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

Zeyu Wu; Cheng Wang; Weidong Liu

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arXiv · 2107.02999

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

Zeyu Wu·Cheng Wang·Weidong Liu

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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 \cite{liu2015fast} 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.

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Zeyu Wu, Cheng Wang, Weidong Liu. 2021-07-07. A unified precision matrix estimation framework via sparse column-wise inverse operator under weak sparsity. https://arxiv.org/abs/2107.02999

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