Learning shared and individual structure in dynamic networks with degree heterogeneity

Dynamic networks provide a powerful framework for analysing connectivity data in many fields such as social science, finance or neuroscience (e.g. along neuroimaging studies). In practice, such networks are typically collected from multiple subjects across time and exhibit both temporal dynamics and subject-specific heterogeneity. Ample connectivity networks also contain hub nodes, defined as highly connected regions that play critical roles. In this work, we propose a mixed-effects dynamic stochastic block model with degree heterogeneity, which simultaneously disentangles the shared connectivity structure from individual variability and recovers the trajectories of hub regions through time-varying degree parameters. We develop an efficient local approximate estimation procedure and evaluate its performance through extensive simulations and a case study from the Human Connectome Project focusing on dynamic functional connectivity.