Abstract

Many types of stochastic block models (SBMs) have been proposed and used to model community structure in networks. In a social network, for example, these methods can reveal tightly-knit friend groups. Across the literature, these models variously appear in canonical and microcanonical, degree-corrected and non-degree corrected, assortative and non-assortative forms. When applied to the same network, variants of the model often yield markedly different groupings of nodes and so produce competing interpretations and predictions. We introduce a parametric model that directly generalizes many of these forms, allowing us to for instance interpolate between a non degree-corrected and a degree-corrected SBM. We discuss how the posterior distribution of the parameter that bridges these models not only reveals which endpoint better represents the network, but also itself measures something meaningful about the network, in this case the inequality of degrees within communities. While individual SBMs can identify interpretable groups of nodes under restricted assumptions, we demonstrate that in an unsupervised, purely data-driven sense (model evidence and predictive power), our generalized model routinely adjudicates between and out-performs existing SBM variants on real-world networks. This unified picture allows us to precisely identify the assumptions latent within each of these models and select between them as appropriate for empirical networks. 

About the speaker

Max is a Omidyar Postdoctoral Fellow at the Santa Fe Institute where he works on various problems in math, physics, and statistics related to network science. He aims to understand the mechanisms driving the formation of observed network structures and to explore the fundamental limits of what such methods can reveal. Max holds a B.A. in Physics from Princeton University and a Ph.D. in Physics from the University of Michigan.