Exact Recovery in the Data Block Model

TL;DR

This paper establishes a sharp threshold for exact community recovery in the Data Block Model, an extension of the stochastic block model with node data, and provides an efficient algorithm matching this threshold.

Contribution

We introduce the Chernoff--TV divergence to characterize the exact recovery threshold in the Data Block Model and develop an efficient algorithm that achieves this threshold.

Findings

Sharp phase transition for exact recovery in the DBM

Efficient algorithm matching the theoretical threshold

Simulations validate the theoretical results and benefits of node data

Abstract

Community detection in networks is a fundamental problem in machine learning and statistical inference, with applications in social networks, biological systems, and communication networks. The stochastic block model (SBM) serves as a canonical framework for studying community structure, and exact recovery, identifying the true communities with high probability, is a central theoretical question. While classical results characterize the phase transition for exact recovery based solely on graph connectivity, many real-world networks contain additional data, such as node attributes or labels. In this work, we study exact recovery in the Data Block Model (DBM), an SBM augmented with node-associated data, as formalized by Asadi, Abbe, and Verd\'{u} (2017). We introduce the Chernoff--TV divergence and use it to characterize a sharp exact recovery threshold for the DBM. We further provide an efficient algorithm that achieves this threshold, along with a matching converse result showing impossibility below the threshold. Finally, simulations validate our findings and demonstrate the benefits of incorporating vertex data as side information in community detection.