Invariant Causal Prediction with Locally Linear Models
Alexander Mey Rui Manuel Castro
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.