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.
Computational optimal transport: With applications to data science.Foundations and Trends®in Machine Learning, 11(5-6):355–607
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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.