Robust sparse covariance estimation by thresholding Tyler’s M-estimator

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...

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...

Supplement to “Adaptive Thresholding for Sparse Covariance Matrix Estimation”

Sparse PCA via Covariance Thresholding

In sparse principal component analysis we are given noisy observations of a low-rank matrix of dimension n × p and seek to reconstruct it under additional sparsity assumptions. In particular, we assume here each of the principal components v1, . . . ,vr has at most s0 non-zero entries. We are particularly interested in the high dimensional regime wherein p is comparable to, or even much larger ...

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...