# A semiparametric extension of the stochastic block model for longitudinal networks

arXiv: https://arxiv.org/abs/1512.07075 · HTML: https://mlsanity.com/paper/1512.07075/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2015.

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

- [Continuous Latent Position Models for Instantaneous Interactions](https://mlsanity.com/paper/2103.17146/) (2021)
- [The Multivariate Community Hawkes Model for Dependent Relational Events in Continuous-time Networks](https://mlsanity.com/paper/2205.00639/) (2022)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Longitudinal Modularity, a Modularity for Link Streams](https://mlsanity.com/paper/2408.16877/) (2024)
- [SimHawNet: A Modified Hawkes Process for Temporal Network Simulation](https://mlsanity.com/paper/2203.07260/) (2022)
- [Recurrent segmentation meets block models in temporal networks](https://mlsanity.com/paper/2205.09862/) (2022)
- [Efficient Estimation for Longitudinal Networks via Adaptive Merging](https://mlsanity.com/paper/2211.07866/) (2022)
- [Dynamic Mixed Membership Stochastic Block Model for Weighted Labeled Networks](https://mlsanity.com/paper/2304.05894/) (2023)
- [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)

To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous Poisson process with intensity driven by the individuals' latent groups. The model is shown to be identifiable and its estimation is based on a semiparametric variational expectation-maximization algorithm. Two versions of the method are developed, using either a nonparametric histogram approach (with an adaptive choice of the partition size) or kernel intensity estimators. The number of latent groups can be selected by an integrated classification likelihood criterion. Finally, we demonstrate the performance of our procedure on synthetic experiments, analyse two datasets to illustrate the utility of our approach and comment on competing methods.