# PAC-Bayesian theory for stochastic LTI systems

arXiv: https://arxiv.org/abs/2103.12866 · HTML: https://mlsanity.com/paper/2103.12866/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 23 Mar 2021.

## Builds on (most cited first, 6 of 6)

- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [PAC-Bayesian Theory Meets Bayesian Inference](https://mlsanity.com/paper/1605.08636/) (2016)
- [Non-asymptotic Identification of LTI Systems from a Single Trajectory](https://mlsanity.com/paper/1806.05722/) (2018)
- [Improved PAC-Bayesian Bounds for Linear Regression](https://mlsanity.com/paper/1912.03036/) (2019)

## Built on by (most cited first, 7 of 7)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [PAC-Bayesian bounds for learning LTI-ss systems with input from empirical loss](https://mlsanity.com/paper/2303.16816/) (2023)
- [PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNs](https://mlsanity.com/paper/2312.09793/) (2023)
- [Empirical PAC-Bayes Bounds for Markov Chains](https://mlsanity.com/paper/2509.20985/) (2025)
- [PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models](https://mlsanity.com/paper/2212.14838/) (2022)
- [Explicit construction of the minimum error variance estimator for stochastic LTI state-space systems](https://mlsanity.com/paper/2109.02384/) (2021)
- [Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds](https://mlsanity.com/paper/2610.20007/) (2026)

## 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.