Mutually exciting point process graphs for modelling dynamic networks

A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG), motivated by a practical application in computer network security. MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection when assessing the significance of previously unobserved connections. The model combines mutually exciting point processes to estimate dependencies between events and latent space models to infer relationships between the nodes. The intensity functions for each network edge are parameterised exclusively by node-specific parameters, which allows information to be shared across the network. Fast inferential procedures using modern gradient ascent algorithms are exploited. The model is tested on simulated graphs and real world computer network datasets, demonstrating excellent performance.