Asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels

TL;DR

This paper establishes the asymptotic normality of maximum likelihood and variational estimators for stochastic blockmodels, providing theoretical performance bounds and extending to various sub-models in network data analysis.

Contribution

It proves asymptotic normality rates for both maximum likelihood and variational estimators in stochastic blockmodels, advancing theoretical understanding of these methods.

Findings

Asymptotic normality rates are established for estimators.

Results apply to various sub-models of stochastic blockmodels.

Theoretical bounds enhance understanding of variational methods in network analysis.

Abstract

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data, by either maximum likelihood or variational estimation. The result also applies to various sub-models of the stochastic blockmodel found in the literature.