Mutual Information in Community Detection with Covariate Information and Correlated Networks
This work addresses community detection in networks with additional data sources, but it appears incremental as it builds on existing theoretical frameworks without claiming broad practical breakthroughs.
The authors tackled the problem of community detection by incorporating covariate information and multiple correlated networks, deriving an asymptotic upper bound on per-node mutual information and analyzing a multivariate performance measure to characterize the combined effects of these information types in terms of low-dimensional Gaussian noise estimation problems.
We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a heuristic analysis of a multivariate performance measure called the MMSE matrix. These results show that the combined effects of seemingly very different types of information can be characterized explicitly in terms of formulas involving low-dimensional estimation problems in additive Gaussian noise. Our analysis is supported by numerical simulations.