相关论文: Estimation of Covariance Matrices under Sparsity C…

In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet…

In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal…

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

We analyze a weighted Frobenius loss for approximating symmetric positive definite matrices in the context of preconditioning iterative solvers. Unlike the standard Frobenius norm, the weighted loss penalizes error components associated…

High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other $\ell_r$ norms. Motivated…

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all…

We study various constraints and conditions on the true coefficient vector and on the design matrix to establish non-asymptotic oracle inequalities for the prediction error, estimation accuracy and variable selection for the Lasso estimator…

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…

The problem of estimating a spiked covariance matrix in high dimensions under Frobenius loss, and the parallel problem of estimating the noise in spiked PCA is investigated. We propose an estimator of the noise parameter by minimizing an…

We propose a novel estimation approach for the covariance matrix based on the $l_1$-regularized approximate factor model. Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes…

We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…