@inproceedings{94f2414c4f6c477eb3e040f4a763da05,
title = "System identification from partial samples: Non-asymptotic analysis",
abstract = "The problem of learning the parameters of a vector autoregressive (VAR) process from partial random measurements is considered. This setting arises due to missing data or data corrupted by multiplicative bounded noise. We present an estimator of the covariance matrix of the evolving state-vector from its partial noisy observations. We analyze the non-asymptotic behavior of this estimator and provide an upper bound for its convergence rate. This expression shows that the effect of partial observations on the first order convergence rate is equivalent to reducing the sample size to the average number of observations viewed, implying that our estimator is order-optimal. We then present and analyze two techniques to recover the VAR parameters from the estimated covariance matrix applicable in dense and in sparse high-dimensional settings. We demonstrate the applicability of our estimation techniques in joint state and system identification of a stable linear dynamic system with random inputs.",
keywords = "autoregressive processes, covariance estimation, high-dimensional analysis, robust estimation, system identification",
author = "Milind Rao and Alon Kipnis and Tara Javidi and Eldar, {Yonina C.} and Andrea Goldsmith",
note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 55th IEEE Conference on Decision and Control, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",
year = "2016",
month = dec,
day = "27",
doi = "10.1109/CDC.2016.7798707",
language = "English (US)",
series = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "2938--2944",
booktitle = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",
address = "United States",
}