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Marginal Screening for Gaussian Graphical Models

Graphical models provide a framework for understanding the relationships among random variables. In the high-dimensional setting in which there are many variables relative to the number of observations, learning the conditional dependence relationships among the variables is notoriously difficult. In contrast, marginal dependence relationships are typically much easier to detect and quantify. Of course, the marginal and conditional dependence relationships are often quite different.

In this talk, I will consider a very simple question: in high dimensions and under multivariate normality, what price do we pay by considering the marginal dependence graph in settings where the conditional dependence graph is of interest? I will present a few lines of evidence in support of a simple claim: estimating the marginal dependence graph, and treating it as an estimate of the conditional dependence graph, might not be so bad.

This talk is based on joint work with Jerry Friedman (Stanford), Noah Simon (UW), and Shikai Luo and Rui Song (NC State).