Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of graphs yields tractable distributional results; in particular, a random dot product latent position graph formulation of the stochastic blockmodel informs a mixture of normal distributions for the adjacency spectral embedding. We employ this new theory to provide an empirical Bayes methodology for estimation of block memberships of vertices in a random graph drawn from the stochastic blockmodel, and demonstrate its practical utility. The posterior inference is conducted using a Metropolis-within-Gibbs algorithm. The theory and methods are illustrated through Monte Carlo simulation studies, both within the stochastic blockmodel and beyond, and experimental results on a Wikipedia graph are presented.
Using attributed graphs to model network data has become an attractive approach for various graph inference tasks. Consider a network containing a small subset of interesting entities whose identities are not fully known and that discovering them will be of some significance. Vertex nomination, a subclass of recommender systems relying on the exploitation of attributed graphs, is a task which seeks to identify the unknown entities that are similarly interesting or exhibit analogous latent attributes. This task is a specific type of community detection and is increasingly becoming a subject of current research in many disciplines. Recent studies have shown that information relevant to this task is contained in both the structure of the network and its attributes, and that jointly exploiting them can provide superior vertex nomination performance than either one used alone. We adopt this new approach to formulate a Bayesian model for the vertex nomination problem. Specifically, the goal here is to construct a ‘nomination list’ where entities that are truly interesting are concentrated at the top of the list. Inference with the model is conducted using a Metropolis‐within‐Gibbs algorithm. Performance of the model is illustrated by a Monte Carlo simulation study and on the well‐known Enron email dataset. WIREs Comput Stat 2015, 7:400–416. doi: 10.1002/wics.1365
This article is categorized under:
Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory
Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC)
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