UCLA

As technology advances, the manner in which humans communicate and collaborate becomes increasingly intricate and the study of complex networks becomes ever important. Exponential-family Random Graph Models (ERGMs) have long been at the forefront of the analysis of relational data due to their interpretability, flexibility, and strong theoretical foundation. However, ERGMs sometimes suffer from a serious condition known as degeneracy, in which the model exhibits unrealistic behavior or a severe lack-of-fit to the observed data if it can even be fit at all.

In an effort to overcome the issue of degeneracy, we take a variety of new approaches to network modeling and also build on the existing work of Fellows and Handcock (2017). We first consider several alternative models motivated by the maximization of various entropies or minimization of different divergence measures, as well as hierarchical models which expand on the ERG model. We derive their degenerate-inhibiting properties, but our analysis shows them ineffective for many purposes. Next, we provide an in-depth investigation of the Tapered ERGM and offer solutions to some related open questions, such as which terms to taper and how much. Several case studies are presented showing the effectiveness of the Tapered model and we derive some theoretical results. We also show, both theoretically and empirically, that the natural parameter estimates are largely numerically unaffected by the amount of tapering. We then extend the ideas behind the Tapered ERGM and generalize it as member of a class of so-called Restorative Force Models (RFMs), which disallow degeneracy through various constraints. A treatment of this general class of models is conducted, and we examine the properties of several types of RFMs such as the Stereo ERGM, MAD ERGM, and LogCosh ERGM.