Topology Inference Of Directed Graphs Using Nonlinear Structural Vector Autoregressive Models

Linear structural vector autoregressive models constitute a generalization of structural equation models (SEMs) and vector autoregressive (VAR) models, two popular approaches for topology inference of directed graphs. Although simple and tractable, linear SVARMs seldom capture nonlinearities that are inherent to complex systems, such as the human brain. To this end, the present paper advocates kernel-based nonlinear SVARMs, and develops an efficient sparsity-promoting least-squares estimator to learn the hidden topology. Numerical tests on real electrocorticographic (ECoG) data from an Epilepsy study corroborate the efficacy of the novel approach.