Identifiability and estimation of mixed membership stochastic blockmodels
He, Shishuang
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https://hdl.handle.net/2142/122228
Description
Title
Identifiability and estimation of mixed membership stochastic blockmodels
Author(s)
He, Shishuang
Issue Date
2023-11-30
Director of Research (if dissertation) or Advisor (if thesis)
Liang, Feng
Yang, Yun
Doctoral Committee Chair(s)
Liang, Feng
Yang, Yun
Committee Member(s)
Chen, Yuguo
Liu, Jingbo
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mixed membership stochastic blockmodels
Identifiability
Volume minimization
Sufficiently scattered
Volume-penalized integrated likelihood
Abstract
The Mixed Membership Stochastic Blockmodel (MMSB) is a widely used method for detecting overlapping communities in large network data. However, MMSB is known to be unidentifiable, which presents a challenge for practical use. Previous approaches to MMSB identifiability rely on pure nodes, or nodes belonging to only one community, which is often too restrictive for real-world applications. In this paper, we propose a new, less restrictive set of identifiability conditions for MMSB and introduce an estimator based on a specific integrated likelihood with a penalty for volume. Our proposed estimator is demonstrated to have desirable asymptotic properties and can be efficiently computed using an MCMC-EM algorithm. We illustrate the benefits of our method through simulation studies and real data applications.
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