  A new class of models for dynamic networks is proposed, called mutually
exciting point process graphs (MEG). 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 future events, including
previously unobserved connections between nodes. 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 characterised exclusively by node-specific
parameters, which allows information to be shared across the network. This
construction enables estimation of intensities even for unobserved edges, which
is particularly important in real world applications, such as computer networks
arising in cyber-security. A recursive form of the log-likelihood function for
MEG is obtained, which is used to derive fast inferential procedures via modern
gradient ascent algorithms. An alternative EM algorithm is also derived. The
model and algorithms are tested on simulated graphs and real world datasets,
demonstrating excellent performance.
