State-Space Systems as Dynamic Generative Models

arXiv:2404.08717v1 Announce Type: cross
Abstract: A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output processes exist and are unique once an input process has been fixed, a property that in the deterministic state-space literature is known as the echo state property. When those conditions are satisfied, the given state-space system becomes a generative model for probabilistic dependences between two sequence …

abstract arxiv cs.lg dynamic framework general generative generative models literature math.ds math.pr math.st process processes property space state stat.ml stat.th study systems type