Switched dynamic structural equation models for tracking social network topologies

Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are measurable, and implicitly depend on the underlying topology, making it possible to track it over time. Interestingly, network topologies often "jump" between discrete states that may account for sudden changes in the observed signals. The present paper advocates a switched dynamic structural equation model to capture the topology-dependent cascade evolution, as well as the discrete states driving the underlying topologies. Leveraging the edge sparsity inherent to social networks, a recursive ℓ₁-norm regularized least-squares estimator is put forth to jointly track the states and network topologies. A first-order proximal-gradient algorithm is developed to solve the resulting optimization problem, and numerical tests on synthetic data corroborate its efficacy.