Co-clustering separately exchangeable network data
The Annals of Statistics · 2014 · Volume 42 · Issue 1
Abstract
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 $\mathcal{O}_{P}(n^{-1/4})$ 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.
Keywords
05C80, 60B20, 62G05, Bipartite graph, network clustering, Oracle inequality, profile likelihood, statistical network analysis, stochastic blockmodel and co-blockmodel
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