A Tutorial on the Non-Asymptotic Theory of System Identification
Ingvar Ziemann Anastasios Tsiamis Bruce Lee Yassir Jedra Nikolai Matni George J. Pappas
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.