PAC-Bayesian theory for stochastic LTI systems
Not on the map. Why?
Abstract (arXiv)
In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems, including recurrent neural networks. In turn, PACBayesian error bounds are known to be useful for analyzing machine learning algorithms and for deriving new ones.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 6 of its 28 references that are in the map. First posted on arXiv 23 Mar 2021.
Builds on
6 of 28 references.
References · 6
- 2017Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Datacited by 527
- 2019A Primer on PAC-Bayesian Learningcited by 130
- 2015On the properties of variational approximations of Gibbs posteriorscited by 121
- 2016PAC-Bayesian Theory Meets Bayesian Inferencecited by 87
- 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 77
- 2019Improved PAC-Bayesian Bounds for Linear Regressioncited by 12
Built on by
Citing papers per year: 2021: 2; 2022: 1; 2023: 2; 2024: 0; 2025: 1.
6 papers.
- 2021User-friendly introduction to PAC-Bayes boundscited by 234
- 2023PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNscited by 4
- 2023PAC-Bayesian bounds for learning LTI-ss systems with input from empirical losscited by 3
- 2025Empirical PAC-Bayes Bounds for Markov Chainscited by 2
- 2022PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Modelscited by 1
- 2021Explicit construction of the minimum error variance estimator for stochastic LTI state-space systemscited by 0
- 2025Empirical PAC-Bayes Bounds for Markov Chains25 Sep 2025
- 2023PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNs15 Dec 2023
- 2023PAC-Bayesian bounds for learning LTI-ss systems with input from empirical loss29 Mar 2023
- 2022PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models30 Dec 2022
- 2021User-friendly introduction to PAC-Bayes bounds21 Oct 2021
- 2021Explicit construction of the minimum error variance estimator for stochastic LTI state-space systems6 Sep 2021
Similar, not cited
Close in wording, no citation either way
- 2023Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification
- 2021Non asymptotic estimation lower bounds for LTI state space models with Cram'er-Rao and van Trees
- 2025UnHiPPO: Uncertainty-aware Initialization for State Space Models
- 2024HiPPO-Prophecy: State-Space Models can Provably Learn Dynamical Systems in Context
- 2024HOPE for a Robust Parameterization of Long-memory State Space Models
- 2026Truncated Neural Likelihood Estimation for Simulation-Based Inference in State-Space Models
- 2022Efficient learning of hidden state LTI state space models of unknown order
- 2026Stochastic Autoregressive Learning