24,811 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
Bayesian nonparametric Plackett-Luce models for the analysis of preferences for college degree programmes
In this paper we propose a Bayesian nonparametric model for clustering
partial ranking data. We start by developing a Bayesian nonparametric extension
of the popular Plackett-Luce choice model that can handle an infinite number of
choice items. Our framework is based on the theory of random atomic measures,
with the prior specified by a completely random measure. We characterise the
posterior distribution given data, and derive a simple and effective Gibbs
sampler for posterior simulation. We then develop a Dirichlet process mixture
extension of our model and apply it to investigate the clustering of
preferences for college degree programmes amongst Irish secondary school
graduates. The existence of clusters of applicants who have similar preferences
for degree programmes is established and we determine that subject matter and
geographical location of the third level institution characterise these
clusters.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS717 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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