Fast and Adaptive Sparse Precision Matrix Estimation in High Dimensions

Abstract

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse Column-wise Inverse Operator, to address these two issues. We analyze an adaptive procedure based on cross validation, and establish its convergence rate under the Frobenius norm. The convergence rates under other matrix norms are also established. This method also enjoys the advantage of fast computation for large-scale problems, via a coordinate descent algorithm. Numerical merits are illustrated using both simulated and real datasets. In particular, it performs favorably on an HIV brain tissue dataset and an ADHD resting-state fMRI dataset.

Maintext: 24 pages. Supplement: 13 pages. R package scio implementing the proposed method is available on CRAN at https://cran.r-project.org/package=scio . Published in J of Multivariate Analysis at http://www.sciencedirect.com/science/article/pii/S0047259X14002607

References in corpus (7)

• Covariance regularization by thresholding
• Sparse permutation invariant covariance estimation
• The huge Package for High-dimensional Undirected Graph Estimation in R
• Optimal rates of convergence for covariance matrix estimation
• Network exploration via the adaptive LASSO and SCAD penalties
• Sparse Matrix Inversion with Scaled Lasso
• Adaptive Lasso for High Dimensional Regression and Gaussian Graphical Modeling

Cited by in corpus (16)

• Generalized Score Matching for Non-Negative Data
• Identification of oscillatory brain networks with Hidden Gaussian Graphical Spectral models of EEG/MEG
• PANDA: AdaPtive Noisy Data Augmentation for Regularization of Undirected Graphical Models
• Thresholded Adaptive Validation: Tuning the Graphical Lasso for Graph Recovery
• An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss
• Penalized Interaction Estimation for Ultrahigh Dimensional Quadratic Regression
• Generalized Score Matching for General Domains
• Estimating covariance and precision matrices along subspaces
• Causal Structural Learning Via Local Graphs
• High-dimensional Precision Matrix Estimation with a Known Graphical Structure
• A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity
• AdaPtive Noisy Data Augmentation (PANDA) for Simultaneous Construction of Multiple Graph Models
• On the inconsistency of ${\ell }_1$-penalised sparse precision matrix estimation
• MARS: A second-order reduction algorithm for high-dimensional sparse precision matrices estimation
• Differentially Private Precision Matrix Estimation
• A greedy algorithm for sparse precision matrix approximation