# Mutually exciting point process graphs for modelling dynamic networks

arXiv: https://arxiv.org/abs/2102.06527 · HTML: https://mlsanity.com/paper/2102.06527/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 11 Feb 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization](https://mlsanity.com/paper/1808.02941/) (2018)
- [A Sufficient Condition for Convergences of Adam and RMSProp](https://mlsanity.com/paper/1811.09358/) (2018)
- [SEISMIC: A Self-Exciting Point Process Model for Predicting Tweet Popularity](https://mlsanity.com/paper/1506.02594/) (2015)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [Discovering Latent Network Structure in Point Process Data](https://mlsanity.com/paper/1402.0914/) (2014)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Additive and multiplicative effects network models](https://mlsanity.com/paper/1807.08038/) (2018)
- [Locally Adaptive Dynamic Networks](https://mlsanity.com/paper/1505.05668/) (2015)
- [Modelling sparsity, heterogeneity, reciprocity and community structure in temporal interaction data](https://mlsanity.com/paper/1803.06070/) (2018)
- [Anomaly Detection in Large Scale Networks with Latent Space Models](https://mlsanity.com/paper/1911.05522/) (2019)

## Built on by (most cited first, 8 of 8)

- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Gaussian Embedding of Temporal Networks](https://mlsanity.com/paper/2405.17253/) (2024)
- [SimHawNet: A Modified Hawkes Process for Temporal Network Simulation](https://mlsanity.com/paper/2203.07260/) (2022)
- [Multiresolution Analysis and Statistical Thresholding on Dynamic Networks](https://mlsanity.com/paper/2506.01208/) (2025)
- [A source separation approach to temporal graph modelling for computer networks](https://mlsanity.com/paper/2303.15950/) (2023)
- [Looking around you: external information enhances representations for event sequences](https://mlsanity.com/paper/2502.10205/) (2025)
- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)

## Abstract (arXiv)

A new class of models for dynamic networks is proposed, called mutually exciting point process graphs (MEG). MEG is a scalable network-wide statistical model for point processes with dyadic marks, which can be used for anomaly detection when assessing the significance of future events, including previously unobserved connections between nodes. The model combines mutually exciting point processes to estimate dependencies between events and latent space models to infer relationships between the nodes. The intensity functions for each network edge are characterised exclusively by node-specific parameters, which allows information to be shared across the network. This construction enables estimation of intensities even for unobserved edges, which is particularly important in real world applications, such as computer networks arising in cyber-security. A recursive form of the log-likelihood function for MEG is obtained, which is used to derive fast inferential procedures via modern gradient ascent algorithms. An alternative EM algorithm is also derived. The model and algorithms are tested on simulated graphs and real world datasets, demonstrating excellent performance.