Signal Detection in Degree Corrected ERGMs

2021/08/20 by Yuanzhe Xu, Xu, Yuanzhe, Sumit Mukherjee +1 · 1 citation
Computer Science · #05C80 #62F03 #62F05 #Blind Source Separation Techniques #FOS: Mathematics #Neural Networks and Applications #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.2108.09255

openalex publication_date 2021/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study sparse signal detection problems in Degree Corrected Exponential Random Graph Models (ERGMs). We study the performance of two tests based on the conditionally centered sum of degrees and conditionally centered maximum of degrees, for a wide class of such ERGMs. The performance of these tests match the performance of the corresponding uncentered tests in the β model. Focusing on the degree corrected two star ERGM, we show that improved detection is possible at criticality using a test based on (unconditional) sum of degrees. In this setting we provide matching lower bounds in all parameter regimes, which is based on correlations estimates between degrees under the alternative, and of possible independent interest.

Citations

• An introduction to exponential random graph (p*) models for social networks

Cited by

• Minimax rates for sparse signal detection under correlation

Related

• Detection Thresholds for the β-Model on Sparse Graphs
• Degeneracy in sparse ERGMs with functions of degrees as sufficient statistics
• Testing Degree Corrections in Stochastic Block Models
• Statistics of the two-star ERGM
• Reproducing the first and second moments of empirical degree distributions