Related papers: Robust Estimation of Sparse Precision Matrix using…
Cellwise outliers are widespread in data and traditional robust methods may fail when applied to datasets under such contamination. We propose a variable selection procedure, that uses a pairwise robust estimator to obtain an initial…
Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…
We propose Nodewise Loreg, a nodewise $L_0$-penalized regression method for estimating high-dimensional sparse precision matrices. We establish its asymptotic properties, including convergence rates, support recovery, and asymptotic…
In covariance matrix estimation, one of the challenges lies in finding a suitable model and an efficient estimation method. Two commonly used modelling approaches in the literature involve imposing linear restrictions on the covariance…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…
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…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…
Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…
We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene…
We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…