Variational Inference for Stochastic Block Models from Sampled Data

TL;DR

This paper develops variational inference methods for stochastic block models with sampled network data, addressing missing data issues and providing tools for model selection and real-world network analysis.

Contribution

It introduces variants of the variational EM algorithm for SBM under different sampling schemes, with accompanying R package and model selection criteria.

Findings

Algorithms perform well in simulations

Sampling design impacts network interpretation

Methods applicable to real-world biological and ethnological networks

Abstract

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.