Семинар HDI Lab: Optimal Estimation in Mixed-Membership Stochastic Block Model

Community detection is one of the central problems in modern network science. It has numerous applications in the analysis of social and biological networks, designing network protocols and many other areas. Recently, much attention has been paid to the detection of overlapping communities, where each node in a network may belong to multiple groups. We consider the parameter estimation problem in Mixed Membership Stochastic Block Model (MMSB), which is a quite general instance of a random graph model allowing for overlapping community structure. We discuss different approaches to parameter estimation in this model, their theoretical properties and practical performance. Finally, we propose an approach to improve over existing estimates that allows obtaining minimax optimal rates of estimation for all the model parameters.