We introduce a concept to quantify the 'intrinsic' causal contribution of each variable in a causal directed acyclic graph to the uncertainty or information of some target variable. By recursively writing each node as function of the noise terms, we separate the information added by each node from the one obtained from its ancestors. To interpret this information as a causal contribution, we consider 'structure-preserving interventions' that randomize each node in a way that mimics the usual dependence on the parents and don't perturb the observed joint distribution. Using Shapley values, the contribution becomes independent of the ordering of nodes. We describe our contribution analysis for variance and entropy as two important examples, but contributions for other target metrics can be defined analogously.

翻译：我们引入了一个概念, 将每个变量的“ 原始” 因果关系贡献量化到一个因果方向的循环图中, 确定某些目标变量的不确定性或信息。 通过将每个节点作为噪声术语的函数反复写入每个节点, 我们将每个节点增加的信息与其祖先提供的信息区分开来。 为了将这些信息解释为因果贡献, 我们考虑“ 结构保护干预 ”, 将每个节点随机化, 以便模仿对父母的通常依赖, 而不是干扰观察到的联合分布 。 使用 Shapley 值, 贡献变得独立于节点的顺序 。 我们用两个重要的例子描述我们对差异和恒温性的贡献分析, 但是其他目标指标的贡献可以类似地定义 。