Debdeep Pati ColloquiumThursday, September 22, 2016 - 2:45pm
Statistics Department Colloquium
Where: LeConte College, Room 210
Speaker: Debdeep Pati
Affiliation: Florida State University, Department of Statistics
Title: Bayesian community detection and goodness of fit tests in stochastic block models
In this talk, I focus on two key problems in Bayesian network 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 (MFM-SBM) 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 benchmark real-datasets. 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.
Debdeep Pati Colloquium.pdf