We present a new representation learning framework, Intensity Profile
Projection, for continuous-time dynamic network data. Given triples (i,j,t),
each representing a time-stamped (t) interaction between two entities
(i,j), our procedure returns a continuous-time trajectory for each node,
representing its behaviour over time. The framework consists of three stages:
estimating pairwise intensity functions, e.g. via kernel smoothing; learning a
projection which minimises a notion of intensity reconstruction error; and
constructing evolving node representations via the learned projection. The
trajectories satisfy two properties, known as structural and temporal
coherence, which we see as fundamental for reliable inference. Moreoever, we
develop estimation theory providing tight control on the error of any estimated
trajectory, indicating that the representations could even be used in quite
noise-sensitive follow-on analyses. The theory also elucidates the role of
smoothing as a bias-variance trade-off, and shows how we can reduce the level
of smoothing as the signal-to-noise ratio increases on account of the algorithm
`borrowing strength' across the network.Comment: 37 pages, 10 figure