Sparse and Low-Rank Covariance Matrix Estimation  

作　　者：Sheng-Long Zhou Nai-Hua Xiu Zi-Yan Luo Ling-Chen Kong 

机构地区：[1]Department of Applied Mathematics,Beijing Jiaotong University,Beijing 100044,China [2]State Key Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University,Beijing 100044,China

出　　处：《Journal of the Operations Research Society of China》2015年第2期231-250,共20页中国运筹学会会刊（英文）

基　　金：The work was supported in part by the National Natural Science Foundation of China(Nos.11431002,11171018,71271021,11301022).

摘　　要：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 l1-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 O(√((slgg p)/n))under a mild case,where s and p denote the number of nonzero entries and the dimension of the population covariance,respectively and n notes 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.

关 键 词：Covariance matrix Sparse and low-rank estimator Estimation rate Alternating direction method of multipliers 

分 类 号：O17[理学—数学]