Nonlinear Causality Inference Using a Robust ERR-Based Method in the Context of Epilepsy

In this paper, a robust error reduction ratio based method is proposed for the estimation of nonlinear causality among dynamic systems. The proposed method copes with the issue of spurious solutions inherent to the original ERR-based method. These spurious solutions are removed by considering a sparse representation of the model coefficient vector. This sparse representation is recovered using the well-known alternating direction method of multipliers combined with an optimal computation of the regularization parameter at each iteration using the discrepancy principle. The robust ERR-based method is evaluated in the context of inferring brain effective connectivity in epilepsy. Results obtained on simulated and real intracerebral electroencephalographic signals confirm its efficiency.