Sparse multivariate autoregressive (mAR)-based partial directed coherence (PDC) for electroencephalogram (EEG) analysis

Partial directed coherence (PDC) has recently been proposed for studying brain connectivity in EEG studies. PDC provides a quantitative spectral measure of the causal relations between signals by its central use of a multivariate autoregressive (mAR) model. Yet, in real applications, the successful estimation of PDC depends on the accuracy of mAR parameter estimation, which is often sensitive to the data size and model order. In addition, it is generally believed that connections between EEG nodes (brain regions) may be sparse. To address these concerns, we propose a sparse mAR-based PDC technique where PDC estimates are computed from sparse mAR coefficient matrices derived from penalized regression. The proposed technique is applied to both simulated data and real EEG recordings, and results show enhanced stability and accuracy of the proposed technique compared to the traditional, non-sparse approach. The sparse mAR-based PDC technique is promising for analyzing brain connectivity in EEG analysis.