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Abstract Details

Activity Number: 481
Type: Invited
Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
Sponsor: WNAR
Abstract - #303473
Title: Fast Graphical Model Estimation and Its Applications
Author(s): Daniela Witten*+
Companies: University of Washington
Address: Biostatistics Department, University of Washington, Seattle, WA, 98195,
Keywords: graphical lasso ; graphical model ; convexity ; high-dimensional
Abstract:

The graphical lasso, recently proposed for Gaussian graphical modeling in high dimensions, involves estimating an inverse covariance matrix under a multivariate normal model by maximizing the L1-penalized log likelihood. I will begin by presenting a very simple but previously unknown necessary and sufficient condition that can be used to identify the connected components in the graphical lasso solution. This condition can be used to achieve massive computational gains: computing the graphical lasso solution with 20,000 features now takes minutes on a standard desktop machine, whereas previously the computations were prohibitive. This opens up new doors for rigorous network analysis of high-dimensional biological data. As a specific example, I will discuss estimation of graphical models under distinct biological conditions, in which we expect some, but not all, aspects of the networks to differ between conditions. An extension of the necessary and sufficient condition developed for the graphical lasso allows for extremely fast network estimation in this setting. Parts of this work are joint with J Friedman, N Simon, P Wang, and P Danaher.


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