Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor

Supplementary Material: Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factor

Sparse Estimation of Large Covariance Matrices via a Nested Lasso Penalty by Elizaveta Levina,1 Adam Rothman

The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, ...

Sparse Estimation of Large Covariance Matrices via a Nested Lasso Penalty

The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the bandwidth adaptively for each row of the Cholesky factor, using a novel penalty we call nested Lasso. This structure has more flexibility than regular banding, ...

A new approach to Cholesky-based covariance regularization in high dimensions

In this paper we propose a new regression interpretation of the Cholesky factor of the covariance matrix, as opposed to the well-known regression interpretation of the Cholesky factor of the inverse covariance, which leads to a new class of regularized covariance estimators suitable for high-dimensional problems. Regularizing the Cholesky factor of the covariance via this regression interpretat...

M ay 2 00 8 Estimation of Large Precision Matrices Through Block Penalization ∗

This paper focuses on exploring the sparsity of the inverse covariance matrix Σ −1 , or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky decomposition, and penalize each block of parameters using the L 2-norm instead of individual elements. We develop a one-step estimator, and prove an oracle property which cons...