Fair Community Detection and Structure Learning in Heterogeneous Graphical Models
This addresses fairness in community detection for heterogeneous graphical models, which is an incremental improvement by incorporating demographic constraints into existing methods.
The paper tackles the problem of community detection in probabilistic graphical models being inconsistent with fairness constraints regarding demographic attributes, proposing a novel $\ell_1$-regularized pseudo-likelihood method to learn sparse graphs and communities that fairly represent demographic groups. It establishes statistical consistency for Gaussian and Ising models, proving recovery of graphs and fair communities with high probability.
Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and under-represented in others. This paper defines a novel $\ell_1$-regularized pseudo-likelihood approach for fair graphical model selection. In particular, we assume there is some community or clustering structure in the true underlying graph, and we seek to learn a sparse undirected graph and its communities from the data such that demographic groups are fairly represented within the communities. In the case when the graph is known a priori, we provide a convex semidefinite programming approach for fair community detection. We establish the statistical consistency of the proposed method for both a Gaussian graphical model and an Ising model for, respectively, continuous and binary data, proving that our method can recover the graphs and their fair communities with high probability.