Community Detection: Fundamental Limits, Methodology, and Variational Inference

Abstract

Network analysis has become one of the most active research areas over the past few years. A core problem in network analysis is community detection. In this thesis, we investigate it under Stochastic Block Model and Degree-corrected Block Model from three different perspectives: 1) the minimax rates of community detection problem, 2) rate-optimal and computationally feasible algorithms, and 3) computational and theoretical guarantees of variational inference for community detection.