swMATH ID: 7432
Software Authors: Mazumder, Rahul; Hastie, Trevor; J. Friedman, T.; R. Tibshirani
Description: The graphical lasso: new insights and alternatives. The graphical lasso [5] is an algorithm for learning the structure in an undirected Gaussian graphical model, using ℓ 1 regularization to control the number of zeros in the precision matrix Θ=Σ -1 [2, 11]. The R package glasso [5] is popular, fast, and allows one to efficiently build a path of models for different values of the tuning parameter. Convergence of glasso can be tricky; the converged precision matrix might not be the inverse of the estimated covariance, and occasionally it fails to converge with warm starts. In this paper we explain this behavior, and propose new algorithms that appear to outperform glasso. By studying the “normal equations” we see that, glasso is solving the dual of the graphical lasso penalized likelihood, by block coordinate ascent; a result which can also be found in [2]. In this dual, the target of estimation is Σ, the covariance matrix, rather than the precision matrix Θ. We propose similar primal algorithms p-glasso and dp-glasso, that also operate by block-coordinate descent, where Θ is the optimization target. We study all of these algorithms, and in particular different approaches to solving their coordinate sub-problems. We conclude that dp-glasso is superior from several points of view.
Homepage: http://cran.r-project.org/web/packages/glasso/index.html
Dependencies: R
Keywords: graphical lasso; sparse inverse covariance selection; precision matrix; convex analysis/optimization; positive definite matrices; sparsity; semidefinite programming
Related Software: R; glmnet; huge; ElemStatLearn; HdBCS; MIM; spcov; QUIC; TETRAD; PMA; igraph; PRMLT; UCI-ml; scout; pcalg; FASTCLIME; CRAN; sparsenet; KEGG; BDgraph
Referenced in: 524 Publications

Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
The graphical lasso: new insights and alternatives. Zbl 1295.62066
Mazumder, Rahul; Hastie, Trevor
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Referenced by 1,102 Authors

9 Bühlmann, Peter
9 Liu, Han
8 Fan, Jianqing
8 Van de Geer, Sara Anna
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6 Purutçuoğlu, Vilda
6 Rothman, Adam J.
6 Wit, Ernst C.
6 Zheng, Zemin
5 Baladandayuthapani, Veerabhadran
5 Li, Hongzhe
5 Liu, Yufeng
5 Nott, David John
5 Shojaie, Ali
5 Toh, Kim Chuan
5 Wainwright, Martin J.
5 Wasserman, Larry Alan
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4 Ağraz, Melih
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4 Drovandi, Christopher C.
4 Guo, Xiao
4 Kolar, Mladen
4 Lafferty, John D.
4 Lim, Johan
4 Loh, Po-Ling
4 Ma, Shiqian
4 Michailidis, George C.
4 Mukherjee, Sach
4 Narisetty, Naveen Naidu
4 Pan, Wei
4 Sejnowski, Terrence J.
4 Shen, Xiaotong
4 Tibshirani, Robert John
4 van Wieringen, Wessel N.
4 Vinciotti, Veronica
4 Yin, Jianxing
4 Zhou, Jia
3 Abbruzzo, Antonino
3 Ambroise, Christophe
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3 Bickel, Peter John
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3 Liu, Weidong
3 Lu, Junwei
3 Ma, Shuangge
3 Mallick, Bani K.
3 Mazumder, Rahul
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3 Pircalabelu, Eugen
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Referenced in 118 Serials

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