  Networks play a central role in modern data analysis, enabling us to reason
about systems by studying the relationships between their parts. Most often in
network analysis, the edges are given. However, in many systems it is difficult
or impossible to measure the network directly. Examples of latent networks
include economic interactions linking financial instruments and patterns of
reciprocity in gang violence. In these cases, we are limited to noisy
observations of events associated with each node. To enable analysis of these
implicit networks, we develop a probabilistic model that combines
mutually-exciting point processes with random graph models. We show how the
Poisson superposition principle enables an elegant auxiliary variable
formulation and a fully-Bayesian, parallel inference algorithm. We evaluate
this new model empirically on several datasets.
