  Networks capture our intuition about relationships in the world. They
describe the friendships between Facebook users, interactions in financial
markets, and synapses connecting neurons in the brain. These networks are
richly structured with cliques of friends, sectors of stocks, and a smorgasbord
of cell types that govern how neurons connect. Some networks, like social
network friendships, can be directly observed, but in many cases we only have
an indirect view of the network through the actions of its constituents and an
understanding of how the network mediates that activity. In this work, we focus
on the problem of latent network discovery in the case where the observable
activity takes the form of a mutually-excitatory point process known as a
Hawkes process. We build on previous work that has taken a Bayesian approach to
this problem, specifying prior distributions over the latent network structure
and a likelihood of observed activity given this network. We extend this work
by proposing a discrete-time formulation and developing a computationally
efficient stochastic variational inference (SVI) algorithm that allows us to
scale the approach to long sequences of observations. We demonstrate our
algorithm on the calcium imaging data used in the Chalearn neural connectomics
challenge.
