  Graph link prediction is an important task in cyber-security: relationships
between entities within a computer network, such as users interacting with
computers, or system libraries and the corresponding processes that use them,
can provide key insights into adversary behaviour. Poisson matrix factorisation
(PMF) is a popular model for link prediction in large networks, particularly
useful for its scalability. In this article, PMF is extended to include
scenarios that are commonly encountered in cyber-security applications.
Specifically, an extension is proposed to explicitly handle binary adjacency
matrices and include known categorical covariates associated with the graph
nodes. A seasonal PMF model is also presented to handle seasonal networks. To
allow the methods to scale to large graphs, variational methods are discussed
for performing fast inference. The results show an improved performance over
the standard PMF model and other statistical network models.
