Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose a novel methodology for estimating such matrices while controlling the false positive rate, percentage of matrix entries incorrectly chosen to be non-zero. We specifically focus on false positive rates tending towards zero with finite sample guarantees. This methodology is distribution free, but is particularly applicable to the problem of Gaussian network recovery. We also consider applications to constructing gene networks in genomics data.

中文翻译：

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非渐近误差控制的稀疏高维精度矩阵估计

高维精度矩阵的估计是许多统计领域的关键问题，包括高斯图形模型和高维数据推理。在稀疏性的结构假设下工作，我们提出了一种新的方法来估计此类矩阵，同时控制误报率、错误选择为非零的矩阵条目的百分比。我们特别关注在有限样本保证下趋于零的误报率。这种方法是免费分发的，但特别适用于高斯网络恢复问题。我们还考虑在基因组数据中构建基因网络的应用。