Asymptotically efficient estimators for stochastic blockmodels: the naive MLE, the rank-constrained MLE, and the spectral [article]

Minh Tang and Joshua Cape and Carey E. Priebe
2017 arXiv   pre-print
We establish asymptotic normality results for estimation of the block probability matrix B in stochastic blockmodel graphs using spectral embedding when the average degrees grows at the rate of ω(√(n)) 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
more » ... the log-likelihood under no rank assumption, and furthermore, can be almost as efficient as the true MLE that assume known rk(B). Our 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.
arXiv:1710.10936v1 fatcat:jq7rq5ghubhy5a4liqvno2gkwm