Addressing Issues of Degeneracy and Phase Transition in Exponential-Family Random Graph Models via Tapering
Open Access
Author:
Landon, Edward
Graduate Program:
Statistics
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 24, 2025
Committee Members:
David Hunter, Thesis Advisor/Co-Advisor Michael Schweinberger, Committee Member Runze Li, Professor in Charge/Director of Graduate Studies
Keywords:
ERGM maximum entropy Ising model bimodality maximum likelihood estimation
Abstract:
Network models are widely used to represent the connections and relationships between different entities, such as people or objects. Exponential-family random graph models (ERGMs) are a common way to model these relationships which arise from data such as social networks and are popular due to their flexibility and ease of implementation and interpretability by users. Some examples from this family of models are known to suffer from issues of degeneracy and intractability, related to the long-studied phenomenon known as phase transition. Recent research has offered a new solution to the issue of degeneracy in the form of the “Tapered ERGM” to control the variance of the models to mitigate the usual degeneracy behavior which forces an ERGM to place most probability mass near the empty and complete networks instead of networks exhibiting average behavior. In this thesis, we provide an overview of the issues that some ERGMs face and discuss the effects of tapering as a way to mitigate degeneracy. We also discuss ways to select the amount of tapering and present an applet to allow users to see the effects of the choice of tapering amount on a small-scale example in a hands-on and easy fashion across the entire range of realizable networks.
