PAC-Bayesian-Like Error Bound for a Class of Linear Time-Invariant Stochastic State-Space Models
This provides theoretical guarantees for learning in stochastic dynamical systems, but it is incremental as it adapts existing PAC-Bayesian frameworks to a specific model class.
The paper tackles the problem of learning linear time-invariant stochastic state-space models, deriving a PAC-Bayesian-like error bound for these systems, which are used in control engineering and econometrics.
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.