In this paper, we estimate the high dimensional precision matrix under the weak sparsity condition where many entries are nearly zero. We study a Lasso-type method for high dimensional precision matrix estimation and derive general error bounds under the weak sparsity condition. The common irrepresentable condition is relaxed and the results are applicable to the weak sparse matrix. As applications, we study the precision matrix estimation for the heavy-tailed data, the non-paranormal data, and the matrix data with the Lasso-type method.

翻译：在本文中,我们估算了在微弱的宽度条件下,许多条目几乎为零的高维精度矩阵。我们研究了高维精度矩阵估算的激光索型方法,并在微弱的宽度条件下得出了一般误差界限。常见的不可代表性条件已经放松,结果适用于微弱的稀薄矩阵。作为应用,我们研究了重尾数据、非异常数据以及使用拉索型方法的矩阵数据的精确矩阵估算。