# Continuous Latent Position Models for Instantaneous Interactions

arXiv: https://arxiv.org/abs/2103.17146 · HTML: https://mlsanity.com/paper/2103.17146/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 54 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 23 of 23)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [A Review of Dynamic Network Models with Latent Variables](https://mlsanity.com/paper/1711.10421/) (2017)
- [Nonparametric Bayes Modeling of Populations of Networks](https://mlsanity.com/paper/1406.7851/) (2014)
- [The Geometry of Continuous Latent Space Models for Network Data](https://mlsanity.com/paper/1712.08641/) (2017)
- [Identifying the latent space geometry of network models through analysis of curvature](https://mlsanity.com/paper/2012.10559/) (2020)
- [A semiparametric extension of the stochastic block model for longitudinal networks](https://mlsanity.com/paper/1512.07075/) (2015)
- [Joint Modelling of Multiple Network Views](https://mlsanity.com/paper/1301.3759/) (2013)
- [Nonparametric Bayes dynamic modeling of relational data](https://mlsanity.com/paper/1311.4669/) (2013)
- [The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks](https://mlsanity.com/paper/1711.10967/) (2017)
- [Additive and multiplicative effects network models](https://mlsanity.com/paper/1807.08038/) (2018)
- [Locally Adaptive Dynamic Networks](https://mlsanity.com/paper/1505.05668/) (2015)
- [Latent Space Models for Dynamic Networks with Weighted Edges](https://mlsanity.com/paper/2005.08261/) (2020)
- [A Review of Latent Space Models for Social Networks](https://mlsanity.com/paper/2012.02307/) (2020)
- [Properties of Latent Variable Network Models](https://mlsanity.com/paper/1506.07806/) (2015)
- [Exact ICL maximization in a non-stationary temporal extension of the stochastic block model for dynamic networks](https://mlsanity.com/paper/1605.02540/) (2016)
- [Computationally efficient inference for latent position network models](https://mlsanity.com/paper/1804.02274/) (2018)
- [Temporal networks of face-to-face human interactions](https://mlsanity.com/paper/1305.3532/) (2013)
- [Process convolution approaches for modeling interacting trajectories](https://mlsanity.com/paper/1703.02112/) (2017)
- [Multiresolution network models](https://mlsanity.com/paper/1608.07618/) (2016)
- [Exact integrated completed likelihood maximisation in a stochastic block transition model for dynamic networks](https://mlsanity.com/paper/1710.03551/) (2017)
- [Measuring systemic risk and contagion in the European financial network](https://mlsanity.com/paper/1911.11488/) (2019)
- [Analysis of the Formation of the Structure of Social Networks using Latent Space Models for Ranked Dynamic Networks](https://mlsanity.com/paper/2005.08269/) (2020)

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

- [A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networks](https://mlsanity.com/paper/2205.09263/) (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)
- [Fast inference of latent space dynamics in huge relational event networks](https://mlsanity.com/paper/2303.17460/) (2023)
- [Multiresolution Analysis and Statistical Thresholding on Dynamic Networks](https://mlsanity.com/paper/2506.01208/) (2025)
- [Spectral clustering for dependent community Hawkes process models of temporal networks](https://mlsanity.com/paper/2505.21845/) (2025)
- [Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations](https://mlsanity.com/paper/2609.08813/) (2026)

## Abstract (arXiv)

We create a framework to analyse the timing and frequency of instantaneous interactions between pairs of entities. This type of interaction data is especially common nowadays, and easily available. Examples of instantaneous interactions include email networks, phone call networks and some common types of technological and transportation networks. Our framework relies on a novel extension of the latent position network model: we assume that the entities are embedded in a latent Euclidean space, and that they move along individual trajectories which are continuous over time. These trajectories are used to characterize the timing and frequency of the pairwise interactions. We discuss an inferential framework where we estimate the individual trajectories from the observed interaction data, and propose applications on artificial and real data.