Selection and Estimation for Mixed Graphical Models

• Activity Number: 474
• Type: Invited
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: WNAR
• Author(s): Daniela Witten*+ and Ali Shojaie and Shizhe Chen
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: Gaussian graphical model ; covariance graph ; binary network ; lasso ; hub

Abstract

We consider the problem of estimating a pairwise graphical model in which the nodes are of different types. In particular, we assume that each node, conditioned on all of the other nodes, has a distribution that is in the exponential family. To begin, we identify restrictions on the parameter space required for the existence of a well-defined joint density in this setting. Next we establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our theoretical results, we investigate the selection of edges between nodes of two different types, and show that efficiency can be gained if edge estimates obtained from the regressions of particular node types are used to reconstruct the graph. These results are illustrated with examples of Gaussian, binary, Poisson, and exponential distributions. Our theoretical findings are corroborated by evidence from simulation studies. We apply the proposed method and competing approaches to a yeast eQTL data set consisting of gene expression and DNA sequence data.