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.