Asymptotic Normality of Maximum Likelihood and its Variational Approximation for Stochastic Blockmodels

By Peter J. Bickel, David S. Choi, Xiangyu Chang, Hai Zhang. 2012

235 citations recorded by the source corpus.

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.

Subfields: Molecular Biology, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, background): “Celisse et al. (2012) and Bickel et al. (2013) analyzed network data using stochastic blockmodels.”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, methodology): “[14] prove consistency of likelihood based methods, and Bickel et al.”
Pseudo-likelihood methods for community detection in large sparse networks (2012, methodology): “Asymptotic behavior of variational methods is studied in [10] and [8], and in [14] this belief propagation method is analyzed for both the sparse [ λ n = O (1)] and the dense ( λ n → ∞ ) regimes, by nonrigorous cavity methods from physics, and a phase transition threshold, below which the labels…”