title: Node-Based Learning of Multiple Gaussian Graphical Models.
abstract: We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory networks on the basis of gene expression data containing heterogeneous samples, such as different disease states, multiple species, or different developmental stages. We assume that most aspects of the conditional dependence networks are shared, but that there are some structured differences between them. Rather than assuming that similarities and differences between networks are driven by individual edges, we take anode-basedapproach, which in many cases provides a more intuitive interpretation of the network differences. We consider estimation under two distinct assumptions: (1) differences between theKnetworks are due to individual nodes that areperturbedacross conditions, or (2) similarities among theKnetworks are due to the presence ofcommon hub nodesthat are shared across allKnetworks. Using arow-column overlap normpenalty function, we formulate two convex optimization problems that correspond to these two assumptions. We solve these problems using an alternating direction method of multipliers algorithm, and we derive a set of necessary and sufficient conditions that allows us to decompose the problem into independent subproblems so that our algorithm can be scaled to high-dimensional settings. Our proposal is illustrated on synthetic data, a webpage data set, and a brain cancer gene expression data set.
authors.affiliation: Department of Electrical Engineering, University of Washington, Seattle WA, 98195.
authors.forename: Karthik
authors.initials: K
authors.lastname: Mohan
authors.affiliation: Department of Electrical Engineering, University of Washington, Seattle WA, 98195.
authors.forename: Palma
authors.initials: P
authors.lastname: London
authors.affiliation: Department of Electrical Engineering, University of Washington, Seattle WA, 98195.
authors.forename: Maryam
authors.initials: M
authors.lastname: Fazel
authors.affiliation: Department of Biostatistics, University of Washingtonm, Seattle WA, 98195.
authors.forename: Daniela
authors.initials: D
authors.lastname: Witten
authors.affiliation: Departments of Computer Science and Engineering, Genome Sciences, University of Washington, Seattle WA, 98195.
authors.forename: Su-In
authors.initials: SI
authors.lastname: Lee
keywords: alternating direction method of multipliers; gene regulatory network; graphical model; lasso; multivariate normal; structured sparsity