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.

Highlights

  • Statistical analysis of networks has seen much growth in recent years with the increasing availability of network data

  • This paper considers two extensions to the stochastic block model (SBM): (i) modelling general edge weights and (ii) estimating the number of blocks

  • This section discusses the benefit of split-merge steps over Gibbs samplers for mixture models, describes the difficulty that arises when designing split-merge moves for block membership in the generalised SBM (GSBM), and presents a split-merge reversible jump Markov chain Monte Carlo (RJMCMC) sampler for the GSBM

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Summary

Introduction

Statistical analysis of networks has seen much growth in recent years with the increasing availability of network data. Some authors (Mørup et al, 2011; Mørup and Schmidt, 2012, 2013; McDaid et al, 2013) have considered both extensions (i) and (ii) and posited collapsed Gibbs samplers to perform inference on the number of blocks, node membership and edge-weight model parameters. All of these methods require a conjugate model for the edge-weight distributions. This article aims to achieve both extensions by generalising the SBM to arbitrary edge-weight distributions and modelling the number of blocks in one Bayesian framework without the restriction of conjugate edge-weight distributions

A generalisation of the stochastic block model
Split-merge sampler
Simulated data
Real data
Macaque sensory data
Enron emails
Concluding remarks
Full Text
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