2 research outputs found
Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel
The mixed membership stochastic blockmodel is a statistical model for a
graph, which extends the stochastic blockmodel by allowing every node to
randomly choose a different community each time a decision of whether to form
an edge is made. Whereas spectral analysis for the stochastic blockmodel is
increasingly well established, theory for the mixed membership case is
considerably less developed. Here we show that adjacency spectral embedding
into , followed by fitting the minimum volume enclosing convex
-polytope to the principal components, leads to a consistent estimate
of a -community mixed membership stochastic blockmodel. The key is to
identify a direct correspondence between the mixed membership stochastic
blockmodel and the random dot product graph, which greatly facilitates
theoretical analysis. Specifically, a norm and central
limit theorem for the random dot product graph are exploited to respectively
show consistency and partially correct the bias of the procedure.Comment: 12 pages, 6 figure
Stratified stochastic variational inference for high-dimensional network factor model
There has been considerable recent interest in Bayesian modeling of
high-dimensional networks via latent space approaches. When the number of nodes
increases, estimation based on Markov Chain Monte Carlo can be extremely slow
and show poor mixing, thereby motivating research on alternative algorithms
that scale well in high-dimensional settings. In this article, we focus on the
latent factor model, a widely used approach for latent space modeling of
network data. We develop scalable algorithms to conduct approximate Bayesian
inference via stochastic optimization. Leveraging sparse representations of
network data, the proposed algorithms show massive computational and storage
benefits, and allow to conduct inference in settings with thousands of nodes.Comment: 25 pages, 1 figures. Corrected compilation issues and minor typo