Hawkes Edge Model.pdf

The Hawkes Edge Partition Model is a novel probabilistic framework for modeling continuous-time interaction events data. It aims to infer the implicit community structure underlying temporal interactions among entities and exploit how this structure influences interaction dynamics. The model uses mutually-exciting Hawkes processes to capture reciprocating interactions between individuals, with the base rate built upon latent representations inferred using the hierarchical gamma process edge partition model (HGaP-EPM).

Key features of the model include:

Capturing overlapping communities, degree heterogeneity, and sparsity underlying observed interactions
Augmenting each interaction with a pair of latent variables to indicate which latent communities lead to the interaction
Automatically determining the number of underlying communities via the inherent shrinkage mechanism of the hierarchical gamma process
Flexibly incorporating auxiliary individuals' attributes or covariates associated with interaction events

The model is applied to temporal link prediction using real-world data and shows competitive performance compared to state-of-the-art models. Efficient approximate inference is performed using closed-form update equations with data augmentation techniques. The contributions of the model include:

Proposing a statistical model for continuous-time dynamic networks that captures underlying community structure
Accounting for heterogeneity in exogenous and endogenous activities
Developing efficient approximate inference methods
Applying the model to temporal link prediction with competitive performance.