Extensions to Exchangeability: Statistical Analysis of Network Data

This lecture explores extensions to exchangeability in the statistical analysis of network data. It covers the limitations of traditional exchangeability models, introduces the graphon Aldous-Hoover framework, and discusses edge exchangeability. The lecture delves into the construction of networks from point processes, the concept of graphex, and the geometry of networks using simplicial complexes. It concludes with a summary of non-parametric network models, clustering techniques, latent space models, and various network analysis methods.