Fundamental limits of community detection from multi-view data: multi-layer, dynamic and partially labeled block models

TL;DR

This paper establishes fundamental theoretical limits for community detection in multi-view, multilayer, dynamic, and partially labeled networks, providing thresholds, mutual information characterizations, and iterative algorithms.

Contribution

It introduces a unified framework for community detection thresholds across various complex network models and develops AMP-based algorithms for practical recovery.

Findings

Sharp detection thresholds for multilayer and dynamic models

Mutual information characterizations for partially labeled networks

Proposed iterative algorithms with numerical validation

Abstract

Multi-view data arises frequently in modern network analysis e.g. relations of multiple types among individuals in social network analysis, longitudinal measurements of interactions among observational units, annotated networks with noisy partial labeling of vertices etc. We study community detection in these disparate settings via a unified theoretical framework, and investigate the fundamental thresholds for community recovery. We characterize the mutual information between the data and the latent parameters, provided the degrees are sufficiently large. Based on this general result, (i) we derive a sharp threshold for community detection in an inhomogeneous multilayer block model \citep{chen2022global}, (ii) characterize a sharp threshold for weak recovery in a dynamic stochastic block model \citep{matias2017statistical}, and (iii) identify the limiting mutual information in an unbalanced partially labeled block model. Our first two results are derived modulo coordinate-wise convexity assumptions on specific functions -- we provide extensive numerical evidence for their correctness. Finally, we introduce iterative algorithms based on Approximate Message Passing for community detection in these problems.