High Dimensional Inverse Covariance Matrix Estimation via Linear Programming

By Ming Yuan. Journal of machine learning research, 2010

455 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9a3edc623b5ffa7522ed8f37c01ce4b5125002ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Statistics and Probability

Citations in the corpus

A Nodewise Regression Approach to Estimating Large Portfolios (2016, methodology): “1 of Zhao et al. (2014). In the simulations that follow, we invert S̃ and use it in our global minimum variance and the Markowitz portfolios.”
Asymptotically Honest Confidence Regions for High Dimensional Parameters by the Desparsified Conservative Lasso (2014, unknown): “1 of Yuan (2010) we know that Θj,j = ( Σj,j − Σj,−jΣ −j,−jΣ−j,j )−1 and Θj,−j = − ( Σj,j − Σj,−jΣ −j,−jΣ−j,j )−1 Σj,−jΣ −1 −j,−j = −Θj,jΣj,−jΣ −j,−j Next, let Xj,i denote the ith element of Xj and X−j,i the ith element of X−j (recall the definition of Xj and X−j just prior to (15)).”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “Over the class HP(cn,p,M), the estimators proposed in Yuan (2010), Cai et al. (2011) and Cai et al. (2012) can be shown to attain the optimal rate under the spectral norm if the matrix 1 norm Mn,p is bounded.”
Feature Selection in High-Dimensional Classification (2013, background): “More recently, Mai et al. (2012) proposed a version of the sparse LDA based on an ℓ1-norm penalized least square formulation.”
Honest confidence regions and optimality in high-dimensional precision matrix estimation (2015, methodology): “The idea was ﬁrst introduced in Meinshausen and B¨uhlmann (2006) as neighbourhood selection for Gaussian graphical models and further studied in Yuan (2010), Cai et al. (2011) and Sun and Zhang (2012).”
Robust regression via mutivariate regression depth (2017, background): “A simple projection step discussed in [38] leads to a positive semidefinite estimator with the same error rate.”
High Dimensional Semiparametric Gaussian Copula Graphical Models (2012, methodology): “Other estimators have been studied based on the use of the Dantzig selector (the gDantzig selector of Yuan (2010)), or based on estimating a sparse precision matrix under constraints on ‖ΩΣ̂n − I‖∞ (the CLIME estimator of Cai et al. (2011)).”
An Overview on the Estimation of Large Covariance and Precision Matrices (2015, unknown): “For this, Yuan (2010) and Cai et al. (2011) propose the graphical Dantzig selector and CLIME respectively, which can be solved by linear programming.”
Global Testing and Large-Scale Multiple Testing for High-Dimensional Covariance Structures (2017, background): “…2015), Fan et al. (2013), and Vu and Lei (2013), and penalized regression for precision matrix estimation, Gaussian graphical models, and differential networks in Meinshausen and Bühlmann (2006), Yuan (2010), Cai et al. (2011), Sun and Zhang (2013), Zhao et al. (2014), and Ren et al. (2015).”
Structured sparsity through convex optimization (2011, methodology): “…regularization has become a popular tool, which benefits both from efficient algorithms (see, e.g., Efron et al., 2004; Beck and Teboulle, 2009; Yuan, 2010; Bach et al., 2012, and multiple references therein) and a well-developed theory for generalization properties and variable selection…”
Confidence intervals for high-dimensional inverse covariance estimation (2014, methodology): “rix . For reader’s convenience we discuss the results in more detail in Section1.3and appendixA. Further methodology on estimation of precision matrices in particular includes the regression approach [21,37,6] and [31] which uses a Lasso-type algorithm or Dantzig selector [7] to estimate each column”
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].”
Two‐sample test of high dimensional means under dependence (2014, background): “See, for example, Yuan and Lin (2007), Bickel and Levina (2008), Rothman et al. (2008), Ravikumar et al. (2008), Cai, Zhang and Zhou (2010), Yuan (2010), Cai and Liu (2011), Cai, Liu, and Luo (2011), and Cai and Yuan (2012).”