An Overview of Asymptotic Normality in Stochastic Blockmodels: Cluster Analysis and Inference

TL;DR

This paper reviews the asymptotic normality results in stochastic blockmodels, linking classical statistical concepts to modern network analysis, and discusses their implications for clustering, inference, and community detection.

Contribution

It provides a thematic survey of various asymptotic normality results in stochastic blockmodels, highlighting their roles in estimation, testing, and understanding network structures.

Findings

Different forms of asymptotic Gaussian behavior are identified in stochastic blockmodels.

Asymptotic normality results are useful for community detection and latent space analysis.

The paper discusses open problems and future research directions in this area.

Abstract

This paper provides a selective review of the statistical network analysis literature focused on clustering and inference problems for stochastic blockmodels and their variants. We survey asymptotic normality results for stochastic blockmodels as a means of thematically linking classical statistical concepts to contemporary research in network data analysis. Of note, multiple different forms of asymptotically Gaussian behavior arise in stochastic blockmodels and are useful for different purposes, pertaining to estimation and testing, the characterization of cluster structure in community detection, and understanding latent space geometry. This paper concludes with a discussion of open problems and ongoing research activities addressing asymptotic normality and its implications for statistical network modeling.