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Title: Asymptotically efficient estimators for stochastic blockmodels Authors:  Minh Tang - North Carolina State University (United States) [presenting]
Joshua Cape - University of Michigan (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: Asymptotic normality results are established for estimation of the block probability matrix $B$ in stochastic blockmodel graphs using spectral embedding when the average degrees grow at the rate of $\omega(n^{1/2}$) in $n$, the number of vertices. As a corollary, we show that when $B$ is of full-rank, estimates of $B$ obtained from spectral embedding are asymptotically efficient. When $B$ is singular the estimates obtained from spectral embedding can have smaller mean square error than those obtained from maximizing the log-likelihood under no rank assumption, and furthermore, can be almost as efficient as the true MLE that assume known $rk(B)$. The results indicate, in the context of stochastic blockmodel graphs, that spectral embedding is not just computationally tractable, but that the resulting estimates are also admissible, even when compared to the purportedly optimal but computationally intractable maximum likelihood estimation under no rank assumption.