Predicting partially observed processes on temporal networks by Dynamics-Aware Node Embeddings (DyANE)

Koya Sato,Mizuki Oka,Alain Barrat,Ciro Cattuto

doi:10.1140/epjds/s13688-021-00277-8

Abstract

Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks – rather than of the network structure itself – with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a lossless modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes’ epidemic states in single instances of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.

Highlights

The ubiquity of network representations of widely different systems has led to a flourishing of methods aimed at the analysis of their structure [1, 2] and of processes taking place on networks, such as information diffusion, epidemic spread, synchronization, etc [3, 4]
We propose a new method for node embedding tailored to the study of dynamical process on temporal networks, using a modified supra-adjacency representation for temporal networks and building on standard random walk based embeddings for static graphs
5 Conclusion We have introduced a new method to recover the dynamical evolution of a single instance of a process that has taken place on a known temporal network, from partial observations

Summary

Introduction

The ubiquity of network representations of widely different systems has led to a flourishing of methods aimed at the analysis of their structure [1, 2] and of processes taking place on networks, such as information diffusion, epidemic spread, synchronization, etc [3, 4]. We show that node embedding methods can be tailored to the study of dynamical processes on temporal networks, and in particular to the task described above of predicting the evolution and outcome of any instance of the dynamics (e.g., an epidemic outbreak) from partial information and without detailed knowledge of the dynamical process itself.

Results

Conclusion