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glasso

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
2012
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Referenced by 1,102 Authors

9 Bühlmann, Peter
9 Liu, Han
8 Fan, Jianqing
8 Van de Geer, Sara Anna
6 Ghosal, Subhashis
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
5 Xue, Lingzhou
5 Zhang, Cun-Hui
4 Ağraz, Melih
4 Bhadra, Anindya
4 Deng, Xinwei
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
3 Augugliaro, Luigi
3 Avagyan, Vahe
3 Banerjee, Sayantan
3 Bickel, Peter John
3 Chen, Zehua
3 Chiquet, Julien
3 Choi, Young-Geun
3 Das, Anup
3 Fan, Yingying
3 Forzani, Liliana
3 Gan, Lingrui
3 Giacometti, Rosella
3 Huang, Haiyan
3 Janková, Jana
3 Jin, Jiashun
3 Khare, Kshitij
3 Kim, Inyoung
3 Lee, Wonyul
3 Levina, Elizaveta
3 Li, Daoji
3 Li, Lexin
3 Liang, Feng
3 Liu, Weidong
3 Lu, Junwei
3 Ma, Shuangge
3 Mallick, Bani K.
3 Mazumder, Rahul
3 Oates, Chris J.
3 Pircalabelu, Eugen
3 Rajaratnam, Bala
3 Ren, Zhao
3 Rütimann, Philipp
3 Scheinberg, Katya
3 Shan, Liang
3 Sun, Will Wei
3 Taylor, Jonathan E.
3 Torri, Gabriele
3 Vannucci, Marina
3 Wang, Weichen
3 Wang, Ying Xiang Rachel
3 Wegkamp, Marten H.
3 Yuan, Ming
3 Zhang, Hai
3 Zhang, Ning
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3 Zhang, Xinsheng
3 Zhou, Harrison H.
3 Zhou, Shuheng
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3 Zou, Hui
2 Adragni, Kofi Placid
2 Akaho, Shotaro
2 Al-Najjar, Elias
2 An, Ziwen
2 Aste, Tomaso
2 Ayyıldız, Ezgi
2 Bai, Jianchao
2 Bazhenov, Maxim
...and 1,002 more Authors
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Referenced in 118 Serials

41 Computational Statistics and Data Analysis
37 Electronic Journal of Statistics
30 The Annals of Statistics
28 Journal of Multivariate Analysis
25 Journal of Computational and Graphical Statistics
23 Journal of the American Statistical Association
21 The Annals of Applied Statistics
20 Journal of Machine Learning Research (JMLR)
16 Statistics and Computing
13 Bayesian Analysis
11 Neural Computation
11 Journal of Statistical Computation and Simulation
10 Communications in Statistics. Simulation and Computation
9 Journal of Statistical Planning and Inference
8 Mathematical Programming. Series A. Series B
7 Statistics & Probability Letters
7 Machine Learning
7 Test
7 Statistical Analysis and Data Mining
6 Computational Statistics
6 European Journal of Operational Research
5 Annals of the Institute of Statistical Mathematics
5 Statistical Science
5 Journal of Applied Statistics
5 Statistical Methods and Applications
4 Psychometrika
4 Journal of Econometrics
4 Communications in Statistics. Theory and Methods
4 Linear Algebra and its Applications
4 Mathematical Problems in Engineering
4 Statistical Applications in Genetics and Molecular Biology
3 Automatica
3 Journal of Scientific Computing
3 Neural Networks
3 Annals of Operations Research
3 Computational Optimization and Applications
3 SIAM Journal on Scientific Computing
3 Bernoulli
3 Statistical Modelling
3 Advances in Data Analysis and Classification. ADAC
3 Statistics Surveys
2 The Canadian Journal of Statistics
2 Inverse Problems
2 Metrika
2 Biometrical Journal
2 Biometrics
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 SIAM Journal on Optimization
2 INFORMS Journal on Computing
2 Acta Mathematica Sinica. English Series
2 Quantitative Finance
2 Journal of Statistical Mechanics: Theory and Experiment
2 Journal of the Korean Statistical Society
2 Computational & Mathematical Methods in Medicine
2 Journal of Statistical Theory and Practice
2 Science China. Mathematics
2 Journal of Agricultural, Biological, and Environmental Statistics
2 Sankhyā. Series A
2 Japanese Journal of Statistics and Data Science
1 Computers & Mathematics with Applications
1 Journal of Fluid Mechanics
1 Scandinavian Journal of Statistics
1 BIT
1 Information Sciences
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 Journal of Computational Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
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 Pattern Recognition
1 Statistical Papers
1 International Journal of Computer Vision
1 Statistica Sinica
1 Journal of Computational Neuroscience
1 Annals of Mathematics and Artificial Intelligence
1 Complexity
1 Journal of Nonparametric Statistics
1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
1 Mathematical Methods of Operations Research
1 Australian & New Zealand Journal of Statistics
1 Data Mining and Knowledge Discovery
1 Journal of the Royal Statistical Society. Series B. Statistical Methodology
1 CEJOR. Central European Journal of Operations Research
1 Optimization and Engineering
1 Biostatistics
1 Brazilian Journal of Probability and Statistics
1 Foundations of Computational Mathematics
1 International Journal of Wavelets, Multiresolution and Information Processing
...and 18 more Serials

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