This is the code for the preprint paper "Estimating Transfer Entropy via Copula Entropy" which available at here. A non-parametric method for estimating Transfer Entropy via estimating three Copula Entropy terms is proposed in this paper.
The proposed method is implemented in the R and Python package 'copent', available at
The method is demonstrated in the experiment with the UCI Beijing PM2.5 data. The following conditional independence measures are compared in the experiment:
- Transfer Entropy via Copula Entropy (TE) [1];
- Conditional Distance Correlation (CDC) [2];
- Kernel-based Conditional Independence (KCI) [3];
- COnditional DEpendence Coefficient (CODEC) [4];
- Generalised Covariance Measure (GCM) [5];
- Kernel Partial Correlation (KPC) [6];
- Partial Correlation (pcor);
- Randomized conditional Correlation Test (RCoT) [7].
- Ma, J. Estimating Transfer Entropy via Copula Entropy. arXiv preprint arXiv:1910.04375, 2019.
- Wang, X.; Pan, W.; Hu, W.; Tian, Y. & Zhang, H. Conditional distance correlation. Journal of the American Statistical Association, 2015, 110, 1726-1734.
- Zhang, K.; Peters, J.; Janzing, D. & Schölkopf, B. Kernel-based conditional independence test and application in causal discovery. Uncertainty in Artificial Intelligence, 2011, 804-813.
- Azadkia, M. & Chatterjee, S. A simple measure of conditional dependence. arXiv preprint arXiv:1910.12327, 2019.
- Shah, R. D. & Peters, J. The hardness of conditional independence testing and the generalised covariance measure. Annals of Statistics, 2020, 48, 1514-1538.
- Huang, Z.; Deb, N. & Sen, B. Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence. arXiv preprint arXiv:2012.14804, 2020.
- Strobl, E. V.; Zhang, K. & Visweswaran, S. Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery. arXiv preprint arXiv:1702.03877, 2017.