Transfer entropy as a tool for reconstructing interaction delays in neural signals

Detecting interactions in complex networks can be very challenging, especially when using model based approaches, due to the dependency on model assumptions. To bypass this challenge, recently a model-free information-theoretic approach, transfer entropy (TE) was introduced. TE functional is capable of detecting linear as well as non-linear directed interactions. However, a full understanding of the network function also requires knowledge on interaction delays. Here we present an extension of TE which also estimates unknown interaction delays. In detail, we show that this TE functional becomes maximal if the interaction delay parameter in our TE functional equals the true interaction delay. Accordingly, in simulations of finite data the difference between estimated and true interaction delay was always within one sample. For the first time we applied this method to reconstruct intra-cerebral interaction delays from noninvasive Magnetoencephalography (MEG) recordings, and obtained biologically plausible values, suggesting a potential diagnostic use of the method.