Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We...

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Veröffentlicht in:Journal of multivariate analysis. - 1998. - 135(2015) vom: 01. März, Seite 153-162
1. Verfasser: Liu, Weidong (VerfasserIn)
Weitere Verfasser: Luo, Xi
Format: Aufsatz
Sprache:English
Veröffentlicht: 2015
Zugriff auf das übergeordnete Werk:Journal of multivariate analysis
Schlagworte:Journal Article Adaptivity Convergence rates Coordinate descent Cross validation Gaussian graphical models Lasso
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520 |a This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset 
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650 4 |a Adaptivity 
650 4 |a Convergence rates 
650 4 |a Coordinate descent 
650 4 |a Cross validation 
650 4 |a Gaussian graphical models 
650 4 |a Lasso 
700 1 |a Luo, Xi  |e verfasserin  |4 aut 
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