical models via two convex bias metrics on precision matrix entries (group-pair and node-wise) and adds them as regularizers to graphical lasso, solved with FISTA-style proximal gradient under a spectral constraint.
Key results
- On School and Friendship networks, FGL with mu_2=1e6 achieves low error (0.1449 and 0.0516) while reducing bias to 0.0308 and 0.0153 versus ground-truth biases of 0.2030 and 0.1487.
- On MovieLens, FGL with mu_2=1e6 is the only method achieving both low error (0.0248) and low bias (0.6106) relative to GL's error 0.0223 and bias 0.9529.
- For 1000-node ER graphs, FGL runs in about 1894 s versus 10226 s for graphical lasso, though GL is faster at p=50 (2.06 s vs 0.55 s for FGL).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply Fair GLASSO with H penalty (μ₂=1) instead of GL | GGM estimation · School | Error: 0.2661 -> 0.1417 | Helped |
| Apply Fair GLASSO with H penalty (μ₂=10⁶) instead of GL | GGM estimation · School | Bias: 0.3111 -> 0.0308 | Helped |
| Apply Fair GLASSO with H penalty (μ₂=1) instead of GL | GGM estimation · Co-authorship | Error: 0.1995 -> 0.1896 | Helped |
| Apply Fair GLASSO with H penalty (μ₂=10⁶) instead of GL | GGM estimation · Co-authorship | Bias: 12.6102 -> 0.1899 | Helped |
| Apply Fair GLASSO with H penalty (μ₂=10⁶) instead of GL | GGM estimation · MovieLens | Bias: 0.9529 -> 0.6106 | Helped |
| Apply Fair GLASSO with H penalty (μ₂=10⁶) instead of GL | GGM estimation · MovieLens | Error: 0.0223 -> 0.0248 | Hurt |
| Apply Fair GLASSO with H penalty (μ₂=1) instead of GL | GGM estimation · Friendship | Error: 0.6477 -> 0.0505 | Helped |
| Apply Fair GLASSO with H penalty (μ₂=10⁶) instead of GL | GGM estimation · Friendship | Bias: 0.4068 -> 0.0153 | Helped |
| Increase the H fairness penalty from μ₂=1 to μ₂=10⁶ (ablation) | FGL on School · School | Bias: 0.4824 -> 0.0308 | Helped |
| Increase the H fairness penalty from μ₂=1 to μ₂=10⁶ (ablation) | FGL on School · School | Error: 0.1417 -> 0.1449 | Hurt |
| Increase the H fairness penalty from μ₂=1 to μ₂=10⁶ (ablation) | FGL on Co-authorship · Co-authorship | Bias: 10.3317 -> 0.1899 | Helped |
| Increase the H fairness penalty from μ₂=1 to μ₂=10⁶ (ablation) | FGL on Co-authorship · Co-authorship | Error: 0.1896 -> 0.2432 | Hurt |
Surprising findings
- Fairness penalties sometimes reduce estimation error when the underlying graph is fair or the observations are biased, acting as informative structural priors.
- Running time comparisons show the proposed method is faster than classical graphical lasso at larger dimensions (p=1000) but the reported baseline timings are not uniformly favorable.
Limitations
- Theoretical guarantees rely on bounded sparsity, bounded spectrum, and equal group sizes assumptions.
- Fairness is defined for Gaussian graphical models and demographic parity; other fairness notions are only mentioned as extensions.
- Results on real-world data show a trade-off where strong fairness penalties can increase error in some datasets (e.g., NFGL on School and Co-authorship).
Experimental setup
Datasets: Zachary's karate club (synthetic Gaussian observations) High school contact/friendship network (School, Friendship) Co-authorship network MovieLens network Synthetic Erdos-Renyi graphs
Benchmarks: Karate club School Friendship Co-authorship MovieLens synthetic ER graphs
Metrics: estimation error (Frobenius norm) bias H running time
Baselines: GL (graphical lasso) FST (spectral templates, group-wise penalty) NFST (spectral templates, node-wise penalty) RWGL (randomly rewired graphical lasso)
Builds on: graphical lasso FISTA demographic parity spectral templates network inference
Closest papers by meaning
- Fairness-Aware Estimation of Graphical Models (NeurIPS 2024 · similarity 0.92)
- FairGP: A Scalable and Fair Graph Transformer Using Graph Partitioning (AAAI 2025 · similarity 0.85)
- Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach (ICLR 2024 · similarity 0.84)
- The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning (NeurIPS 2024 · similarity 0.84)
- FairSIN: Achieving Fairness in Graph Neural Networks through Sensitive Information Neutralization (AAAI 2024 · similarity 0.84)
- Who’s the (Multi-)Fairest of Them All: Rethinking Interpolation-Based Data Augmentation Through the Lens of Multicalibration (AAAI 2025 · similarity 0.84)
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