International Symposium on Nonlinear Theory and its Applications
Entropy-Based Measures of Causality and Application to Epilepsy
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Among different measures of coupling and causality, measures based on entropies have gained much attention recently, such as the transfer entropy (TE) and its extensions based on permutation entropies, i.e. the socalled symbolic transfer entropy (STE) and the transfer entropy on rank vectors (TERV). All these measures make use of univariate embedding of each of the two time series. Very recently, we proposed a measure for coupling and causality that is derived from mixed embedding, which relies on information criteria regarding past, current and future states. The components of the mixed embedding vector indicate the presence of information transfer, and a measure is formed to quantify it, called mutual information from mixed embedding (MIME). We compare the measures from univariate embedding, TE, STE and TERV, and the measure from multivariate embedding, MIME. For this, we make simulations on a number of known nonlinear dynamical systems. Further, we apply the four measures to EEG records containing preictal and ictal states. It turns out that MIME is rather robust and conservative in detecting causal effects while the other three measures are positively biased indicating often false causal effects.