Model selection and estimation in the Gaussian graphical model

By Ming Yuan, Yi Lin. 2007

1,878 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/20ee888ca9c3bae784f266405b4d6395c6f32955

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Citations in the corpus

New Insights and Faster Computations for the Graphical Lasso (2011, methodology): “Yuan and Lin (2007) proposed that rather than maximizing the log-likelihood (1.1), one should instead maximize the penalized log-likelihood over nonnegative deﬁnite matrices (cid”
Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications (2016, background): “In particular, motivation of this paper comes from the estimation and inference problems for large covariance matrix and its related functionals [55, 74, 64, 59, 73, 13, 10, 20, 21].”
The Graphical Horseshoe Estimator for Inverse Covariance Matrices (2017, background): “|) in Equation (1) can be taken with or without a penalty on the diagonal terms (Rothman et al. 2008; Meinshausen and Bühlmann 2006; Yuan and Lin 2007; Friedman, Hastie, and Tibshirani 2008).”
Sparse inverse covariance matrix estimation using quadratic approximation (2011, background): “For further details on the background of !1 regularization in the context of GMRFs, we refer the reader to [20, 2, 8, 15].”
Learning brain connectivity of Alzheimer’s disease by sparse inverse covariance estimation (2010, methodology): “(1) and achieve the SICE in recent years (Yuan and Lin, 2007; Friedman et al., 2007; Levina et al., 2008; Li and Gui, 2006), including a method by us (Sun et al.”
Fast alternating linearization methods for minimizing the sum of two convex functions (2009, neutral): “…covariance matrix from sample data by solving the following maximum likelihood problem with an ℓ 1 -regularization term, (see e.g., [3, 18, 49, 52]). max { log det( X ) − Σ , X − ρ X 1 } , or equivalently, min {− log det( X ) + Σ , X + ρ X 1 } , (1.7) where ρ > 0 and Σ ∈ S n + (the set of…”
Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation (2017, background): “tion is vast, so we cannot possibly give a complete coverage of it here; some influential papers include [32, 48, 19, 36, 9].”
Asymptotic normality and optimalities in estimation of large Gaussian graphical models (2013, background): “Yuan and Lin (2007) proposed to use the lasso penalty and studied its asymptotic properties when p is fixed. Ravikumar et al. (2011) derived the rate of convergence when the dimension p is high by applying a primal-dual witness”
Covariance Estimation: The GLM and Regularization Perspectives (2011, methodology): “has been redicovered recently by Dégerine and Lambert-Lacroix (2003), Kurowicka and Cooke (2003) and Joe (2006), but its origin can be traced to a notable and somewhat neglected paper of Yule (1907), equation (25).”
On the distribution of the adaptive LASSO estimator (2008, neutral): “…a variety of penalized maximum likelihood or related estimators (e.g., Bunea (2004), Bunea & McKeague (2005), Fan & Li (2002, 2004), Li & Liang (2007), Wang & Leng (2007), Wang, G. Li and Jiang (2007), Wang, G. Li and Tsai (2007), Wang, R. Li and Tsai (2007), Yuan & Lin (2007), Zhang & Lu (2007)).”
Covariance regularization by thresholding (2009, methodology): “The common approach of [5, 31, 35] is to add an L 1 (lasso) penalty on the entries of the concentration matrix to the normal likelihood, which results in shrinking some of the elements of the inverse to zero.”
A Critical Review of LASSO and Its Derivatives for Variable Selection Under Dependence Among Covariates (2020, methodology): “Besides, for consistent variable selection using ˆ S L 1 = { j : ˆ β L 1 j = 0 } , it turns out that the design matrix of the model, X , needs to satisfy some assumptions.”
Sparse and Locally Constant Gaussian Graphical Models (2009, methodology): “Second, since optimization methods for structure learning on Gaussian graphical models [5, 6, 4, 7] are unable to handle local constancy constraints, we propose an efficient algorithm by maximizing with respect to one row and column of the precision matrix at a time.”
Estimating Sparse Precision Matrix: Optimal Rates of Convergence and Adaptive Estimation (2012, background): “Yuan and Lin (2007) proposed an ℓ1 penalized normal likelihood estimator and studied its theoretical properties.”
Connecting the Dots: Identifying Network Structure via Graph Signal Processing (2018, methodology): “reasons, the neighborhood-based lasso method in [36] is computationally faster while the graphical lasso tends to be more (statistically) efficient [64].”
Regularized rank-based estimation of high-dimensional nonparanormal graphical models (2012, methodology): “Penalized likelihood methods have been studied for Gaussian graphical modeling [Yuan and Lin ( 2007)].”