Adaptive Thresholding for Sparse Covariance Matrix Estimation

Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covarianc...

Supplement to “Adaptive Thresholding for Sparse Covariance Matrix Estimation”

Adaptive Covariance Matrix Estimation through Block Thresholding

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collectio...

Iterative Thresholding Algorithm for Sparse Inverse Covariance Estimation

The `1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing `1-regularized covariance matrix estimation is presented. Although numerous algorithms have be...

ITERATIVE THRESHOLDING ALGORITHM FOR SPARSE INVERSE COVARIANCE ESTIMATION By

The `1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing `1-regularized covariance matrix estimation is presented. Although numerous algorithms have be...