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.

中文翻译：

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高维快速自适应稀疏精度矩阵估计


本文提出了一种在高维环境下估计稀疏精度矩阵的新方法。研究这个问题的快速计算和自适应过程已经很流行。我们提出了一种称为稀疏列逆运算符的新颖方法来解决这两个问题。我们分析了基于交叉验证的自适应过程，并在 Frobenius 范数下建立了其收敛速度。还建立了其他矩阵范数下的收敛率。该方法还具有通过坐标下降算法快速计算大规模问题的优点。使用模拟和真实数据集说明了数值优点。特别是，它在 HIV 脑组织数据集和 ADHD 静息态 fMRI 数据集上表现良好。