# A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks

arXiv: https://arxiv.org/abs/2205.09263 · HTML: https://mlsanity.com/paper/2205.09263/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 16 of 16)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [A Survey on Network Embedding](https://mlsanity.com/paper/1711.08752/) (2017)
- [DynGEM: Deep Embedding Method for Dynamic Graphs](https://mlsanity.com/paper/1805.11273/) (2018)
- [dyngraph2vec: Capturing Network Dynamics using Dynamic Graph Representation Learning](https://mlsanity.com/paper/1809.02657/) (2018)
- [Dynamic Graph Representation Learning via Self-Attention Networks](https://mlsanity.com/paper/1812.09430/) (2018)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [A Survey on Dynamic Network Embedding](https://mlsanity.com/paper/2006.08093/) (2020)
- [Joint Modelling of Multiple Network Views](https://mlsanity.com/paper/1301.3759/) (2013)
- [The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks](https://mlsanity.com/paper/1711.10967/) (2017)
- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [Latent Space Models for Dynamic Networks with Weighted Edges](https://mlsanity.com/paper/2005.08261/) (2020)
- [Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data](https://mlsanity.com/paper/1803.06070/) (2018)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)
- [Surfacing Estimation Uncertainty in the Decay Parameters of Hawkes Processes with Exponential Kernels](https://mlsanity.com/paper/2104.01029/) (2021)

## Built on by (most cited first, 10 of 10)

- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Continuous-time Graph Representation with Sequential Survival Process](https://mlsanity.com/paper/2312.13068/) (2023)
- [Gaussian Embedding of Temporal Networks](https://mlsanity.com/paper/2405.17253/) (2024)
- [A Latent Space Model for HLA Compatibility Networks in Kidney Transplantation](https://mlsanity.com/paper/2211.02234/) (2022)
- [The co-varying ties between networks and item responses via latent variables](https://mlsanity.com/paper/2409.19400/) (2024)
- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)
- [LIT-LVM: Structured Regularization for Interaction Terms in Linear Predictors using Latent Variable Models](https://mlsanity.com/paper/2506.15492/) (2025)
- [Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes](https://mlsanity.com/paper/2510.20414/) (2025)
- [How Predicted Links Influence Network Evolution: Disentangling Choice and Algorithmic Feedback in Dynamic Graphs](https://mlsanity.com/paper/2603.03945/) (2026)
- [Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations](https://mlsanity.com/paper/2609.08813/) (2026)

## Abstract (arXiv)

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.