An Information Criterion for Inferring Coupling in Distributed Dynamical Systems

TL;DR

This paper introduces an information criterion for inferring the structure of coupled dynamical systems, leveraging time delay embeddings to compute globally optimal network structures from observed data.

Contribution

It proposes a novel information-theoretic approach for structure learning in distributed dynamical systems, exploiting properties of dynamical systems for global optimality.

Findings

Provides a new criterion based on information transfer for structure inference.

Uses time delay embedding theorems to achieve global optimality.

Offers a framework for analyzing coupled systems with latent variables.

Abstract

The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical systems. Specifically, we study the structure learning problem for spatially distributed dynamical systems coupled via a directed acyclic graph. Unlike established structure learning procedures that find locally maximum posterior probabilities of a network structure containing latent variables, our work exploits the properties of dynamical systems to compute globally optimal approximations of these distributions. We arrive at this result by the use of time delay embedding theorems. Taking an information-theoretic perspective, we show that the log-likelihood has an intuitive interpretation in terms of information transfer.