Identifying key drivers in a stochastic dynamical system through estimation of transfer entropy between univariate and multivariate time series

Transfer entropy (TE) is a widely used tool for quantifying causal relationships in stochastic dynamical systems. Traditionally, TE and its conditional variants are applied pairwise between dynamic variables to infer these relationships. However, identifying key drivers in such systems requires a measure of the causal influence exerted by each component on the entire system. I propose using outgoing transfer entropy (OutTE), the transfer entropy from a given variable to the collection of remaining variables, to quantify the causal influence of the variable on the rest of the system. Conversely, the incoming transfer entropy (InTE) is also defined to quantify the causal influence received by a component from the rest of the system. Since OutTE and InTE involve transfer entropy between univariate and multivariate time series, naive estimation methods can result in significant errors, especially when the number of variables is large relative to the number of samples. To address this, I introduce a novel estimation scheme that computes outgoing and incoming TE only between significantly interacting partners. The feasibility and effectiveness of this approach are demonstrated using synthetic data and real oral microbiota data. The method successfully identifies the bacterial species known to be key players in the bacterial community, highlighting its potential for uncovering causal drivers in complex systems.