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We consider the task of identifying the causal parents of a target variableamong a set of candidate variables from observational data. Our main assumptionis that the candidate variables are observed in different environments whichmay, for example, correspond to different settings of a machine or differenttime intervals in a dynamical process. Under certain assumptions differentenvironments can be regarded as interventions on the observed system. We assumea linear relationship between target and covariates, which can be different ineach environment with the only restriction that the causal structure isinvariant across environments. This is an extension of the ICP($\textbf{I}$nvariant $\textbf{C}$ausal $\textbf{P}$rediction) principle byPeters et al. [2016], who assumed a fixed linear relationship across allenvironments. Within our proposed setting we provide sufficient conditions foridentifiability of the causal parents and introduce a practical method calledLoLICaP ($\textbf{Lo}$cally $\textbf{L}$inear $\textbf{I}$nvariant$\textbf{Ca}$usal $\textbf{P}$rediction), which is based on a hypothesis testfor parent identification using a ratio of minimum and maximum statistics. Wethen show in a simplified setting that the statistical power of LoLICaPconverges exponentially fast in the sample size, and finally we analyze thebehavior of LoLICaP experimentally in more general settings.

Invariant Causal Prediction with Locally Linear Models