Robust High-Dimensional Precision Matrix Estimation

Approaches to High-Dimensional Covariance and Precision Matrix Estimation

An R Package flare for High Dimensional Linear Regression and Precision Matrix Estimation

This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, `q Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation (TIGER and CLIME). These methods exploit different nonsmooth loss functions to gain modeling flexibility, estimation robustness, and tuning insensitiveness. The devel...

The flare package for high dimensional linear regression and precision matrix estimation in R

This paper describes an R package named flare, which implements a family of new high dimensional regression methods (LAD Lasso, SQRT Lasso, ℓ q Lasso, and Dantzig selector) and their extensions to sparse precision matrix estimation (TIGER and CLIME). These methods exploit different nonsmooth loss functions to gain modeling exibility, estimation robustness, and tuning insensitiveness. The develo...

Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates

We present a new estimator for precision matrix in high dimensional Gaussian graphical models. At the core of the proposed estimator is a collection of node-wise linear regression with nonconvex penalty. In contrast to existing estimators for Gaussian graphical models with O(s √ log d/n) estimation error bound in terms of spectral norm, where s is the maximum degree of a graph, the proposed est...

High Dimensional Multivariate Regression and Precision Matrix Estimation via Nonconvex Optimization

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the nonconvex estimator, and it attains a linear rate of convergence to the true regression coefficients and precision matrix simultaneously, up to the statistical ...