Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

TL;DR

This paper reviews statistical methods for inferring the structure of nonlinear coupled dynamical systems, emphasizing Bayesian model reduction for efficient model comparison, with applications in neurovascular coupling research.

Contribution

It introduces Bayesian model reduction as a powerful tool for rapid structure learning in coupled dynamical systems, especially in neuroscience.

Findings

Bayesian model reduction enables quick comparison of network models.

The methods are effective in modeling neurovascular coupling.

The approach improves understanding of complex neuronal and vascular interactions.

Abstract

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems.