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（Transfer Entropy, TE）是确定网络系统内定向信息流的主要方法，但在进行成对计算和条件计算时，由于所考虑动态过程与系统中用于条件化的其余过程之间存在高阶依赖关系，可能导致偏差（不足或过剩）。在此，我们提出一种新方法。与完全条件化版本中对除驱动者和目标外的所有网络过程进行条件化，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最大化信息流的变量多重集和最小化信息流的变量多重集。这提供了对传递熵唯一、冗余和协同原子的分解。我们的方法能够量化信息传递中相对于纯二体效应的高阶效应的相对重要性，同时突出与驱动者共同构建这些高阶效应的过程。我们通过分析厄尔尼诺-南方涛动数据，在气候学中展示了该方法的应用。