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Title: Community detection and goodness of fit tests in random graph models: a probabilistic approach Authors:  Anirban Bhattacharya - Texas AM University (United States)
Debdeep Pati - Texas A&M University (United States) [presenting]
Junxian Geng - Florida State University (United States)
Abstract: In this talk, I focus on two key problems in random graph models models. The first part of the talk deals with clustering the nodes of a network into groups which share a similar connectivity pattern. Existing algorithms for community detection assume the knowledge of the number of clusters or estimate it a priori using various selection criteria and subsequently estimate the community structure. Ignoring the uncertainty in the first stage may lead to erroneous clustering, particularly when the community structure is vague. I instead propose a coherent probabilistic framework for simultaneous estimation of the number of communities and the community structure. The methodology is shown to outperform recently developed community detection algorithms in a variety of synthetic data examples and in recovering activation regions from brain connectivity matrices. In addition, I derive minimax optimal bounds for the Bayes risk, which is novel in the Bayesian context to best of my knowledge. In the second part of the talk, I focus on deriving goodness of fit tests when the number of communities is unknown. The test relies on algebraic geometric techniques, which can potentially be generalized to construct goodness of fit tests in latent class models.