dataset: Causal Directions in Noisy Environment
Guido Nolte, Fraunhofer FIRST, Germany
This challenge has two parts, a simulation and real data.
Simulation: Data are simulated as superposition of bivariate unidirectional
interaction plus additive mixed and non-white noise. The simulations were
done with AR-models with uniformly distributed input. The challenge is to
estimate the causal direction. For each out of 1000 examples you get +1 point
for the correct answer, -10 points for the wrong answer, and 0 points for
Real Data: These are high quality EEG data for 10 subjects for 19 channels.
The data contain a prominent peak at around 10 Hz predominantly in occipital
(back) channels. No ground truth is known. A submission must be a single
19x19 matrix corresponding to a causality estimate between all pairs of channels
averaged across subjects. Any submission will be visualized and, with the
agreement of the authors, put on the net for an open discussion.
Comparison of Granger Causality and Phase Slope Index
Guido Nolte, Andreas Ziehe (Fraunhofer FIRST, Germany) and Nicole Krämer,
Klaus-Robert Müller (TU Berlin, Germany)
We recently proposed a new measure, termed Phase Slope Index (PSI), to estimate the causal
direction of interactions designed to be robust to instantaneous mixtures of independent sources with
arbitrary spectral content. We compared this method to Granger Causality for linear systems containing
spatially and temporarily mixed noise and found that, in contrast to PSI, the latter was not able to
properly distinguish truly interacting systems from mixed noise. Here, we extent this analysis with
respect to two aspects: a) we analyze Granger causality and PSI also for non-mixed noise, and b)
we analyze PSI for nonlinear interactions. We found a) that Granger causality, in contrast to PSI,
fails also for non-mixed noise if the memory-time of the sender of information is long compared to
the transmission time of the information, and b) that PSI, being a linear method, eventually misses
nonlinear interactions but is unlikely to give false positive results.