Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes. Transfer entropy from a process X to another process Y is the amount of uncertainty reduced in future values of Y by knowing the past values of X given past values of Y. More specifically, if and for denote two random processes and the amount of information is measured using Shannon's entropy, the transfer entropy can be written as:
Transfer entropy is conditional mutual information, with the history of the influenced variable in the condition. Transfer entropy reduces to Granger causality for vector auto-regressive processes. Hence, it is advantageous when the model assumption of Granger causality doesn't hold, for example, analysis of non-linear signals. However, it usually requires more samples for accurate estimation. The probabilities in the entropy formula can be estimated using different approaches (binning, nearest neighbors) or, in order to reduce complexity, using a non-uniform embedding. While it was originally defined for bivariate analysis, transfer entropy has been extended to multivariate forms, either conditioning on other potential source variables or considering transfer from a collection of sources, although these forms require more samples again.
- Conditional mutual information
- Causality (physics)
- Structural equation modeling
- Rubin causal model
- Mutual Information
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- "Transfer Entropy Toolbox". Google Code., a toolbox, developed in C++ and MATLAB, for computation of transfer entropy between spike trains.
- "Java Information Dynamics Toolkit (JIDT)". GitHub., a toolbox, developed in Java and usable in MATLAB, GNU Octave and Python, for computation of transfer entropy and related information-theoretic measures in both discrete and continuous-valued data.
- "Multivariate Transfer Entropy (MuTE) toolbox". GitHub., a toolbox, developed in MATLAB, for computation of transfer entropy with different estimators.