A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity

2021/07/07 by Wu, Zeyu, Wang, Cheng, Liu, Weidong · 1 citation
#62H12 #62H22 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2107.02999

Abstract

In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We revisit the sparse column-wise inverse operator (SCIO) estimator \citeliu2015fast and derive its general error bounds under the weak sparsity condition. A unified framework is established to deal with various cases including the heavy-tailed data, the non-paranormal data, and the matrix variate data. These new methods can achieve the same convergence rates as the existing methods and can be implemented efficiently.

Cited by

• Graph Estimation Based on Neighborhood Selection for Matrix-variate Data

Related

• Robust Sparse Precision Matrix Estimation and its Application
• Estimation When Both Covariance And Precision Matrices Are Sparse
• Honest confidence regions and optimality in high-dimensional precision\n matrix estimation
• A greedy algorithm for sparse precision matrix approximation
• MARS: A second-order reduction algorithm for high-dimensional sparse precision matrices estimation