Understanding Exponential Random Network Models

Abstract

Graphs and Networks seem to be everywhere nowadays. Naturally, statisticians and mathematicians have introduced a host of models to work with this kind of data. One surprise: Even simple models lead to intractable estimation and testing problems. In joint work with Sourav Chatterjee, we have harnessed 'graph limit theory' to help explain the findings of social and computer scientists in this area. This in turn leads to strange, infinite dimensional, non-convex optimization problems, even for simple models such as the 'edge-triangle' model. I will explain the models and background from the beginning and ask for help with the many open problems.