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

• Gao, Chao ^[1] ; Ma, Zongming ^[2]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
  2. [2] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
• Localización: Statistical science, ISSN 0883-4237, Vol. 36, Nº. 1, 2021, págs. 16-33
• Idioma: inglés
• DOI: 10.1214/19-STS736
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.