hglasso swMATH ID: 11202 Software Authors: Tan, Kean Ming; London, Palma; Mohan, Karthik; Lee, Su-In; Fazel, Maryam; Witten, Daniela Description: hglasso: Learning graphical models with hubs: Implements the hub graphical lasso and hub covariance graph proposal by: Learning graphical models with hubs. We consider the problem of learning a high-dimensional graphical model in which there are a few hub nodes that are densely-connected to many other nodes. Many authors have studied the use of an ℓ 1 penalty in order to learn a sparse graph in the high-dimensional setting. However, the ℓ 1 penalty 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. Homepage: http://cran.r-project.org/web/packages/hglasso/index.html Source Code: https://github.com/cran/hglasso Dependencies: R Keywords: Gaussian graphical model; covariance graph; binary network; lasso; hub; alternating direction method of multipliers Related Software: glasso; R; MIM; glmnet; Julia; MatrixLMnet; sma; GitHub; data.table; R/qtl; selectiveInference; Mutoss; limma; MESS; fda (R); rare; PMA; QUIC; SCIP-SDP; Biq Mac Cited in: 12 Documents all top 5 Cited by 36 Authors 1 Bertsimas, Dimitris John 1 Chaudhuri, Sanjay 1 Fazel, Maryam 1 Fop, Michael 1 Fujisawa, Hironori 1 Guo, Xiao 1 Hirose, Kei-ichi 1 Kawano, Shuichi 1 Khalili, Abbas 1 Lamperski, Jourdain B. 1 Lee, Su-In 1 Lei, Jing 1 Liang, Jane W. 1 Liang, Yong 1 Liu, Han 1 Liu, Li 1 London, Palma 1 McGillivray, Annaliza 1 Michailidis, George C. 1 Mohan, Karthik 1 Murphy, Thomas Brendan 1 Ning, Yang 1 Ong, Meng Hwee Victor 1 Pauphilet, Jean 1 Roeder, Kathryn 1 Scrucca, Luca 1 Sen, Śaunak 1 Sese, Jun 1 Stephens, David A. 1 Tan, Kean Ming 1 Tarzanagh, Davoud Ataee 1 Turlach, Berwin A. 1 Wang, Yao 1 Witten, Daniela M. 1 Yang, Zhuoran 1 Zhang, Hai all top 5 Cited in 8 Serials 3 Journal of Machine Learning Research (JMLR) 2 Journal of Multivariate Analysis 2 The Annals of Applied Statistics 1 Computational Statistics 1 Journal of Statistical Computation and Simulation 1 Mathematical Programming. Series A. Series B 1 Advances in Data Analysis and Classification. ADAC 1 Statistics and Computing Cited in 5 Fields 12 Statistics (62-XX) 3 Operations research, mathematical programming (90-XX) 1 Combinatorics (05-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) Citations by Year