  The increasing prevalence of network data in a vast variety of fields and the
need to extract useful information out of them have spurred fast developments
in related models and algorithms. Among the various learning tasks with network
data, community detection, the discovery of node clusters or "communities," has
arguably received the most attention in the scientific community. In many
real-world applications, the network data often come with additional
information in the form of node or edge covariates that should ideally be
leveraged for inference. In this paper, we add to a limited literature on
community detection for networks with covariates by proposing a Bayesian
stochastic block model with a covariate-dependent random partition prior. Under
our prior, the covariates are explicitly expressed in specifying the prior
distribution on the cluster membership. Our model has the flexibility of
modeling uncertainties of all the parameter estimates including the community
membership. Importantly, and unlike the majority of existing methods, our model
has the ability to learn the number of the communities via posterior inference
without having to assume it to be known. Our model can be applied to community
detection in both dense and sparse networks, with both categorical and
continuous covariates, and our MCMC algorithm is very efficient with good
mixing properties. We demonstrate the superior performance of our model over
existing models in a comprehensive simulation study and an application to two
real datasets.

Methodology;Social and Information Networks;Computation;Machine Learning