# Bayesian stochastic blockmodeling

## TL;DR

This paper introduces Bayesian inference methods for stochastic blockmodels to identify modular structures in networks, emphasizing nonparametric approaches that prevent overfitting and facilitate model selection.

## Contribution

It presents a comprehensive Bayesian framework for stochastic blockmodeling, including degree-corrected and overlapping variants, with efficient algorithms and insights into model choice and limitations.

## Key findings

- Bayesian methods improve detection of network modules.
- Nonparametric formulations prevent overfitting.
- Inference can predict missing or spurious links.

## Abstract

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.