# Tensor State Space-based Dynamic Multilayer Network Modeling

arXiv: https://arxiv.org/abs/2506.02413 · HTML: https://mlsanity.com/paper/2506.02413/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 20 of 20)

- [Frequentist Consistency of Variational Bayes](https://mlsanity.com/paper/1705.03439/) (2017)
- [Inference for multiple heterogeneous networks with a common invariant subspace](https://mlsanity.com/paper/1906.10026/) (2019)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [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)
- [Dynamic stochastic blockmodels for time-evolving social networks](https://mlsanity.com/paper/1403.0921/) (2014)
- [The multilayer random dot product graph](https://mlsanity.com/paper/2007.10455/) (2020)
- [Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness](https://mlsanity.com/paper/1404.4412/) (2014)
- [Latent space models for multiplex networks with shared structure](https://mlsanity.com/paper/2012.14409/) (2020)
- [Joint Embedding of Graphs](https://mlsanity.com/paper/1703.03862/) (2017)
- [Clustering Network Layers With the Strata Multilayer Stochastic Block Model](https://mlsanity.com/paper/1507.01826/) (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)
- [Additive and multiplicative effects network models](https://mlsanity.com/paper/1807.08038/) (2018)
- [Bayesian Learning of Dynamic Multilayer Networks](https://mlsanity.com/paper/1608.02209/) (2016)
- [An Eigenmodel for Dynamic Multilayer Networks](https://mlsanity.com/paper/2103.12831/) (2021)
- [Structured Optimal Variational Inference for Dynamic Latent Space Models](https://mlsanity.com/paper/2209.15117/) (2022)
- [A dynamic network model with persistent links and node-specific latent variables, with an application to the interbank market](https://mlsanity.com/paper/1801.00185/) (2017)
- [A Multilayered Block Network Model to Forecast Large Dynamic Transportation Graphs: an Application to US Air Transport](https://mlsanity.com/paper/1911.13136/) (2019)
- [Dynamic Stochastic Blockmodel Regression for Network Data: Application to International Militarized Conflicts](https://mlsanity.com/paper/2103.00702/) (2021)

## Abstract (arXiv)

Understanding the complex interactions within dynamic multilayer networks is critical for advancements in various scientific domains. Existing models often fail to capture such networks' temporal and cross-layer dynamics. This paper introduces a novel Tensor State Space Model for Dynamic Multilayer Networks (TSSDMN), utilizing a latent space model framework. TSSDMN employs a symmetric Tucker decomposition to represent latent node features, their interaction patterns, and layer transitions. Then by fixing the latent features and allowing the interaction patterns to evolve over time, TSSDMN uniquely captures both the temporal dynamics within layers and across different layers. The model identifiability conditions are discussed. By treating latent features as variables whose posterior distributions are approximated using a mean-field variational inference approach, a variational Expectation Maximization algorithm is developed for efficient model inference. Numerical simulations and case studies demonstrate the efficacy of TSSDMN for understanding dynamic multilayer networks.