Alert button
Picture for Emma Ceccherini

Emma Ceccherini

Alert button

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

Jun 09, 2023
Alexander Modell, Ian Gallagher, Emma Ceccherini, Nick Whiteley, Patrick Rubin-Delanchy

Figure 1 for Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks
Figure 2 for Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks
Figure 3 for Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks
Figure 4 for Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks

We present a new algorithmic framework, Intensity Profile Projection, for learning continuous-time representations of the nodes of a dynamic network, characterised by a node set and a collection of instantaneous interaction events which occur in continuous time. Our framework consists of three stages: estimating the intensity functions underlying the interactions between pairs of nodes, e.g. via kernel smoothing; learning a projection which minimises a notion of intensity reconstruction error; and inductively constructing evolving node representations via the learned projection. We show that our representations preserve the underlying structure of the network, and are temporally coherent, meaning that node representations can be meaningfully compared at different points in time. We develop estimation theory which elucidates the role of smoothing as a bias-variance trade-off, and shows how we can reduce smoothing as the signal-to-noise ratio increases on account of the algorithm `borrowing strength' across the network.

* 36 pages, 8 figures 
Viaarxiv icon