Date of Original Version

1-2014

Type

Article

Rights Management

© Institute of Mathematical Statistics, 2014

Abstract or Description

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 OP(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.

DOI

10.1214/13-AOS1173

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Published In

Annals of Statistics, 42, 1, 29-63.