The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks

TL;DR

The paper introduces MULCH, a flexible multivariate Hawkes process-based model for continuous-time networks that captures dependencies between node pairs, outperforming existing models in accuracy for prediction and generation.

Contribution

The paper presents MULCH, a novel community-based multivariate Hawkes model that incorporates dependencies between edges in continuous-time networks, addressing limitations of prior independent-edge models.

Findings

MULCH significantly improves predictive accuracy over existing models.

MULCH effectively captures higher-order motifs like triangles.

The model demonstrates superior generative capabilities.

Abstract

The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks.