Fair GLASSO: Estimating Fair Graphical Models with Unbiased Statistical Behavior

TL;DR

This paper introduces Fair GLASSO, a method for estimating Gaussian graphical models that incorporates fairness constraints to reduce bias across sensitive groups, ensuring more equitable statistical dependencies.

Contribution

The paper presents a novel fairness regularizer for graphical models, an efficient proximal gradient algorithm, and theoretical analysis of the fairness-accuracy tradeoff.

Findings

Fair GLASSO achieves unbiased statistical dependencies across groups.

The algorithm converges rapidly and scales well to large problems.

Empirical results demonstrate improved fairness without sacrificing accuracy.

Abstract

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.