  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.
