Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the dimensionality increases. In this work, we propose robust estimation of the inverse covariance matrix based on an $l_1$ regularized objective function with a weighted sample covariance matrix. The robustness of the proposed objective function can be justified by a nonparametric technique of the integrated squared error criterion. To address the non-convexity of the objective function, we develop an efficient algorithm in a similar spirit of majorization-minimization. Asymptotic consistency of the proposed estimator is also established. The performance of the proposed method is compared with several existing approaches via numerical simulations. We further demonstrate the merits of the proposed method with application in genetic network inference.

翻译：精确矩阵(即逆共变矩阵)的估算被广泛用于利用连续变量之间的有条件独立性。随着维度的提高,异常观测的影响在高维环境中会加剧。在这项工作中,我们提议以加权样本共变矩阵,以1美元固定目标函数为基础,对反共变矩阵进行强有力的估计。拟议目标功能的强性可以用综合正方差标准的非参数技术来证明。为了解决目标功能的非共性,我们以类似主要化-最小化精神发展一种有效的算法。还确定了拟议估算器的单一一致性。通过数字模拟,将拟议方法的性能与若干现有方法进行比较。我们进一步展示了拟议方法在基因网络推断中应用的优点。