Improving transfer entropy and partial transfer entropy for relative detection of effective connectivity strength between time series

Abstract

Information theory-based measures have recently been considered in determining functional and effective connectivity. Transfer Entropy (TE) and Partial Transfer Entropy (Partial TE) are two such measures that investigate causal connectivity in bivariate and multivariate systems, respectively. The existence or absence of causal connectivity between variables is determined through statistical testing that compares TE or Partial TE values under different conditions or between the original TE or Partial TE values and surrogate data. However, using normal TE or Partial TE provides no information about coupling strength between variables. In this study, we present a repeating statistical test method for TE and Partial TE values in linear dynamic systems to determine the relative coupling strength between connectivity in the networks. In this method, segments with different time lengths (N) were considered for each variable in a system. Using the proposed method, the number of segments with statistically significant TE or partial TE values for each pair of time series was counted and analyzed as N increased. Our research results demonstrated that the proposed statistical test distinguishes stronger linear couplings with fewer segments and shorter time lengths (N) from weaker couplings. The proposed method also confirmed that Partial TE is more capable of determining direct causal connectivity than TE. Therefore, our proposed method can not only detect direct causal connections, but also determine the causal effect size of linear connectivity between time series relative to each other in a system, thus improving the performance of TE and Partial TE criteria.