Inference for the stochastic blockmodel is currently of burgeoning interestin the statistical community, as well as in various application domains asdiverse as social networks, citation networks, brain connectivity networks(connectomics), etc. Recent theoretical developments have shown that spectralembedding of graphs yields tractable distributional results; in particular, arandom dot product latent position graph formulation of the stochasticblockmodel informs a mixture of normal distributions for the adjacency spectralembedding. We employ this new theory to provide an empirical Bayes methodologyfor estimation of block memberships of vertices in a random graph drawn fromthe stochastic blockmodel, and demonstrate its practical utility. The posteriorinference is conducted using a Metropolis-within-Gibbs algorithm. The theoryand methods are illustrated through Monte Carlo simulation studies, both withinthe stochastic blockmodel and beyond, and experimental results on a Wikipediadata set are presented.
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