Sparse inverse covariance estimation with the graphical lasso.

By Jerome H. Friedman, Trevor J. Hastie, Robert Tibshirani. 2008

3,087 citations recorded by the source corpus.

Subfields: Molecular Biology, Spectroscopy, Statistics and Probability

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Citations in the corpus

Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data (2016, positive): “By treating the set of variables observed at every location as a group, the use of group Lasso ensured that if a location is selected, all of the climate variables observed at that location will be used as relevant features.”
Inferring networks of diffusion and influence (2010, neutral): “Our work relates to static sparse graph estimation using graphical Lasso methods [Wain-wright et al. 2006; Schmidt et al. 2007; Friedman et al. 2008; Meinshausen and Buehlmann 2006], unsupervised structure network inference using kernel methods [Lippert et al. 2009], mutual information relevance…”
Regularization Paths for Generalized Linear Models via Coordinate Descent (2010, positive): “The graphical lasso (Friedman et al. 2008) for sparse covariance estimation and undirected graphs.”
Coordinate descent algorithms (2015, positive): “Friedman, Hastie, and Tibshirani [18] propose a block CD algorithm for estimating a sparse inverse covariance matrix, given a sample covariance matrix S and taking the variable in their formulation to be a modiﬁcation W of S , such that W − 1 is sparse.”
Stability selection (2008, positive): “There has been interest recently in using l1-penalties for model selection in Gaussian graphical models due to their computational efficiency for moderate and large graphs (Meinshausen and Bühlmann, 2006; Yuan and Lin, 2007; Friedman et al., 2008; Banerjee and El Ghaoui, 2008; Bickel and Levina, 200”
Sparse Overcomplete Word Vector Representations (2015, positive): “Our work builds on recent explorations of sparsity as a useful form of inductive bias in NLP and machine learning more broadly (Kazama and Tsu-jii, 2003; Goodman, 2004; Friedman et al., 2008; Glorot et al., 2011; Yogatama and Smith, 2014, inter alia ).”
On asymptotically optimal confidence regions and tests for high-dimensional models (2013, neutral): “We note that using, for example, the GLasso estimator of [19] for ̂ may not be optimal because with this choice a bound for ‖̂ ̂j − ej‖∞ is not readily available and this means we cannot directly derive desirable componentwise properties of the estimator b̂ in (5) as established in Section 2.”
Elliptical graphical modelling (2011, neutral): “Miyamura and Kano (2006) propose an alternative M-type estimation, and Finegold & Drton (arXiv:1009.3669) consider robustiﬁed versions of the graphical lasso by Friedman et al. (2008).”
High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence (2008, positive): “This makes the corresponding problem (11) easier to optimize, and has been taken advantage of by the optimization algorithms in [9, 11].”
Brain covariance selection: better individual functional connectivity models using population prior (2010, neutral): “Optimal solutions to this problem can be computed very efficiently in O ( p(3) ) time [15, 16, 17].”
Copulas in Machine Learning (2013, neutral): “Orthogonally, the graphical lasso (glasso) [13] employs similar sparsity constraints to facilitate high-dimensional estimation of undirected Gaussian graphical models.”
Tracking whole-brain connectivity dynamics in the resting state. (2014, positive): “Following the graphical LASSO method of Friedman et al. 2008, we placed a penalty on the L1 norm of the precision matrix to promote sparsity.”
Confidence intervals for high-dimensional inverse covariance estimation (2014, neutral): “The optimization problem corresponding to graphical Lasso is a convex optimization problem that can be solved with coordinate descent methods [10, 11] in polynomial time.”
Regularized M-estimators with nonconvexity: statistical and algorithmic theory for local optima (2013, neutral): “tries of Θ, and deﬁne Ω := Θ ∈ Rp×p| Θ = ΘT,Θ 0 . A host of statistical and algorithmic results have been established for the graphical Lasso in the case of Gaussian observations with an ℓ1-penalty [3, 8, 21, 25], and more recently for discrete-valued observations, as well [14]. In addition, a vers”
High Dimensional Semiparametric Gaussian Copula Graphical Models. (2012, neutral): “The computation of Spearman’s rho statistic only requires one sort of the data, which has complexity O ( n log n ).”
A million variables and more: the Fast Greedy Equivalence Search algorithm for learning high-dimensional graphical causal models, with an application to functional magnetic resonance images (2016, neutral): “Causal interpreta-51 tionsareusuallynotcorrectforMarkovRandomField(MRF) models, including those obtained for high dimensions by var-53 ious penalized inverse covariance methods such as GLASSO and LASSO [1,2], in part because like correlation graphs MRF graphs are undirected, and in the large sample ”
Fast alternating linearization methods for minimizing the sum of two convex functions (2009, neutral): “…inverse 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…”
So Many Variables: Joint Modeling in Community Ecology. (2015, neutral): “For example, graphical models assume that correlations are driven by a smaller network of key species interactions [48,49].”