Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks
This work addresses the challenge of reliable inference in dynamic network analysis for researchers and practitioners, though it appears incremental as it builds on existing kernel smoothing and projection techniques.
The authors tackled the problem of learning continuous-time representations for dynamic networks from timestamped interactions, proposing the Intensity Profile Projection framework that yields node trajectories with structural and temporal coherence, supported by estimation theory providing tight error control and insights into bias-variance trade-offs.
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.