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

arXiv: https://arxiv.org/abs/2212.14838 · HTML: https://mlsanity.com/paper/2212.14838/

## Key facts

- Cited by 1 papers 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 (most cited first, 19 of 19)

- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [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)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [PAC-Bayesian Theory Meets Bayesian Inference](https://mlsanity.com/paper/1605.08636/) (2016)
- [Data-dependent Sample Complexity of Deep Neural Networks via Lipschitz Augmentation](https://mlsanity.com/paper/1905.03684/) (2019)
- [Finite Sample Analysis of Stochastic System Identification](https://mlsanity.com/paper/1903.09122/) (2019)
- [Learning Linear Dynamical Systems with Semi-Parametric Least Squares](https://mlsanity.com/paper/1902.00768/) (2019)
- [Simpler PAC-Bayesian Bounds for Hostile Data](https://mlsanity.com/paper/1610.07193/) (2016)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [On Generalization Bounds of a Family of Recurrent Neural Networks](https://mlsanity.com/paper/1910.12947/) (2019)
- [Logarithmic Regret for Adversarial Online Control](https://mlsanity.com/paper/2003.00189/) (2020)
- [Spectral Filtering for General Linear Dynamical Systems](https://mlsanity.com/paper/1802.03981/) (2018)
- [Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterization](https://mlsanity.com/paper/1803.09327/) (2018)
- [Improved PAC-Bayesian Bounds for Linear Regression](https://mlsanity.com/paper/1912.03036/) (2019)
- [Learning Recurrent Neural Net Models of Nonlinear Systems](https://mlsanity.com/paper/2011.09573/) (2020)
- [PAC-Bayesian theory for stochastic LTI systems](https://mlsanity.com/paper/2103.12866/) (2021)

## Built on by (most cited first, 1 of 1)

- [Generalization bounds for mixing processes via delayed online-to-PAC conversions](https://mlsanity.com/paper/2406.12600/) (2024)

## 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.