Uncovering the Temporal Dynamics of Diffusion Networks

TL;DR

This paper introduces a scalable, convex optimization-based method to infer the structure and transmission rates of diffusion networks from cascade data, enabling better understanding and prediction of information or disease spread.

Contribution

It presents a novel, scalable convex model that jointly infers network edges and transmission rates from observed cascade data without heuristics or parameter tuning.

Findings

Successfully recovers network edges from cascade data.

Accurately estimates transmission rates between nodes.

Scales efficiently to large networks with hundreds of thousands of nodes.

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.