# Flexible inference in heterogeneous and attributed multilayer networks

arXiv: https://arxiv.org/abs/2405.20918 · HTML: https://mlsanity.com/paper/2405.20918/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 12 of 12)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Automatic Differentiation Variational Inference](https://mlsanity.com/paper/1603.00788/) (2016)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Structure and inference in annotated networks](https://mlsanity.com/paper/1507.04001/) (2015)
- [Community detection, link prediction, and layer interdependence in multilayer networks](https://mlsanity.com/paper/1701.01369/) (2017)
- [Community detection with node attributes in multilayer networks](https://mlsanity.com/paper/2004.09160/) (2020)
- [Stochastic Block Models with Multiple Continuous Attributes](https://mlsanity.com/paper/1803.02726/) (2018)
- [Network structure, metadata and the prediction of missing nodes and annotations](https://mlsanity.com/paper/1604.00255/) (2016)
- [Structure and inference in hypergraphs with node attributes](https://mlsanity.com/paper/2311.03857/) (2023)
- [Laplace Matching for fast Approximate Inference in Latent Gaussian Models](https://mlsanity.com/paper/2105.03109/) (2021)
- [Mixed-Membership of Experts Stochastic Blockmodel](https://mlsanity.com/paper/1404.0221/) (2014)
- [General Latent Feature Models for Heterogeneous Datasets](https://mlsanity.com/paper/1706.03779/) (2017)

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

- [Broad Spectrum Structure Discovery in Large-Scale Higher-Order Networks](https://mlsanity.com/paper/2505.21748/) (2025)
- [How do Probabilistic Graphical Models and Graph Neural Networks Look at Network Data?](https://mlsanity.com/paper/2506.11869/) (2025)

## Abstract (arXiv)

Networked datasets can be enriched by different types of information about individual nodes or edges. However, most existing methods for analyzing such datasets struggle to handle the complexity of heterogeneous data, often requiring substantial model-specific analysis. In this paper, we develop a probabilistic generative model to perform inference in multilayer networks with arbitrary types of information. Our approach employs a Bayesian framework combined with the Laplace matching technique to ease interpretation of inferred parameters. Furthermore, the algorithmic implementation relies on automatic differentiation, avoiding the need for explicit derivations. This makes our model scalable and flexible to adapt to any combination of input data. We demonstrate the effectiveness of our method in detecting overlapping community structures and performing various prediction tasks on heterogeneous multilayer data, where nodes and edges have different types of attributes. Additionally, we showcase its ability to unveil a variety of patterns in a social support network among villagers in rural India by effectively utilizing all input information in a meaningful way.