Health Research and Policy

Abstract

DATE: November 8, 2012
TIME: 1:15 - 3:00 pm
LOCATION: Li Ka Shing Center for Learning (LKSC)
291 Campus Dr, Room LK 209
1:15 pm - 3:00 pm
TITLE: Structured Learning of Multiple Gaussian Graphical Models
SPEAKER: Daniela Witten
Assistant Professor, Department of Biostatistics, University of Washington

I will consider the task of estimating high-dimensional Gaussian graphical models (or networks) corresponding to a single set of nodes under several distinct conditions. In other words, I wish to estimate K distinct networks, each on the same set of variables. I assume that most aspects of the networks are shared, but that there are some structured differences between them. The goal is to exploit the similarity among the networks in order to obtain more accurate estimates of each individual network, as well as to identify the differences between the networks.

To begin, I will assume that network differences arise from edge perturbations. In this case, estimating the networks by maximizing the log likelihood subject to fused lasso or group lasso penalties on the differences between the precision matrices can lead to very good results. Next, I will discuss a more structured type of network difference that arises from node (rather than edge) perturbations. In order to estimate networks in this setting, I will present the "row-column overlap norm penalty", a type of overlapping group lasso penalty.

Finally, I will present an application of these network estimation techniques to a gene expression data set, in which the goal is to identify genes whose regulatory patterns are perturbed across various subtypes of brain cancer.

The work described is joint with Pei Wang, Su-In Lee, Maryam Fazel, and others.

Suggested readings:
Danaher, Wang, and Witten (2012) The joint graphical lasso for inverse covariance estimation across multiple classes. http://arxiv.org/abs/1111.0324

Guo, J., Levina, E., Michailidis, G. and Zhu, J. (2011) Joint estimation of multiple graphical models. Biometrika. 98(1): 1-15.

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