mlsanityData to 14 Oct 2026

A Tutorial on the Non-Asymptotic Theory of System Identification

arXiv 2309.03873 ↗First posted 7 Sep 2023eess.SY cs.LG cs.SYcited by 26

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Abstract (arXiv)

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.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Builds on 21 of its 52 references that are in the map. First posted on arXiv 7 Sep 2023.

Builds on

21 of 52 references.

References · 21

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  3. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 78
  4. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  5. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  6. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  7. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  8. 2014Learning without Concentrationcited by 50
  9. 2020Learning nonlinear dynamical systems from a single trajectorycited by 46
  10. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
  11. 2015Learning with Square Loss: Localization through Offset Rademacher Complexitycited by 38
  12. 2020Active Learning for Identification of Linear Dynamical Systemscited by 33
9 more
  1. 2022Learning with little mixingcited by 33
  2. 2022Learning from many trajectoriescited by 24
  3. 2021Linear Systems can be Hard to Learncited by 20
  4. 2021Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systemscited by 17
  5. 2020Improved rates for prediction and identification of partially observed linear dynamical systemscited by 12
  6. 2019Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reductioncited by 9
  7. 2023The noise level in linear regression with dependent datacited by 6
  8. 2021Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systemscited by 4
  9. 2022A note on the smallest eigenvalue of the empirical covariance of causal Gaussian processescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 12; 2025: 6; 2026: 6.

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  1. 2024Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Losscited by 10
  2. 2024Active Learning for Control-Oriented Identification of Nonlinear Systemscited by 7
  3. 2023Nonasymptotic Regret Analysis of Adaptive Linear Quadratic Control with Model Misspecificationcited by 6
  4. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  5. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 5
  6. 2024Regret Analysis of Multi-task Representation Learning for Linear-Quadratic Adaptive Controlcited by 4
  7. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  8. 2024Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Methodcited by 3
  9. 2024Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samplescited by 2
  10. 2025Nonconvex Linear System Identification with Minimal State Representationcited by 2
  11. 2025LUCID: Learning-Enabled Uncertainty-Aware Certification of Stochastic Dynamical Systemscited by 2
  12. 2024Finite Sample Frequency Domain Identificationcited by 1
14 more
  1. 2024A least-square method for non-asymptotic identification in linear switching controlcited by 1
  2. 2024Finite-Sample Identification of Linear Regression Models with Residual-Permuted Sumscited by 1
  3. 2024Sample Complexity of the Sign-Perturbed Sums Methodcited by 1
  4. 2024End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic datacited by 1
  5. 2025Logarithmic Regret and Polynomial Scaling in Online Multi-step-ahead Predictioncited by 1
  6. 2026Optimistic Online LQR via Intrinsic Rewardscited by 1
  7. 2026Recovery Guarantees for Continual Learning of Dependent Tasks: Memory, Data-Dependent Regularization, and Data-Dependent Weightscited by 1
  8. 2023Estimation Sample Complexity of a Class of Nonlinear Continuous-time Systemscited by 0
  9. 2025Frequency Response Identification of Low-Order Systems: Finite-Sample Analysiscited by 0
  10. 2025Near-optimal Rank Adaptive Inference of High Dimensional Matricescited by 0
  11. 2026Online Learning for Supervisory Switching Controlcited by 0
  12. 2026CLT-Optimal Parameter Error Bounds for Linear System Identificationcited by 0
  13. 2026Two-Layer Linear Auto-Regressive Models Estimate Latent Statescited by 0
  14. 2026Learning Linear Systems under Heavy-Tailed Noise: A Non-Asymptotic Analysis from A Single Trajectorycited by 0