Parsimonious Hawkes Processes for temporal networks modelling

TL;DR

This paper introduces a parsimonious Hawkes process model for temporal networks that captures community structure and node activity heterogeneity, improving prediction accuracy and providing detailed interaction insights.

Contribution

The paper presents a novel continuous Hawkes process model that incorporates community structure and node activity heterogeneity for temporal network analysis.

Findings

Improves prediction performance over previous models.

Achieves systematic increase in log-likelihood.

Provides detailed characterization of influencer-node interactions.

Abstract

Temporal networks are characterised by interdependent link events between nodes, forming ordered sequences of links that may represent specific information flows in the system. Nevertheless, representing temporal networks using discrete snapshots in time partially cancels the effect of time-ordered links on each other, while continuous time models, such as Poisson or Hawkes processes, can describe the full influence between all the potential pairs of links at all times. In this paper, we introduce a continuous Hawkes temporal network model which accounts both for a community structure of the aggregate network and a strong heterogeneity in the activity of individual nodes, thus accounting for the presence of highly heterogeneous clusters with isolated high-activity influencer nodes, communities and low-activity nodes. Our model improves the prediction performance of previously available continuous time network models, and obtains a systematic increase in log-likelihood. Characterising the direct interaction between influencer nodes and communities, we can provide a more detailed description of the system that can better outline the sequence of activations in the components of the systems represented by temporal networks.