Dynamic Structural Equation Models for Social Network Topology Inference

TL;DR

This paper introduces dynamic structural equation models to infer evolving social network topologies from observed adoption times, employing sparsity regularization and efficient algorithms, validated on synthetic and real data including political event cascades.

Contribution

It proposes a novel dynamic SEM framework with sparsity regularization and develops efficient solvers for real-time topology inference in social networks.

Findings

Effective in unveiling sparse, evolving network topologies

Algorithms perform well on synthetic and real data

Captures external influences on adoption times

Abstract

Many real-world processes evolve in cascades over complex networks, whose topologies are often unobservable and change over time. However, the so-termed adoption times when blogs mention popular news items, individuals in a community catch an infectious disease, or consumers adopt a trendy electronics product are typically known, and are implicitly dependent on the underlying network. To infer the network topology, a \textit{dynamic} structural equation model is adopted to capture the relationship between observed adoption times and the unknown edge weights. Assuming a slowly time-varying topology and leveraging the sparse connectivity inherent to social networks, edge weights are estimated by minimizing a sparsity-regularized exponentially-weighted least-squares criterion. To this end, solvers with complementary strengths are developed by leveraging (pseudo) real-time sparsity-promoting proximal gradient iterations, the improved convergence rate of accelerated variants, or reduced computational complexity of stochastic gradient descent. Numerical tests with both synthetic and real data demonstrate the effectiveness of the novel algorithms in unveiling sparse dynamically-evolving topologies, while accounting for external influences in the adoption times. Key events in the recent succession of political leadership in North Korea, explain connectivity changes observed in the associated network inferred from global cascades of online media.