Co-clustering separately exchangeable network data

TL;DR

This paper demonstrates that stochastic blockmodels effectively solve the co-clustering problem for binary arrays generated by nonparametric, separately exchangeable processes, with proven convergence rates and interpretability as optimal approximations.

Contribution

It establishes theoretical performance bounds for stochastic blockmodels in co-clustering under separate exchangeability, linking them to nonparametric models and providing consistency results.

Findings

Oracle inequalities with convergence rate $\\mathcal{O}_P(n^{-1/4})$

Blockmodels as optimal piecewise-constant approximations

High-probability detection of equal-sized co-clusters

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.