Tracking Switched Dynamic Network Topologies from Information Cascades

TL;DR

This paper introduces a switched dynamic structural equation model to track evolving network topologies from observable social signals, effectively capturing sudden changes in cascade propagation over time.

Contribution

It proposes a novel switched model for dynamic networks, establishes conditions for identifiability, and develops an efficient algorithm for joint topology and state tracking.

Findings

Successfully tracks network topology changes in synthetic data

Accurately detects discrete state transitions in real cascade data

Demonstrates robustness of the method over one-year real-world cascades

Abstract

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. Conditions under which the proposed switched model is identifiable are established. Leveraging the edge sparsity inherent to social networks, a recursive $\ell_1$-norm regularized least-squares estimator is put forth to jointly track the states and network topologies. An efficient first-order proximal-gradient algorithm is developed to solve the resulting optimization problem. Numerical experiments on both synthetic data and real cascades measured over the span of one year are conducted, and test results corroborate the efficacy of the advocated approach.