Life sciences · Preprint

PAC-Bayesian Bounds for Learning Partially Observed Stochastic Linear Time-Invariant State-Space Systems with Inputs and Sub-Gaussian Noise

arXiv · September 8, 2026

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AI Summary

This is a preprint presenting a theoretical PAC-Bayesian error bound for partially observed linear time-invariant stochastic systems with inputs and sub-Gaussian noise. The work derives finite-sample bounds relating prediction and parameter estimation errors, framed as a potential foundation for similar bounds on recurrent neural networks, but contains no empirical validation or clinical data.

What was studied

Preprint.

Key findings

Derives PAC-Bayesian error bound for partially observed LTI stochastic dynamical systems with inputs and sub-Gaussian noise Shows bound can be used to derive parameter estimation error bounds Proposes application to finite-sample error bounds for system identification algorithms

Safety

Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.

Who this may help

The source did not state who this applies to in practice.

Plain-language summary

This is a theoretical contribution deriving PAC-Bayesian bounds for a specific class of dynamical systems; it is a mathematical framework paper without empirical validation or clinical application.

Caveats

This is a preprint and has not undergone peer review.
No empirical validation, simulation results, or numerical examples provided in the abstract.
No comparison to existing bounds or alternative methods reported.
Applicability to RNNs described as future work, not demonstrated.

Evidence assessment

Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.

Study design

insufficient

Mathematical derivation; no empirical study design employed.

Directness

limited

Bounds are for partially observed LTI systems; applicability to RNNs stated as future work.

Consistency

insufficient

No comparison to prior bounds or empirical validation reported.

Risk of bias

insufficient

Not applicable to theoretical derivation; not peer reviewed.

Sample adequacy

insufficient

No empirical data; theoretical framework only.

What is missing. This record has no reported figures. That is a gap in the analysis, not a judgement about the study.

Source abstract

In this paper we derive a Probably Approximately Correct (PAC)-Bayesian error bound for partially observed linear time-invariant (LTI) stochastic dynamical systems in state-space form with inputs and sub-Gaussian noise. Such bounds are widespread in machine learning, and they are useful for characterizing the predictive power of models learned from finitely many data points. The bound derived in this paper relates the expectation of prediction errors with the prediction error generated by the model on the data used for learning. In addition, we show that it can also be used to derive bounds for the parameter estimation error. In turn, this allows us to provide finite-sample error bounds for the prediction error and parameter estimation error for a wide class of system identification algorithms. Furthermore, as LTI systems are a sub-class of recurrent neural networks (RNNs), these error bounds could be a first step towards PAC-Bayesian bounds for RNNs.

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John LethMohamad Al AhdabMihaly Petreczky