PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.14838
- arXiv:
- arXiv:2212.14838
- Bibcode:
- 2022arXiv221214838E
- Keywords:
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- Statistics - Machine Learning;
- Computer Science - Machine Learning;
- Mathematics - Dynamical Systems;
- Mathematics - Statistics Theory