为带输入的随机线性时不变系统提供可学习的误差界，支持有限样本分析。
PAC-Bayesian Bounds for Learning Partially Observed Stochastic Linear Time-Invariant State-Space Systems with Inputs and Sub-Gaussian Noise
- 基于PAC-Bayesian框架推导系统预测误差上界
- 给出有限样本下预测与参数估计的误差界
- 适用于多种系统辨识算法，为RNN理论奠基
本文为具有输入和次高斯噪声的局部可观测线性时不变（LTI）随机动力系统在状态空间形式下的学习，推导出一个可能近似正确的（PAC）贝叶斯误差界。此类界在机器学习中广泛应用，可用于刻画从有限数据点中学习到的模型的预测能力。本文推导的界将预测误差期望与学习数据上的模型预测误差联系起来。此外，我们还证明该界可用于推导参数估计误差的界。由此可为一大类系统辨识算法提供有限样本预测误差与参数估计误差的界。由于LTI系统是循环神经网络（RNN）的一个子类，这些误差界或可成为建立RNN PAC-Bayesian界的初步步骤。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。