Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphs

arXiv:2308.16859v2 Announce Type: replace-cross
Abstract: In this article, the optimal sample complexity of learning the underlying interactions or dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. We call such a DAG underlying an LDS as dynamical DAG (DDAG). In particular, we consider a DDAG where the nodal dynamics are driven by unobserved exogenous noise sources that are wide-sense stationary (WSS) in time but are mutually uncorrelated, and have the same {power spectral density …

abstract article arxiv call complexity cs.lg cs.sy dag dependencies eess.sy graph graphs information interactions linear math.oc sample stat.ml type