Related papers: Non-asymptotic error controlled sparse high dimens…
Iterative methods for fitting a Gaussian Random Field (GRF) model via maximum likelihood (ML) estimation requires solving a nonconvex optimization problem. The problem is aggravated for anisotropic GRFs where the number of covariance…
Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…
The effectiveness of using model sparsity as a priori information when solving linear inverse problems is studied. We investigate the reconstruction quality of such a method in the non-idealized case and compute some typical recovery errors…
Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
Gaussian graphical models emerge in a wide range of fields. They model the statistical relationships between variables as a graph, where an edge between two variables indicates conditional dependence. Unfortunately, well-established…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
Matrix completion aims to estimate missing entries in a data matrix, using the assumption of a low-complexity structure (e.g., low rank) so that imputation is possible. While many effective estimation algorithms exist in the literature,…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…
Sparse linear regression is one of the classic problems in the field of statistics, which has deep connections and high intersections with optimization, computation, and machine learning. To address the effective handling of…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…
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 a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…