A Fast and Efficient Ensemble Transfer Entropy and Applications in Neural Signals

The ensemble transfer entropy ([Formula: see text]) refers to the transfer entropy estimated from an ensemble of realizations. Due to its time-resolved analysis, it is adapted to analyze the dynamic interaction between brain regions. However, in the traditional [Formula: see text] , multiple sets of surrogate data should be used to construct the null hypothesis distribution, which dramatically increases the computational complexity. To reduce the computational cost, a fast, efficient [Formula: see text] with a simple statistical test method is proposed here, in which just one set of surrogate data is involved. To validate the improved efficiency, the simulated neural signals are used to compare the characteristics of the novel [Formula: see text] with those of the traditional [Formula: see text]. The results show that the time consumption is reduced by two or three magnitudes in the novel [Formula: see text]. Importantly, the proposed [Formula: see text] could accurately track the dynamic interaction process and detect the strength and the direction of interaction robustly even in the presence of moderate noises. The novel [Formula: see text] reaches its steady state with the increased samples, which is slower than the traditional method. Furthermore, the effectiveness of the novel [Formula: see text] was verified in the actual neural signals. Accordingly, the [Formula: see text] proposed in this work may provide a suitable way to investigate the dynamic interactions between brain regions.