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Activity Number: 482 - Statistical Methods in the Analysis of High-Order Structural Data with Possible Structural Changes
Type: Invited
Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #300199
Title: Simultaneous Change Point Detection and Structure Recovery for High-Dimensional Gaussian Graphical Models
Author(s): Yufeng Liu*
Companies: University of North Carolina at Chapel Hill
Keywords: Change point detection; Gaussian graphical models; Neighborhood selection; Sparsity

Gaussian graphical models represent conditional dependence relationships among the associated variables. In the literature, a lot of research developments have been made for high dimensional Gaussian graphical models based on i.i.d observations. In some practical problems, the underlying graphical structure can undergo "some changes", and the methods designed for i.i.d cases are no longer applicable. In this talk, we investigate the problem of simultaneous change point identification and structure recovery in the context of high dimensional Gaussian graphical models with abrupt changes. To recover the graphical structure correctly, a data-driven thresholding procedure is introduced. We establish estimation consistency of the change point estimator, by allowing the number of nodes being much larger than the sample size. Furthermore it is shown that, in terms of structure recovery of Gaussian graphical models, the proposed procedure achieves model selection consistency and controls the number of false positives. The validity of our proposed method is justified via extensive numerical studies.

Authors who are presenting talks have a * after their name.

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