# A Latent Space Model for Multilayer Network Data

arXiv: https://arxiv.org/abs/2102.09560 · HTML: https://mlsanity.com/paper/2102.09560/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 75 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Builds on (most cited first, 21 of 21)

- [Understanding predictive information criteria for Bayesian models](https://mlsanity.com/paper/1307.5928/) (2013)
- [Latent Space Models for Dynamic Networks](https://mlsanity.com/paper/2005.08808/) (2020)
- [Multilinear tensor regression for longitudinal relational data](https://mlsanity.com/paper/1412.0048/) (2014)
- [Spectral and matrix factorization methods for consistent community detection in multi-layer networks](https://mlsanity.com/paper/1704.07353/) (2017)
- [A Review of Dynamic Network Models with Latent Variables](https://mlsanity.com/paper/1711.10421/) (2017)
- [Community detection in multi-relational data with restricted multi-layer stochastic blockmodel](https://mlsanity.com/paper/1506.02699/) (2015)
- [Combinatorial Analysis of Multiple Networks](https://mlsanity.com/paper/1303.4986/) (2013)
- [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)
- [Bayesian Inference and Testing of Group Differences in Brain Networks](https://mlsanity.com/paper/1411.6506/) (2014)
- [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)
- [Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks](https://mlsanity.com/paper/1904.05330/) (2019)
- [Latent Space Approaches to Community Detection in Dynamic Networks](https://mlsanity.com/paper/2005.08276/) (2020)
- [Computationally efficient inference for latent position network models](https://mlsanity.com/paper/1804.02274/) (2018)
- [Stochastic blockmodels for exchangeable collections of networks](https://mlsanity.com/paper/1606.05277/) (2016)
- [Stratified stochastic variational inference for high-dimensional network factor model](https://mlsanity.com/paper/2006.14217/) (2020)
- [Exploration of Large Networks with Covariates via Fast and Universal Latent Space Model Fitting](https://mlsanity.com/paper/1705.02372/) (2017)
- [A Latent Space Model for Cognitive Social Structures Data](https://mlsanity.com/paper/1711.03662/) (2017)
- [Modelling heterogeneity in Latent Space Models for Multidimensional Networks](https://mlsanity.com/paper/1807.03874/) (2018)
- [Faster MCMC for Gaussian Latent Position Network Models](https://mlsanity.com/paper/2006.07687/) (2020)

## Built on by (most cited first, 2 of 2)

- [Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Network](https://mlsanity.com/paper/2505.08395/) (2025)
- [A Transfer Learning Framework for Multilayer Networks via Model Averaging](https://mlsanity.com/paper/2506.12455/) (2025)

## Abstract (arXiv)

In this work, we propose a Bayesian statistical model to simultaneously characterize two or more social networks defined over a common set of actors. The key feature of the model is a hierarchical prior distribution that allows us to represent the entire system jointly, achieving a compromise between dependent and independent networks. Among others things, such a specification easily allows us to visualize multilayer network data in a low-dimensional Euclidean space, generate a weighted network that reflects the consensus affinity between actors, establish a measure of correlation between networks, assess cognitive judgements that subjects form about the relationships among actors, and perform clustering tasks at different social instances. Our model's capabilities are illustrated using several real-world data sets, taking into account different types of actors, sizes, and relations.