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
Source Code:  https://github.com/cran/glasso
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; BDgraph; igraph; PRMLT; PMA; UCI-ml; pcalg; KEGG; FASTCLIME; scout; fda (R); CRAN
Cited in: 658 Documents

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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Cited by 1,387 Authors

9 Bühlmann, Peter
9 Liu, Han
8 Fan, Jianqing
8 Van de Geer, Sara Anna
7 Ghosal, Subhashis
7 Rothman, Adam J.
7 Shojaie, Ali
7 Xue, Lingzhou
6 Bhadra, Anindya
6 Li, Hongzhe
6 Li, Lexin
6 Liu, Yufeng
6 Pircalabelu, Eugen
6 Purutçuoğlu, Vilda
6 Wit, Ernst
6 Zhang, Hai
6 Zheng, Zemin
5 Baladandayuthapani, Veerabhadran
5 Cai, Tony Tony
5 Chen, Li-Pang
5 Deng, Xinwei
5 Guo, Xiao
5 Ma, Shuangge
5 Michailidis, George C.
5 Nott, David John
5 Shen, Xiaotong
5 Toh, Kim Chuan
5 Vannucci, Marina
5 Wainwright, Martin J.
5 Wasserman, Larry Alan
5 Zhang, Cun-Hui
5 Zou, Hui
4 Ağraz, Melih
4 Avagyan, Vahe
4 Banerjee, Sayantan
4 Datta, Jyotishka
4 Drovandi, Christopher C.
4 Kang, Jian
4 Khare, Kshitij
4 Kolar, Mladen
4 Kundu, Suprateek
4 Lafferty, John D.
4 Lim, Johan
4 Loh, Po-Ling
4 Lu, Junwei
4 Ma, Shiqian
4 Massam, Helene M.
4 Narisetty, Naveen Naidu
4 Pan, Wei
4 Sejnowski, Terrence J.
4 Tibshirani, Robert John
4 van Wieringen, Wessel N.
4 Vinciotti, Veronica
4 Yin, Jianxing
4 Zhang, Qingzhao
4 Zhou, Jia
4 Zhou, Shuheng
3 Abbruzzo, Antonino
3 Ambroise, Christophe
3 Aste, Tomaso
3 Augugliaro, Luigi
3 Bickel, Peter John
3 Boyd, Stephen Poythress
3 Castelletti, Federico
3 Chen, Zehua
3 Chiquet, Julien
3 Choi, Young-Geun
3 Claeskens, Gerda
3 Consonni, Guido
3 Das, Anup
3 Drton, Mathias
3 Eskandari, Farzad
3 Fan, Yingying
3 Feng, Yang
3 Forzani, Liliana
3 Gan, Lingrui
3 Gao, Xin
3 Giacometti, Rosella
3 Huang, Haiyan
3 Janková, Jana
3 Jin, Jiashun
3 Kang, Xiaoning
3 Kim, Inyoung
3 Lee, Wonyul
3 Levina, Elizaveta
3 Li, Bing
3 Li, Daoji
3 Liang, Feng
3 Liu, Weidong
3 Mai, Qing
3 Mallick, Bani K.
3 Mazumder, Rahul
3 Molstad, Aaron J.
3 Müller, Samuel
3 Oates, Chris J.
3 Paterlini, Sandra
3 Peterson, Christine B.
3 Pourahmadi, Mohsen
3 Qiu, Yumou
3 Rajaratnam, Bala
...and 1,287 more Authors
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Cited in 134 Serials

47 Computational Statistics and Data Analysis
41 Journal of the American Statistical Association
41 Electronic Journal of Statistics
33 The Annals of Statistics
33 Journal of Multivariate Analysis
30 The Annals of Applied Statistics
29 Journal of Computational and Graphical Statistics
21 Journal of Machine Learning Research (JMLR)
19 Biometrics
19 Statistics and Computing
17 Bayesian Analysis
14 Journal of Statistical Computation and Simulation
11 Neural Computation
10 Journal of Statistical Planning and Inference
10 Machine Learning
10 Communications in Statistics. Simulation and Computation
9 Test
8 Computational Statistics
8 Mathematical Programming. Series A. Series B
7 Annals of the Institute of Statistical Mathematics
7 Statistics & Probability Letters
7 Statistical Analysis and Data Mining
6 Journal of Econometrics
6 European Journal of Operational Research
6 Journal of Applied Statistics
5 Statistical Science
5 Neural Networks
5 Communications in Statistics. Theory and Methods
5 Linear Algebra and its Applications
5 Statistical Methods and Applications
4 The Canadian Journal of Statistics
4 Psychometrika
4 Bernoulli
4 Mathematical Problems in Engineering
4 Statistical Applications in Genetics and Molecular Biology
4 Statistics Surveys
3 Automatica
3 Biometrical Journal
3 Journal of Classification
3 Journal of Scientific Computing
3 Annals of Operations Research
3 SIAM Journal on Optimization
3 Computational Optimization and Applications
3 SIAM Journal on Scientific Computing
3 Statistical Modelling
3 Journal of the Korean Statistical Society
3 Advances in Data Analysis and Classification. ADAC
3 Journal of Agricultural, Biological, and Environmental Statistics
2 Inverse Problems
2 Journal of the Franklin Institute
2 Metrika
2 Scandinavian Journal of Statistics
2 Information Sciences
2 International Statistical Review
2 Journal of Optimization Theory and Applications
2 Econometric Reviews
2 SIAM Journal on Matrix Analysis and Applications
2 International Journal of Computer Mathematics
2 Statistical Papers
2 Statistica Sinica
2 INFORMS Journal on Computing
2 Mathematical Methods of Operations Research
2 Australian & New Zealand Journal of Statistics
2 Acta Mathematica Sinica. English Series
2 Optimization and Engineering
2 Quantitative Finance
2 Journal of Statistical Mechanics: Theory and Experiment
2 Computational & Mathematical Methods in Medicine
2 Journal of Statistical Theory and Practice
2 Science China. Mathematics
2 Sankhyā. Series A
2 Journal of the Japan Statistical Society. Japanese Issue
2 Japanese Journal of Statistics and Data Science
2 Statistical Theory and Related Fields
2 SIAM Journal on Mathematics of Data Science
1 Computers & Mathematics with Applications
1 Journal of Fluid Mechanics
1 Journal of Computer and System Sciences
1 Kybernetika
1 Mathematics and Computers in Simulation
1 Mathematics of Operations Research
1 Operations Research
1 Quarterly of Applied Mathematics
1 Statistica Neerlandica
1 Acta Mathematicae Applicatae Sinica
1 Journal of Computational Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Statistics
1 Chinese Journal of Applied Probability and Statistics
1 Probability Theory and Related Fields
1 International Journal of Approximate Reasoning
1 Journal of Economic Dynamics & Control
1 Multidimensional Systems and Signal Processing
1 Journal of Global Optimization
1 Computational Mathematics and Mathematical Physics
1 Applied Mathematical Modelling
1 Pattern Recognition
1 International Journal of Computer Vision
1 Journal of Computational Neuroscience
...and 34 more Serials

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