mlsanityData to 7 Oct 2026

Rate-Optimal Non-Asymptotics for the Quadratic Prediction Error Method

arXiv 2404.07937 ↗First posted 11 Apr 2024math.ST cs.LG cs.SYcited by 1

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Abstract (arXiv)

We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve the optimal rate for a wide range of problems, there have been no non-asymptotic results matching these optimal rates outside of a select few, typically linear, model classes. By leveraging modern tools from learning with dependent data, we provide the first rate-optimal non-asymptotic analysis of this method for our more general setting of nonlinearly parametrized model classes. Moreover, we show that our results can be applied to a particular class of identifiable AutoRegressive Moving Average (ARMA) models, resulting in the first optimal non-asymptotic rates for identification of ARMA models.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 14 of its 43 references that are in the map. First posted on arXiv 11 Apr 2024.

Builds on

14 of 43 references.

References · 14

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2020Active Learning for Nonlinear System Identification with Guaranteescited by 78
  3. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  4. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  5. 2022Statistical Learning Theory for Control: A Finite Sample Perspectivecited by 52
  6. 2020Learning nonlinear dynamical systems from a single trajectorycited by 46
  7. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
  8. 2015Learning with Square Loss: Localization through Offset Rademacher Complexitycited by 37
  9. 2022Learning with little mixingcited by 33
  10. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
  11. 2023A Tutorial on the Non-Asymptotic Theory of System Identificationcited by 26
  12. 2021Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systemscited by 17
2 more
  1. 2021On Empirical Risk Minimization with Dependent and Heavy-Tailed Datacited by 16
  2. 2024Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Losscited by 10

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Citing papers per year: 2025: 1.

1 paper.

  1. 2025Adaptive prediction theory combining offline and online learningcited by 0