In the Gaussian case, invariant features predicting Y independent of confounders Z are given by the top d eigenvectors of a matrix derived from the optimal transport barycenter of Z given Y.
Causal inference by using invariant prediction: identification and confidence intervals.Journal of the Royal Statistical Society Series B: Statistical Methodology, 78(5)
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Invariant Feature Extraction Through Conditional Independence and the Optimal Transport Barycenter Problem: the Gaussian case
In the Gaussian case, invariant features predicting Y independent of confounders Z are given by the top d eigenvectors of a matrix derived from the optimal transport barycenter of Z given Y.