Speaker: Yuzhou Gu

Affiliation:NYU Center for Data Science & Courant Institute

Title: Community detection in the hypergraph stochastic block model

Abstract:

Community detection is a fundamental problem in network
science, and its theoretical study has received significant attention
over the last decade. In this talk I will present some recent advances
on the community detection problem in sparse hypergraphs. In
particular, we determine the weak recovery threshold for the
hypergraph stochastic block model for a wide range of parameters. This
resolves conjectures made by physicists in the corresponding regimes
and has implications to phase transitions of random constraint
satisfaction problems. A key component in this study is to analyze the
behavior of information channels under repeated applications of the
belief propagation operator. We introduce a framework for performing
this analysis based on information-theoretical methods for channel
comparison. Along the way, we formulate a rigorous version of the
population dynamics algorithm, an approach commonly used in practice
but lacks theoretical guarantees.