We consider the problem of analyzing timestamped relational events between a set of entities, such as messages between users of an on-line social network. Such data are often analyzed using static or discrete-time network models, which discard a significant amount of information by aggregating events over time to form network snapshots. In this paper, we introduce a block point process model (BPPM) for continuous-time event-based dynamic networks. The BPPM is inspired by the well-known stochastic block model (SBM) for static networks. We show that networks generated by the BPPM follow an SBM in the limit of a growing number of nodes. We use this property to develop principled and efficient local search and variational inference procedures initialized by regularized spectral clustering. We fit BPPMs with exponential Hawkes processes to analyze several real network data sets, including a Facebook wall post network with over 3,500 nodes and 130,000 events.
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A mutually exciting latent space Hawkes process model for continuous-time networks
Networks and temporal point processes serve as fundamental building blocks for modeling complex dynamic relational data in various domains. We propose the latent space Hawkes (LSH) model, a novel generative model for continuous-time networks of relational events, using a latent space representation for nodes. We model relational events between nodes using mutually exciting Hawkes processes with baseline intensities dependent upon the distances between the nodes in the latent space and sender and receiver specific effects. We demonstrate that our proposed LSH model can replicate many features observed in real temporal networks including reciprocity and transitivity, while also achieving superior prediction accuracy and providing more interpretable fits than existing models.
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- NSF-PAR ID:
- 10357301
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 180
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 863-873
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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