Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models

TL;DR

This paper introduces a flexible Bayesian inference method for a generalized stochastic block model that handles non-conjugate, weighted network data without losing information, estimating both community structure and number of blocks.

Contribution

It develops a reversible jump MCMC algorithm for the generalized SBM, allowing for non-conjugate edge weight distributions and unknown number of communities.

Findings

Effective on synthetic and real-world networks

Accurately estimates number of blocks and community structure

Handles non-conjugate edge weight distributions

Abstract

The stochastic block model (SBM) is a popular model for capturing community structure and interaction within a network. Network data with non-Boolean edge weights is becoming commonplace; however, existing analysis methods convert such data to a binary representation to apply the SBM, leading to a loss of information. A generalisation of the SBM is considered, which allows edge weights to be modelled in their recorded state. An effective reversible jump Markov chain Monte Carlo sampler is proposed for estimating the parameters and the number of blocks for this generalised SBM. The methodology permits non-conjugate distributions for edge weights, which enable more flexible modelling than current methods as illustrated on synthetic data, a network of brain activity and an email communication network.