# Stochastic Block Models with Multiple Continuous Attributes

arXiv: https://arxiv.org/abs/1803.02726 · HTML: https://mlsanity.com/paper/1803.02726/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2018.

## Built on by (most cited first, 11 of 11)

- [An iterative clustering algorithm for the Contextual Stochastic Block Model with optimality guarantees](https://mlsanity.com/paper/2112.10467/) (2021)
- [Exact Recovery and Bregman Hard Clustering of Node-Attributed Stochastic Block Model](https://mlsanity.com/paper/2310.19854/) (2023)
- [Semi-Supervised Clustering with Inaccurate Pairwise Annotations](https://mlsanity.com/paper/2104.02146/) (2021)
- [Flexible inference in heterogeneous and attributed multilayer networks](https://mlsanity.com/paper/2405.20918/) (2024)
- [Heterogeneous Multi-agent Multi-armed Bandits on Stochastic Block Models](https://mlsanity.com/paper/2502.08003/) (2025)
- [Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models](https://mlsanity.com/paper/2401.00688/) (2024)
- [Node metadata can produce predictability transitions in network inference problems](https://mlsanity.com/paper/2103.14424/) (2021)
- [Reconstructing Sparse Multiplex Networks with Application to Covert Networks](https://mlsanity.com/paper/2208.01739/) (2022)
- [Multi-view clustering integrating anchor attribute and structural information](https://mlsanity.com/paper/2410.21711/) (2024)
- [Deep Sparse Latent Feature Models for Knowledge Graph Completion](https://mlsanity.com/paper/2411.15694/) (2024)
- [Clustering Node Attributed Networks with Graph Neural Networks and Self Learning](https://mlsanity.com/paper/2606.13444/) (2026)

## Abstract (arXiv)

The stochastic block model (SBM) is a probabilistic model for community structure in networks. Typically, only the adjacency matrix is used to perform SBM parameter inference. In this paper, we consider circumstances in which nodes have an associated vector of continuous attributes that are also used to learn the node-to-community assignments and corresponding SBM parameters. While this assumption is not realistic for every application, our model assumes that the attributes associated with the nodes in a network's community can be described by a common multivariate Gaussian model. In this augmented, attributed SBM, the objective is to simultaneously learn the SBM connectivity probabilities with the multivariate Gaussian parameters describing each community. While there are recent examples in the literature that combine connectivity and attribute information to inform community detection, our model is the first augmented stochastic block model to handle multiple continuous attributes. This provides the flexibility in biological data to, for example, augment connectivity information with continuous measurements from multiple experimental modalities. Because the lack of labeled network data often makes community detection results difficult to validate, we highlight the usefulness of our model for two network prediction tasks: link prediction and collaborative filtering. As a result of fitting this attributed stochastic block model, one can predict the attribute vector or connectivity patterns for a new node in the event of the complementary source of information (connectivity or attributes, respectively). We also highlight two biological examples where the attributed stochastic block model provides satisfactory performance in the link prediction and collaborative filtering tasks.