Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks

TL;DR

This paper introduces Intensity Profile Projection, a novel framework for continuous-time representation learning in dynamic networks, enabling trajectories that capture node behavior over time with theoretical error bounds.

Contribution

The framework provides a new method for continuous-time dynamic network representation with theoretical guarantees and insights into smoothing effects.

Findings

Provides tight error bounds for trajectory estimation.

Demonstrates the role of smoothing as a bias-variance trade-off.

Shows how to adapt smoothing based on signal-to-noise ratio.

Abstract

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.