title: Learning Graphical Models With Hubs.
abstract: We consider the problem of learning a high-dimensional graphical model in which there are a fewhubnodes that aredensely-connectedto many other nodes. Many authors have studied the use of anℓ1penalty in order to learn a sparse graph in the high-dimensional setting. However, theℓ1penalty implicitly assumes that each edge is equally likely and independent of all other edges. We propose a general framework to accommodate more realistic networks with hub nodes, using a convex formulation that involves a row-column overlap norm penalty. We apply this general framework to three widely-used probabilistic graphical models: the Gaussian graphical model, the covariance graph model, and the binary Ising model. An alternating direction method of multipliers algorithm is used to solve the corresponding convex optimization problems. On synthetic data, we demonstrate that our proposed framework outperforms competitors that do not explicitly model hub nodes. We illustrate our proposal on a webpage data set and a gene expression data set.
authors.affiliation: Department of Biostatistics, University of Washington, Seattle WA, 98195.
authors.forename: Kean Ming
authors.initials: KM
authors.lastname: Tan
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: Karthik
authors.initials: K
authors.lastname: Mohan
authors.affiliation: Department of Computer Science and Engineering, Genome Sciences, University of Washington, Seattle WA, 98195.
authors.forename: Su-In
authors.initials: SI
authors.lastname: Lee
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 Washington, Seattle, WA 98195.
authors.forename: Daniela
authors.initials: D
authors.lastname: Witten
keywords: Gaussian graphical model; alternating direction method of multipliers; binary network; covariance graph; hub; lasso