Achieving Optimal Misclassification Proportion in Stochastic Block Model

TL;DR

This paper introduces a computationally feasible two-stage method for community detection in stochastic block models that achieves the optimal misclassification proportion, matching theoretical limits.

Contribution

It proposes a novel two-stage algorithm that refines initial community detection procedures to reach optimal statistical performance under weak conditions.

Findings

Achieves optimal misclassification proportion in stochastic block models.

Demonstrates competitive numerical results.

Provides a practical refinement procedure for community detection.

Abstract

Community detection is a fundamental statistical problem in network data analysis. Many algorithms have been proposed to tackle this problem. Most of these algorithms are not guaranteed to achieve the statistical optimality of the problem, while procedures that achieve information theoretic limits for general parameter spaces are not computationally tractable. In this paper, we present a computationally feasible two-stage method that achieves optimal statistical performance in misclassification proportion for stochastic block model under weak regularity conditions. Our two-stage procedure consists of a generic refinement step that can take a wide range of weakly consistent community detection procedures as initializer, to which the refinement stage applies and outputs a community assignment achieving optimal misclassification proportion with high probability. The practical effectiveness of the new algorithm is demonstrated by competitive numerical results.