Estimation of network connectivity strengths in linear causal dynamic systems

Identification of network structure and quantifying the connectivity strengths in multivariate systems is an important problem in many scientific areas. Data-driven approach to network reconstruction based on causality measures is an emerging field of research in this respect. Among several recently introduced data-driven causality measures, the partial directed coherence (PDC) and direct power transfer (DPT) have been shown to be very effective for linear systems. While the PDC is useful in reconstructing the network, DPT has been proved to be effective in both identifying the network structure as well as quantifying the strength of connectivity. In this work, we study the problem of obtaining efficient estimates of network connectivity strengths, which has hitherto not been addressed in the literature. To this end, we study two different estimation methods for network connectivity strengths and demonstrate that the goodness of estimates depends on nature of the data generating process (DGP). In order to characterize the multivariate DGP, we introduce two statistics, namely, the vector-valued autocorrelation function (VACF) and the vector-valued partial autocorrelation function (VPACF), and estimators of the same. Our studies show that the parametric models used in estimating connectivity strengths should be commensurate with the dynamics of the process as characterized by the newly introduced VACF and VPACF. Simulation studies are presented under different scenarios to support our findings and the newly introduced measures.