We consider the task of identifying the causal parents of a target variable
among a set of candidate variables from observational data. Our main assumption
is that the candidate variables are observed in different environments which
may, for example, correspond to different settings of a machine or different
time intervals in a dynamical process. Under certain assumptions different
environments can be regarded as interventions on the observed system. We assume
a linear relationship between target and covariates, which can be different in
each environment with the only restriction that the causal structure is
invariant across environments. This is an extension of the ICP
($\textbf{I}$nvariant $\textbf{C}$ausal $\textbf{P}$rediction) principle by
Peters et al. [2016], who assumed a fixed linear relationship across all
environments. Within our proposed setting we provide sufficient conditions for
identifiability of the causal parents and introduce a practical method called
LoLICaP ($\textbf{Lo}$cally $\textbf{L}$inear $\textbf{I}$nvariant
$\textbf{Ca}$usal $\textbf{P}$rediction), which is based on a hypothesis test
for parent identification using a ratio of minimum and maximum statistics. We
then show in a simplified setting that the statistical power of LoLICaP
converges exponentially fast in the sample size, and finally we analyze the
behavior of LoLICaP experimentally in more general settings.

我们考虑从观测数据中识别目标变量的因果父节点的任务，我们的主要假设是候选变量在不同环境中被观测到，不同环境可以被视为对观测系统的干预，我们假设目标变量和协变量之间存在线性关系，但在每个环境中可能不同，关键是因果结构在各种环境中保持不变，我们提供了因果父节点可辨识性的充分条件，并介绍了一种基于假设检验的实际方法 LoLICaP（本地线性不变因果预测），该方法利用最小值和最大值统计量的比率进行父节点识别，然后我们在简化的设置中展示了 LoLICaP 的统计功效以指数速度随样本大小收敛，并最后实验性地分析了 LoLICaP 在更一般设置下的行为。