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closeError in the proof given in http://arxiv.org/abs/1304.7930v1 by Runge et al.
Posted by MichaelW on 11 Nov 2013 at 10:26 GMT
Dear Jakob,
after critical evaluation we found that the proof of interaction delay reconstruction via MIT given in your above reference on arXiv contains an error in equation (4):
On both sides of the equation the conditioning is performed for the Parents of x(t-delta-xi); for a proof of delay reconstruction using the momentary information transfer, however, the conditioning on the right hand side of equation (4) should be on the parents of x(t-delta) not on those of x(t-delta-xi). Otherwise the the conditioning ...
(a) ... does not represent MIT for x(t-delta), as it should for a proof of maximality at the correct delay.
(b) ... is potentially on a future sample of x as xi is allowed to be negative in our original proof.
In addition, we have carefully checked the example given in our PLOS one paper, and still find that MIT does not reconstruct the delay correctly, even though this is a very simple case with one source and one target, and the number of Parents of the source x, and the target y is very small.
Michael Wibral