  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.
