Sparse and Low-Rank Covariance Matrix Estimation
Sparse and Low-Rank Covariance Matrix Estimation
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DOI：
10.1007/s40305-014-0058-7
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发表时间：
2015-06
影响因子：
1.4
通讯作者：
Shenglong Zhou;N. Xiu;Ziyan Luo;Lingchen Kong
中科院分区：
文献类型：
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作者：
Shenglong Zhou;N. Xiu;Ziyan Luo;Lingchen Kong
本文旨在从半确定总体协方差矩阵中获得一个同时稀疏的低秩估计量。我们首先受益于凸优化，它开发了范数惩罚以鼓励稀疏性和核范数以支持低秩性。对于所提出的估计量，我们在高概率下证明了在温和情况下估计率的Frobenius范数为$${\fancyscript{O}}\left({\sqrt{(s\log p)/n}}\right) $$阶，其中和分别表示非零条目的个数和总体协方差的维数，并表示样本容量。最后，提出了一种全局收敛的乘法器交替方向法来解决这一问题，并通过数值模拟说明了该方法的优点。
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops-norm penalty to encourage the sparsity and nuclear norm to favor the low-rank property. For the proposed estimator, we then prove that with high probability, the Frobenius norm of the estimation rate can be of order $${\fancyscript{O}}\left({\sqrt{(s\log p)/n}}\right) $$ under a mild case, wheresandpdenote the number of nonzero entries and the dimension of the population covariance, respectively andnnotes the sample capacity. Finally, an efficient alternating direction method of multipliers with global convergence is proposed to tackle this problem, and merits of the approach are also illustrated by practicing numerical simulations.