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.
Anchor regression: Heterogeneity-aware regression.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83(2), 2021
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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.