mlsanityData to 14 Oct 2026

A Tutorial on Concentration Bounds for System Identification

arXiv 1906.11395 ↗First posted 27 Jun 2019math.OC cs.LG stat.MLcited by 19

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Abstract (arXiv)

We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both data-dependent and independent bounds on the learning rate.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 Jun 2019.

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Citing papers per year: 2021: 3; 2022: 2; 2023: 4; 2024: 7; 2025: 2; 2026: 1.

19 papers.

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  1. 2023Transformers as Algorithms: Generalization and Stability in In-context Learningcited by 222
  2. 2021Outside the Echo Chamber: Optimizing the Performative Riskcited by 96
  3. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 53
  4. 2024From Self-Attention to Markov Models: Unveiling the Dynamics of Generative Transformerscited by 34
  5. 2021Linear Systems can be Hard to Learncited by 20
  6. 2021Data-Driven Reachability Analysis from Noisy Datacited by 14
  7. 2022Learning to Control Linear Systems can be Hardcited by 11
  8. 2023Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inferencecited by 9
  9. 2023Learning Dynamical Systems by Leveraging Data from Similar Systemscited by 8
  10. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  11. 2025In-Context Learning of Linear Dynamical Systems with Transformers: Approximation Bounds and Depth-Separationcited by 4
  12. 2024Sample Complexity Bounds for Linear System Identification from a Finite Setcited by 3
7 more
  1. 2025A variational approach to dimension-free self-normalized concentrationcited by 2
  2. 2024End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic datacited by 1
  3. 2026Recovery Guarantees for Continual Learning of Dependent Tasks: Memory, Data-Dependent Regularization, and Data-Dependent Weightscited by 1
  4. 2023Estimation Sample Complexity of a Class of Nonlinear Continuous-time Systemscited by 0
  5. 2024Online Identification of Stochastic Continuous-Time Wiener Models Using Sampled Datacited by 0
  6. 2024Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problemcited by 0
  7. 2024Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systemscited by 0