New Insights and Faster Computations for the Graphical Lasso

By Daniela M. Witten, Jerome H. Friedman, Noah R. Simon. 2011

369 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2915ad9f44fca117e7e6f469432954c14c39f3bb

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Citations in the corpus

Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “A modified GLasso algorithm is proposed by Witten et al. (2011) to im- prove the speed from O(p3) to O(p2+ ∑m i=1 |Ci| 3 ) when the solution Ω̂λ is block diagonal with blocks C1, . . . , Cm, where |Ci| is the size of the ith block.”
Handbook of Big Data (2016, background): “26 is known as the graphical lasso and has been studied extensively from a computational (Friedman et al., 2007; d’Aspremont et al., 2008; Yuan, 2008; Boyd et al., 2010; Scheinberg et al., 2010; Hsieh et al., 2011; Witten et al., 2011; Mazumder and Hastie, 2012a; Tran-Dinh et al., 2015) and theoreti”
Structure Learning in Graphical Modeling (2016, methodology): “Recent implementations exploit that simply thresholding the sample covariance matrix S yields the connected components of ˆ G gl (Witten et al., 2011; Mazumder & Hastie, 2012a).”
Strong rules for discarding predictors in lasso-type problems (2010, methodology): “After this article was completed, a better screening rule for the graphical lasso was discovered by both Witten et al. (2011) and Mazumder & Hastie (2012) independently.”
The joint graphical lasso for inverse covariance estimation across multiple classes (2011, result): “Our results mirror recent improvements in algorithms for solving the graphical lasso problem (Witten et al., 2011; Mazumder and Hastie, 2012).”
Sparse inverse covariance matrix estimation using quadratic approximation (2011, methodology): “We note that when the solution has a block-diagonal structure as described in Mazumder and Hastie [2012], Witten et al. [2011], the ﬁxed / free set selection in QUIC can automatically identify this sparsity structure and avoid updates to the oﬀ-diagonal block elements.”