2 research outputs found
Fair Community Detection and Structure Learning in Heterogeneous Graphical Models
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 -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
Community-Based Group Graphical Lasso
A new strategy for probabilistic graphical modeling is developed that draws parallels to community detection analysis. The method jointly estimates an undirected graph and homogenous communities of nodes. The structure of the communities is taken into account when estimating the graph and at the same time, the structure of the graph is accounted for when estimating communities of nodes. The procedure uses a joint group graphical lasso approach with community detection-based grouping, such that some groups of edges co-occur in the estimated graph. The grouping structure is unknown and is estimated based on community detection algorithms. Theoretical derivations regarding graph convergence and sparsistency, as well as accuracy of community recovery are included, while the method's empirical performance is illustrated in an fMRI context, as well as with simulated examples