Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing
It provides a comprehensive overview of fundamental limits and optimal algorithms in network analysis, connecting these problems to broader statistical inference, but it is incremental as it surveys existing literature rather than presenting new findings.
The paper surveys recent developments in minimax optimal rates for three fundamental network analysis problems: graphon estimation, community detection, and hypothesis testing, reviewing state-of-the-art results and general principles behind optimal procedures.
This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the literature followed by general principles behind the optimal procedures that lead to minimax estimation and testing. This allows us to connect problems in network analysis to other statistical inference problems from a general perspective.