PAC-Bayesian theory for stochastic LTI systems

TL;DR

This paper develops a PAC-Bayesian error bound specifically for stochastic linear time-invariant (LTI) systems, aiming to extend such bounds to more complex dynamical systems like RNNs, with implications for machine learning analysis.

Contribution

It introduces a PAC-Bayesian error bound for stochastic LTI systems, providing a foundation for analyzing and designing learning algorithms for dynamical systems.

Findings

Derived a PAC-Bayesian error bound for stochastic LTI models

The bound can be extended to more general dynamical systems

Facilitates analysis of machine learning algorithms for dynamical systems

Abstract

In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems, including recurrent neural networks. In turn, PACBayesian error bounds are known to be useful for analyzing machine learning algorithms and for deriving new ones.