TY - GEN
T1 - Estimation in autoregressive processes with partial observations
AU - Rao, Milind
AU - Javidi, Tara
AU - Eldar, Yonina C.
AU - Goldsmith, Andrea
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/16
Y1 - 2017/6/16
N2 - We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented. More refined estimators, factoring in structural constraints on the covariance matrix such as sparsity, bandedness, sparsity of the inverse and low-rankness are then introduced that are particularly useful in the high-dimensional regime. These estimates are then used to perform system identification by estimating the state transition matrix with or without further structural assumptions. Non-asymptotic guarantees are presented for all estimators.
AB - We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented. More refined estimators, factoring in structural constraints on the covariance matrix such as sparsity, bandedness, sparsity of the inverse and low-rankness are then introduced that are particularly useful in the high-dimensional regime. These estimates are then used to perform system identification by estimating the state transition matrix with or without further structural assumptions. Non-asymptotic guarantees are presented for all estimators.
KW - autoregressive processes
KW - covariance estimation
KW - high-dimensional analysis
KW - robust estimation
KW - system identification
UR - http://www.scopus.com/inward/record.url?scp=85023755888&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85023755888&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2017.7952950
DO - 10.1109/ICASSP.2017.7952950
M3 - Conference contribution
AN - SCOPUS:85023755888
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4212
EP - 4216
BT - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Y2 - 5 March 2017 through 9 March 2017
ER -