We study the problem of identifying the unknown intervention targets in structural causal models where we have access to heterogeneous data collected from multiple environments. The unknown intervention targets are the set of endogenous variables whose corresponding exogenous noises change across the environments. We propose a two-phase approach which in the first phase recovers the exogenous noises corresponding to unknown intervention targets whose distributions have changed across environments. In the second phase, the recovered noises are matched with the corresponding endogenous variables. For the recovery phase, we provide sufficient conditions for learning these exogenous noises up to some component-wise invertible transformation. For the matching phase, under the causal sufficiency assumption, we show that the proposed method uniquely identifies the intervention targets. In the presence of latent confounders, the intervention targets among the observed variables cannot be determined uniquely. We provide a candidate intervention target set which is a superset of the true intervention targets. Our approach improves upon the state of the art as the returned candidate set is always a subset of the target set returned by previous work. Moreover, we do not require restrictive assumptions such as linearity of the causal model or performing invariance tests to learn whether a distribution is changing across environments which could be highly sample inefficient. Our experimental results show the effectiveness of our proposed algorithm in practice.

我们研究了在具有多个环境收集的异构数据的结构因果模型中，识别未知干预目标的问题。我们提出了一个两阶段方法，第一阶段恢复了在环境之间分布发生变化的未知干预目标对应的外源性噪声，第二阶段将恢复的噪声与相应的内源性变量进行匹配。在有潜在混淆因素存在的情况下，观察到的变量中的干预目标无法确定唯一。我们提供了一个候选干预目标集，它是真实干预目标集的超集。我们的方法改进了现有方法，返回的候选集始终是以前的工作返回的目标集的子集。此外，我们不需要诸如因果模型的线性性或执行不变性测试等限制性假设，以了解分布是否在环境之间发生变化，这可能会导致样本效率低下。我们的实验结果显示了我们提出的算法的有效性。

从异质数据中学习结构因果模型中的未知干预目标