Variational Bayesian inference for the Latent Position Cluster Model

Many recent approaches to modeling social networks have focussed on embedding
the actors in a latent “social space”. Links are more likely for actors that are
close in social space than for actors that are distant in social space. In particular,
the Latent Position Cluster Model (LPCM) [1] allows for explicit modelling of
the clustering that is exhibited in many network datasets. However, inference for
the LPCM model via MCMC is cumbersome and scaling of this model to large
or even medium size networks with many interacting nodes is a challenge. Variational
Bayesian methods offer one solution to this problem. An approximate,
closed form posterior is formed, with unknown variational parameters. These
parameters are tuned to minimize the Kullback-Leibler divergence between the
approximate variational posterior and the true posterior, which known only up to
proportionality. The variational Bayesian approach is shown to give a computationally
efficient way of fitting the LPCM. The approach is demonstrated on a
number of data sets and it is shown to give a good fit.