We propose a notion of causal influence that describes the `intrinsic' part of the contribution of a node on a target node in a DAG. By recursively writing each node as a function of the upstream noise terms, we separate the intrinsic information added by each node from the one obtained from its ancestors. To interpret the intrinsic information as a {\it causal} contribution, we consider `structure-preserving interventions' that randomize each node in a way that mimics the usual dependence on the parents and does not perturb the observed joint distribution. To get a measure that is invariant with respect to relabelling nodes we use Shapley based symmetrization and show that it reduces in the linear case to simple ANOVA after resolving the target node into noise variables. We describe our contribution analysis for variance and entropy, but contributions for other target metrics can be defined analogously. The code is available in the package gcm of the open source library DoWhy.

翻译：我们提出了一种因果影响的概念，用于描述有向无环图中节点对目标节点的'固有'贡献部分。通过将每个节点递归地表示为上游噪声项的函数，我们将每个节点添加的固有信息与其从祖先获得的信息分离开来。为了将固有信息解释为因果贡献，我们考虑了'保持结构干预'——以模仿对父节点通常依赖关系的方式随机化每个节点，且不扰动观测到的联合分布。为获得对节点重标定不变的度量，我们采用基于沙普利值的对称化方法，并证明在线性情况下，该方法在将目标节点分解为噪声变量后简化为简单的方差分析。我们描述了方差和熵的贡献分析，但其他目标度量的贡献可类似定义。代码已开源在库DoWhy的gcm包中。