ONLINE IDENTIFICATION OF DIRECTIONAL GRAPH TOPOLOGIES CAPTURING DYNAMIC AND NONLINEAR DEPENDENCIES^†

摘要

Linear structural vector autoregressive models (SVARMs) have well-documented merits for topology inference of directional graphs emerging in diverse applications, including gene-regulatory, brain, and social networks. Although simple and tractable, linear SVARMs cannot capture nonlinearities that are inherent to complex systems, such as the human brain, that can also vary over time. Given nodal measurements, these considerations motivate the dynamic nonlinear SVARM approach developed here to track the possibly directed and dynamic nonlinear interactions among network nodes. For slow-varying topologies, nonlinear model parameters are estimated via functional stochastic gradient descent. Numerical tests showcase the effectiveness of the novel algorithms in unveiling sparse dynamically-evolving topologies.