A Tutorial on the Non-Asymptotic Theory of System Identification
Systems and Control
2024-06-18 v2 Machine Learning
Systems and Control
Machine Learning
Abstract
This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as the covering technique, the Hanson-Wright Inequality and the method of self-normalized martingales. We then employ these tools to give streamlined proofs of the performance of various least-squares based estimators for identifying the parameters in autoregressive models. We conclude by sketching out how the ideas presented herein can be extended to certain nonlinear identification problems.
Cite
@article{arxiv.2309.03873,
title = {A Tutorial on the Non-Asymptotic Theory of System Identification},
author = {Ingvar Ziemann and Anastasios Tsiamis and Bruce Lee and Yassir Jedra and Nikolai Matni and George J. Pappas},
journal= {arXiv preprint arXiv:2309.03873},
year = {2024}
}