# Variational Inference for Stochastic Block Models from Sampled Data

arXiv: https://arxiv.org/abs/1707.04141 · HTML: https://mlsanity.com/paper/1707.04141/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2017.

## Built on by (most cited first, 7 of 7)

- [An Introduction to Variational Inference](https://mlsanity.com/paper/2108.13083/) (2021)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [A useful criterion on studying consistent estimation in community detection](https://mlsanity.com/paper/2109.14950/) (2021)
- [Consistency of Lloyd's Algorithm Under Perturbations](https://mlsanity.com/paper/2309.00578/) (2023)
- [SubSearch: Robust Estimation and Outlier Detection for Stochastic Block Models via Subgraph Search](https://mlsanity.com/paper/2506.03657/) (2025)
- [Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals](https://mlsanity.com/paper/2509.15989/) (2025)
- [From topology learning to graph generation: A unifying perspective](https://mlsanity.com/paper/2609.02286/) (2026)

## Abstract (arXiv)

This paper deals with non-observed dyads during the sampling of a network and consecutive issues in the inference of the Stochastic Block Model (SBM). We review sampling designs and recover Missing At Random (MAR) and Not Missing At Random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM under various sampling designs (MAR and NMAR) all available as an R package. Model selection criteria based on Integrated Classification Likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore two real-world networks from ethnology (seed circulation network) and biology (protein-protein interaction network), where the interpretations considerably depends on the sampling designs considered.