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We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models.
Regression shrinkage and selection via the lasso
R. Tibshirani · 1996
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On the distribution of the largest eigenvalue in principal components analysis
Iain M. Johnstone · 2001
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Optimal structure identification with greedy search
D.M. Chickering · 2002
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Least Angle Regression
B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani · 2004
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High-dimensional graphs and variable selection with the lasso
N. Meinshausen and P. Bühlmann · 2006
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The dantzig selector: Statistical estimation when p is much larger than n
E. Candes and T. Tao · 2007
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Model selection and estimation in the Gaussian graphical model
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First-order methods for sparse covariance selection
Alexandre d’Aspremont, Onureena Banerjee, and Laurent El Ghaoui · 2008
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Operator norm consistent estimation of large dimensional sparse covariance matrices
N. El Karoui · 2008
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Sparse inverse covariance estimation with the graphical lasso
J. Friedman, T. Hastie, and R. Tibshirani · 2008
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High-dimensional covariance estimation by minimizing l1-penalized log-determinant divergence
P. Ravikumar, G. Raskutti, M. J. Wainwright, and B. Yu · 2008
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Sparse permutation invariant covariance estimation
A. J. Rothman, P. J. Bickel, E. Levina, and J. Zhu · 2008
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On consistency and sparsity for principal components analysis in high dimensions
I. M. Johnstone and A. Y. Lu · 2009
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On the conditions used to prove oracle results for the lasso
S. van de Geer and P. Bühlmann · 2009
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High-dimensional Ising model selection using ℓ1-regularized logistic regression
Pradeep Ravikumar, Martin J Wainwright, John D Lafferty, et al · 2010
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High dimensional inverse covariance matrix estimation via linear programming
Ming Yuan · 2010
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Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming
A. Belloni, V. Chernozhukov, and L. Wang · 2011
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Statistics for high-dimensional data
P. Bühlmann and S. van de Geer · 2011
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Central Limit Theorems and Bootstrap in High Dimensions
V. Chernozhukov, D. Chetverikov, and K. Kato · 2014
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Confidence intervals for high-dimensional inverse covariance estimation
J. Janková and S. van de Geer · 2014
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Confidence intervals and hypothesis testing for high-dimensional regression
A. Javanmard and A. Montanari · 2014
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Identifiability of Gaussian structural equation models with equal error variances
J. Peters and P. Bühlmann · 2014
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On asymptotically optimal confidence regions and tests for high-dimensional models
S. van de Geer, P. Bühlmann, Y. Ritov, and R. Dezeure · 2014
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Berry-Esseen bounds for estimating undirected graphs
Larry Wasserman, Mladen Kolar, Alessandro Rinaldo, et al · 2014
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A constrained l1 minimization approach to sparse precision matrix estimation
T. Cai, W. Liu, and X. Luo · 2011
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Characterization and greedy learning of inter- ventional Markov equivalence classes of directed acyclic graphs
A. Hauser and P. Bühlmann · 2012
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The Graphical Lasso: New Insights and Alternatives
R. Mazumder and T. Hastie · 2012
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Sparse matrix inversion with scaled Lasso
T. Sun and C.-H. Zhang · 2012
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Gaussian graphical model estimation with false discovery rate control
Weidong Liu et al · 2013
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ℓ 0 \ell_{0} -penalized maximum likelihood for sparse directed acyclic graphs
S. van de Geer and P. Bühlmann · 2013
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Confidence intervals for low-dimensional parameters in high-dimensional linear models
C.-H. Zhang and S. S. Zhang · 2014
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Asymptotic normality and optimalities in estimation of large gaussian graphical models
Zhao Ren, Tingni Sun, Cun-Hui Zhang, Harrison H Zhou, et al · 2015
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Causality: Models, Reasoning and Inference
J. Pearl · 2016
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Estimation and Testing under Sparsity: École d’Été de Saint-Flour XLV
S. van de Geer · 2016
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Worst possible sub-directions in high-dimensional models
Sara van de Geer · 2016
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Statistical inference for pairwise graphical models using score matching
Ming Yu, Mladen Kolar, and Varun Gupta · 2016
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