Inference of Edge Correlations in Multilayer Networks
This work addresses the challenge of modeling correlated interactions in multilayer networks, which is incremental as it builds upon existing stochastic block models by adding correlation features.
The paper tackles the problem of inferring community structure in multilayer networks by relaxing the common assumption of independent edges across layers, incorporating edge correlations into a stochastic block model. The result is improved prediction accuracy in both synthetic networks and a real-world temporal network of shoppers and grocery products.
Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent type of method for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but {potentially} inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between connectivity patterns in different layers. Finally, we explain how to use correlated models for edge "prediction" (i.e., inference) in multilayer networks. By taking into account edge correlations, prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously-purchased grocery products.