Cauchy-Schwarz Divergence Transfer Entropy

Transfer entropy (TE) is a powerful information-theoretic tool for analyzing causality in time series and complex systems. In this work, we propose a new formulation of TE using the Cauchy-Schwarz (CS) divergence. The resulting CS-TE offers a closed-form estimator and naturally extends to capture more complex causal relationships, such as indirect causation and synergistic effects, beyond just pairwise interactions. We also explore the feasibility of using a classifier, rather than regression models, to perform Granger tests in a supervised way. Lastly, we demonstrate the effectiveness of CS-TE on benchmark simulated data and stock indices from 14 stock markets. The code and supplementary material are available in our project repository: https://github.com/SJYuCNEL/Cauchy-Schwarz-Transfer-Entropy.