mlsanityData to 14 Oct 2026

PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models

arXiv 2212.14838 ↗First posted 30 Dec 2022stat.ML cs.LG math.DScited by 1

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Abstract (arXiv)

In this paper we derive a PAC-Bayesian-Like error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian-Like error bound for such systems, 3) discuss various consequences of this error bound.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 19 of its 50 references that are in the map. First posted on arXiv 30 Dec 2022.

Builds on

19 of 50 references.

References · 19

  1. 2017Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Datacited by 533
  2. 2021User-friendly introduction to PAC-Bayes boundscited by 239
  3. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  4. 2019A Primer on PAC-Bayesian Learningcited by 132
  5. 2015On the properties of variational approximations of Gibbs posteriorscited by 121
  6. 2020Naive Exploration is Optimal for Online LQRcited by 116
  7. 2016PAC-Bayesian Theory Meets Bayesian Inferencecited by 88
  8. 2019Data-dependent Sample Complexity of Deep Neural Networks via Lipschitz Augmentationcited by 71
  9. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  10. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  11. 2016Simpler PAC-Bayesian Bounds for Hostile Datacited by 46
  12. 2020Logarithmic Regret Bound in Partially Observable Linear Dynamical Systemscited by 46
7 more
  1. 2019On Generalization Bounds of a Family of Recurrent Neural Networkscited by 42
  2. 2020Logarithmic Regret for Adversarial Online Controlcited by 41
  3. 2018Spectral Filtering for General Linear Dynamical Systemscited by 37
  4. 2018Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterizationcited by 35
  5. 2019Improved PAC-Bayesian Bounds for Linear Regressioncited by 12
  6. 2020Learning Recurrent Neural Net Models of Nonlinear Systemscited by 11
  7. 2021PAC-Bayesian theory for stochastic LTI systemscited by 7

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Citing papers per year: 2024: 1.

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  1. 2024Generalization bounds for mixing processes via delayed online-to-PAC conversionscited by 9

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  7. 2022Efficient learning of hidden state LTI state space models of unknown order
  8. 2024Central Limit Theorem for Two-Timescale Stochastic Approximation with Markovian Noise: Theory and Applications