# A finite-sample generalization bound for stable LPV systems

arXiv: https://arxiv.org/abs/2405.10054 · HTML: https://mlsanity.com/paper/2405.10054/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 82 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 28 of 28)

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- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projections](https://mlsanity.com/paper/2206.12037/) (2022)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [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)
- [Statistical Learning Theory for Control: A Finite Sample Perspective](https://mlsanity.com/paper/2209.05423/) (2022)
- [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)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [State-space Models with Layer-wise Nonlinearity are Universal Approximators with Exponential Decaying Memory](https://mlsanity.com/paper/2309.13414/) (2023)
- [Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories](https://mlsanity.com/paper/2009.00739/) (2020)
- [On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis](https://mlsanity.com/paper/2009.07799/) (2020)
- [Framing RNN as a kernel method: A neural ODE approach](https://mlsanity.com/paper/2106.01202/) (2021)
- [Generalization bounds for neural ordinary differential equations and deep residual networks](https://mlsanity.com/paper/2305.06648/) (2023)
- [Learning Recurrent Neural Net Models of Nonlinear Systems](https://mlsanity.com/paper/2011.09573/) (2020)
- [Rademacher Complexity of Neural ODEs via Chen-Fliess Series](https://mlsanity.com/paper/2401.16655/) (2024)
- [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)
- [Reduced-order modeling of LPV systems in the Loewner framework](https://mlsanity.com/paper/2104.10767/) (2021)
- [LPVcore: MATLAB Toolbox for LPV Modelling, Identification and Control](https://mlsanity.com/paper/2105.03695/) (2021)
- [Towards Efficient Maximum Likelihood Estimation of LPV-SS Models](https://mlsanity.com/paper/1808.01633/) (2018)

## Abstract (arXiv)

One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured on some finite sample. In machine learning, a popular class of such bounds are the so-called Probably Approximately Correct (PAC) bounds. In this paper, we derive a PAC bound for stable continuous-time linear parameter-varying (LPV) systems. Our bound depends on the H2 norm of the chosen class of the LPV systems, but does not depend on the time interval for which the signals are considered.