## The Annals of Statistics

### Co-clustering separately exchangeable network data

#### 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.

#### Article information

Source
Ann. Statist., Volume 42, Number 1 (2014), 29-63.

Dates
First available in Project Euclid: 15 January 2014

https://projecteuclid.org/euclid.aos/1389795744

Digital Object Identifier
doi:10.1214/13-AOS1173

Mathematical Reviews number (MathSciNet)
MR3161460

Zentralblatt MATH identifier
1294.62059

#### Citation

Choi, David; Wolfe, Patrick J. Co-clustering separately exchangeable network data. Ann. Statist. 42 (2014), no. 1, 29--63. doi:10.1214/13-AOS1173. https://projecteuclid.org/euclid.aos/1389795744

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