TY - GEN
T1 - Estimating high-dimensional covariance matrices with misses for Kronecker product expansion models
AU - Zamanighomi, Mahdi
AU - Wang, Zhengdao
AU - Giannakis, Georgios B.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - We study the problem of high-dimensional covariance matrix estimation from partial observations. We consider covariance matrices modeled as Kronecker products of matrix factors, and rely on observations with missing values. In the absence of missing data, observation vectors are assumed to be i.i.d multivariate Gaussian. In particular, we propose a new procedure computationally affordable in high dimension to extend an existing permuted rank-penalized least-squares method to the case of missing data. Our approach is applicable to a large variety of missing data mechanisms, whether the process generating missing values is random or not, and does not require imputation techniques. We introduce a novel unbiased estimator and characterize its convergence rate to the true covariance matrix measured by the spectral norm of a permutation operator. We establish a tight outer bound on the square error of our estimate, and elucidate consequences of missing values on the estimation performance. Different schemes are compared by numerical simulations in order to test our proposed estimator.
AB - We study the problem of high-dimensional covariance matrix estimation from partial observations. We consider covariance matrices modeled as Kronecker products of matrix factors, and rely on observations with missing values. In the absence of missing data, observation vectors are assumed to be i.i.d multivariate Gaussian. In particular, we propose a new procedure computationally affordable in high dimension to extend an existing permuted rank-penalized least-squares method to the case of missing data. Our approach is applicable to a large variety of missing data mechanisms, whether the process generating missing values is random or not, and does not require imputation techniques. We introduce a novel unbiased estimator and characterize its convergence rate to the true covariance matrix measured by the spectral norm of a permutation operator. We establish a tight outer bound on the square error of our estimate, and elucidate consequences of missing values on the estimation performance. Different schemes are compared by numerical simulations in order to test our proposed estimator.
KW - Kronecker product
KW - covariance matrices
KW - high-dimensional
KW - missing data
UR - http://www.scopus.com/inward/record.url?scp=84973359524&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84973359524&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2016.7472161
DO - 10.1109/ICASSP.2016.7472161
M3 - Conference contribution
AN - SCOPUS:84973359524
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 2667
EP - 2671
BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Y2 - 20 March 2016 through 25 March 2016
ER -