Uncovering the Temporal Dynamics of Diffusion Networks

TLDR

Time is a critical factor in the spread of information, influence, and disease across networks, yet often only node events are observed while connectivity, transmission rates, and sources remain unknown, making the inference of underlying dynamics essential for forecasting, influencing, and mitigating infections. The study aims to model diffusion processes as discrete networks of continuous temporal processes occurring at different rates. Using cascade data of node infection times, the authors infer the global diffusion network edges and estimate each edge’s transmission rate to best explain the observed data. The convex optimization framework yields sparse, parameter‑free solutions that decompose into independent subproblems, enabling efficient scaling to hundreds of thousands of nodes, and experiments confirm accurate recovery of network edges and transmission rates from cascade data.

Abstract

Time plays an essential role in the diffusion of information, influence and disease over networks. In many cases we only observe when a node copies information, makes a decision or becomes infected -- but the connectivity, transmission rates between nodes and transmission sources are unknown. Inferring the underlying dynamics is of outstanding interest since it enables forecasting, influencing and retarding infections, broadly construed. To this end, we model diffusion processes as discrete networks of continuous temporal processes occurring at different rates. Given cascade data -- observed infection times of nodes -- we infer the edges of the global diffusion network and estimate the transmission rates of each edge that best explain the observed data. The optimization problem is convex. The model naturally (without heuristics) imposes sparse solutions and requires no parameter tuning. The problem decouples into a collection of independent smaller problems, thus scaling easily to networks on the order of hundreds of thousands of nodes. Experiments on real and synthetic data show that our algorithm both recovers the edges of diffusion networks and accurately estimates their transmission rates from cascade data.