High Dimensional Inverse Covariance Matrix Estimation via Linear Programming
High Dimensional Inverse Covariance Matrix Estimation via Linear Programming
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DOI：
10.5555/1756006.1859930
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发表时间：
2010-03
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影响因子：
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通讯作者：
M. Yuan
中科院分区：
文献类型：
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作者：
M. Yuan
本文考虑了高维逆协方差矩阵的估计问题，它可以很好地近似为“稀疏”矩阵。利用多元线性回归和逆协方差矩阵的条目之间的连接，我们提出了一个估计过程，可以有效地利用这种“稀疏性”。所提出的方法可以使用线性规划计算，因此有可能被用于非常高维的问题。对估计误差建立了几种算子范数的Oracle不等式，表明该方法对不同类型的稀疏性问题具有较好的适应性。
This paper considers the problem of estimating a high dimensional inverse covariance matrix that can be well approximated by "sparse" matrices. Taking advantage of the connection between multivariate linear regression and entries of the inverse covariance matrix, we propose an estimating procedure that can effectively exploit such "sparsity". The proposed method can be computed using linear programming and therefore has the potential to be used in very high dimensional problems. Oracle inequalities are established for the estimation error in terms of several operator norms, showing that the method is adaptive to different types of sparsity of the problem.