  There is an increasing interest in studying the neural interaction mechanisms
behind patterns of cognitive brain activity. This paper proposes a new approach
to infer such interaction mechanisms from electroencephalographic (EEG) data
using a new estimator of directed information (DI) called logit shrinkage
optimized directed information assessment (L-SODA). Unlike previous directed
information measures applied to neural decoding, L-SODA uses shrinkage
regularization on multinomial logistic regression to deal with the high
dimensionality of multi-channel EEG signals and the small sizes of many
real-world datasets. It is designed to make few a priori assumptions and can
handle both non-linear and non-Gaussian flows among electrodes. Our L-SODA
estimator of the DI is accompanied by robust statistical confidence intervals
on the true DI that make it especially suitable for hypothesis testing on the
information flow patterns. We evaluate our work in the context of two different
problems where interaction localization is used to determine highly interactive
areas for EEG signals spatially and temporally. First, by mapping the areas
that have high DI into Brodmann area, we identify that the areas with high DI
are associated with motor-related functions. We demonstrate that L-SODA
provides better accuracy for neural decoding of EEG signals as compared to
several state-of-the-art approaches on the Brain Computer Interface (BCI) EEG
motor activity dataset. Second, the proposed L-SODA estimator is evaluated on
the CHB-MIT Scalp EEG database. We demonstrate that compared to the
state-of-the-art approaches, the proposed method provides better performance in
detecting the epileptic seizure.
