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

2026-09-08

AI Summary

本文推导了部分观测的线性时不变随机系统的PAC-Bayesian误差界，用以评估有限数据下模型预测和参数估计误差。

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.

Problem

• PAC-Bayesian Bounds
• Stochastic Linear Time-Invariant Systems
• Sub-Gaussian Noise
• Prediction Error
• Parameter Estimation

Innovation

• PAC-Bayesian error bounds
• partially observed LTI systems
• sub-Gaussian noise
• parameter estimation error
• system identification