The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks

Networks and graphs, which consist of objects of interest and a vast array of possible relationships between them, arise very naturally in fields as diverse as political science (party affiliations among voters); bioinformatics (gene interactions); physics (dimer systems); and sociology (social network analysis), to name but a few. As such, they are a useful data structure for modeling complex interactions between different experimental entities. Network data, however, is qualitatively distinct from more traditional Euclidean data, and statistical inference on networks is a comparatively new discipline, one that has seen explosive growth over the last two decades. While there is a significant literature devoted to the rigorous statistical study of single networks, multiple network inference-- the analogue of the classical problem of multiple-sample Euclidean inference--is still relatively nascent. Much recent progress in network inference has relied on extracting Euclidean representations of networks, and popular methods include spectral embeddings of network adjacency [3] or Laplacian [45] matrices, representation learning [20, 44], or Bayesian hierarchical methods [16].