Transfer Entropy (TE), the primary method for determining directed information flow within a network system, can exhibit bias - either in deficiency or excess - during both pairwise and conditioned calculations, owing to high-order dependencies among the dynamic processes under consideration and the remaining processes in the system used for conditioning. Here, we propose a novel approach. Instead of conditioning TE on all network processes except the driver and target, as in its fully conditioned version, or not conditioning at all, as in the pairwise approach, our method searches for both the multiplets of variables that maximize information flow and those that minimize it. This provides a decomposition of TE into unique, redundant, and synergistic atoms. Our approach enables the quantification of the relative importance of high-order effects compared to pure two-body effects in information transfer between two processes, while also highlighting the processes that contribute to building these high-order effects alongside the driver. We demonstrate the application of our approach in climatology by analyzing data from El Ni\~{n}o and the Southern Oscillation.

翻译：传递熵（TE）作为确定网络系统内有向信息流的主要方法，在成对计算和条件化计算中，由于所考虑的动态过程与系统内用于条件化的其他过程之间存在高阶依赖性，可能会产生信息流缺失或冗余的偏差。本文提出了一种新方法。与完全条件化版本中对除驱动过程和目标过程外的所有网络过程进行TE条件化处理，或成对方法中完全不进行条件化不同，我们的方法同时搜索能最大化信息流的变量多重组和能最小化信息流的变量多重组。这实现了将传递熵分解为独特原子、冗余原子和协同原子。我们的方法能够量化信息传递过程中高阶效应相对于纯二体效应的相对重要性，同时还能凸显与驱动过程共同构建这些高阶效应的相关过程。我们通过分析厄尔尼诺-南方涛动数据，展示了该方法在气候学中的应用。