Fairness-Aware Estimation of Graphical Models

TL;DR

This approach involves the integration of the pairwise graph disparity error and a tailored loss function into a nonsmooth multi-objective optimization problem, striving to achieve fairness across different sensitive groups while maintaining the effectiveness of the GMs.

Abstract

This paper examines the issue of fairness in the estimation of graphical models (GMs), particularly Gaussian, Covariance, and Ising models. These models play a vital role in understanding complex relationships in high-dimensional data. However, standard GMs can result in biased outcomes, especially when the underlying data involves sensitive characteristics or protected groups. To address this, we introduce a comprehensive framework designed to reduce bias in the estimation of GMs related to protected attributes. Our approach involves the integration of the pairwise graph disparity error and a tailored loss function into a nonsmooth multi-objective optimization problem, striving to achieve fairness across different sensitive groups while maintaining the effectiveness of the GMs. Experimental evaluations on synthetic and real-world datasets demonstrate that our framework effectively mitigates bias without undermining GMs' performance.

Figures (20)

• Figure 1: Illustration of a GM and its fair variant. (a) displays the entire dataset, split into Group Blue (b) and Group Orange (c). (d) and (e) show GMs for each group, detailing the relationships between variables. (f) uses a GM for the entire dataset. The fair model in (g) adjusts these relationships to ensure equitable representation and minimize biases in subgroup analysis.
• Figure 2: GLasso $\hbox{\boldmath $\Theta$}_1$
• Figure 3: GLasso $\hbox{\boldmath $\Theta$}_2$
• Figure 4: CovGraph $\hbox{\boldmath $\Sigma$}_1$
• Figure 5: CovGraph $\hbox{\boldmath $\Sigma$}_2$

Theorems & Definitions (31)

• Definition 1: Graph Disparity Error
• Definition 2: Fair GM
• Definition 3: Pairwise Graph Disparity Error
• Definition 4: Pareto Optimality
• Definition 5: Pareto Stationary
• Theorem 6
• Theorem 7
• Theorem 8
• Remark 9: Iteration Complexity of Algorithm \ref{['alg:fairgms']}
• Remark 10: Computational Complexity of Algorithm \ref{['alg:fairgms']}