Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing

TL;DR

This paper reviews recent advances in understanding the fundamental limits and optimal algorithms for network analysis tasks like graphon estimation, community detection, and hypothesis testing, highlighting minimax rates and their underlying principles.

Contribution

It provides a comprehensive survey of minimax optimal rates and algorithms across key network analysis problems, linking them to broader statistical inference frameworks.

Findings

Summarizes state-of-the-art minimax rates for graphon estimation, community detection, and hypothesis testing.

Identifies general principles behind optimal procedures in network analysis.

Connects network analysis problems to broader statistical inference concepts.

Abstract

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.