A Generic Sample Splitting Approach for Refined Community Recovery in Stochastic Block Models

TL;DR

This paper introduces a versatile sample splitting method that refines community detection in stochastic block models, achieving exact recovery with high probability when node degrees are sufficiently large, and enhances existing algorithms.

Contribution

It presents a generic, simple refinement technique based on sample splitting that improves community recovery in stochastic block models, extending previous theoretical results.

Findings

Achieves exact community recovery with high probability for degrees of order log n or higher.

Simplifies and extends previous community detection methods.

Compatible with various existing algorithms for practical implementation.

Abstract

We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are of order $\log n$ or higher. Starting from a roughly correct community partition given by some conventional community recovery algorithm, this method refines the partition in a cross clustering step. Our results simplify and extend some of the previous work on exact community recovery, discovering the key role played by sample splitting. The proposed method is simple and can be implemented with many practical community recovery algorithms.