  A measure to estimate the direct and directional coupling in multivariate
time series is proposed. The measure is an extension of a recently published
measure of conditional Mutual Information from Mixed Embedding (MIME) for
bivariate time series. In the proposed measure of Partial MIME (PMIME), the
embedding is on all observed variables, and it is optimized in explaining the
response variable. It is shown that PMIME detects correctly direct coupling,
and outperforms the (linear) conditional Granger causality and the partial
transfer entropy. We demonstrate that PMIME does not rely on significance test
and embedding parameters, and the number of observed variables has no effect on
its statistical accuracy, it may only slow the computations. The importance of
these points is shown in simulations and in an application to epileptic
multi-channel scalp EEG.
