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Activity Number: 366
Type: Invited
Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract #310811
Title: Sure Independence Screening for Gaussian Graphical Models
Author(s): Shikai Luo and Daniela Witten and Rui Song*+
Companies: North Carolina State University and University of Washington and North Carolina State University
Keywords: Sure Independence Screening ; Gaussian Graphical Models ; Covariance Matrix ; Precision Matrix
Abstract:

In high-dimensional genomic studies, it is of interest to understand the regulatory network underlying tens of thousands of genes based on hundreds or at most thousands of observations for which gene expression data is available. Because graphical models can identify how variables, such as the coexpresion of genes, are related, they are frequently used to study genetic networks. Although various efficient algorithms have been proposed, statisticians still face huge computational challenges when the number of variables is in tens of thousands of dimensions or higher. Motivated by the fact that the columns of the precision matrix can be obtained by solving $p$ regression problems, each of which involves regressing that feature onto the remaining $p-1$ features, we consider covariance screening for Gaussian graphical models. The proposed methods and algorithms possess theoretical properties such as sure screening properties and satisfactory empirical behavior.


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