Journal
ANNALS OF STATISTICS
Volume 42, Issue 1, Pages 29-63Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AOS1173
Keywords
Bipartite graph; network clustering; oracle inequality; profile likelihood; statistical network analysis; stochastic blockmodel and co-blockmodel
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Funding
- US Army Research Office [W911NF-09-1-0555, W911NF-11-1-0036]
- UK EPSRC [EP/K005413/1, EP/K503459/1]
- UK Royal Society
- Marie Curie FP7 Integration Grant within the 7th European Union Framework Program [PCIG12-GA-2012-334622]
- Engineering and Physical Sciences Research Council [EP/K005413/1, EP/K503459/1] Funding Source: researchfish
- EPSRC [EP/K005413/1] Funding Source: UKRI
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This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence O-P(n(-1/4)) corresponding to profile likelihood maximization and mean-square error minimization, and show that the blockmodel can be interpreted in this setting as an optimal piecewise-constant approximation to the generative nonparametric model. We also show for large sample sizes that the detection of co-clusters in such data indicates with high probability the existence of co-clusters of equal size and asymptotically equivalent connectivity in the underlying generative process.
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