We introduce 'Causal Information Contribution (CIC)' and 'Causal Variance Contribution (CVC)' to quantify the influence of each variable in a causal directed acyclic graph on some target variable. CIC is based on the underlying Functional Causal Model (FCM), in which we define 'structure preserving interventions' as those that act on the unobserved noise variables only. This way, we obtain a measure of influence that quantifies the contribution of each node in its 'normal operation mode'. The total uncertainty of a target variable (measured in terms of variance or Shannon entropy) can then be attributed to the information from each noise term via Shapley values. CIC and CVC are inspired by Analysis of Variance (ANOVA), but also applies to non-linear influence with causally dependent causes.

中文翻译：

---

通过结构保护干预量化因果贡献

我们引入了“因果信息贡献（CIC）”和“因果方差贡献（CVC）”来量化因果有向无环图中每个变量对某些目标变量的影响。CIC 基于基本的功能因果模型 (FCM)，其中我们将“结构保留干预”定义为仅作用于未观察到的噪声变量的干预。通过这种方式，我们获得了量化每个节点在其“正常操作模式”中的贡献的影响度量。目标变量的总不确定性（以方差或香农熵衡量）然后可以通过沙普利值归因于来自每个噪声项的信息。CIC 和 CVC 受到方差分析 (ANOVA) 的启发，但也适用于具有因果关系的非线性影响。