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With the goal of generalizing to out-of-distribution (OOD) data, recentdomain generalization methods aim to learn "stable" feature representationswhose effect on the output remains invariant across domains. Given thetheoretical connection between generalization and privacy, we ask whetherbetter OOD generalization leads to better privacy for machine learning models,where privacy is measured through robustness to membership inference (MI)attacks. In general, we find that the relationship does not hold. Throughextensive evaluation on a synthetic dataset and image datasets like MNIST,Fashion-MNIST, and Chest X-rays, we show that a lower OOD generalization gapdoes not imply better robustness to MI attacks. Instead, privacy benefits arebased on the extent to which a model captures the stable features. A model thatcaptures stable features is more robust to MI attacks than models that exhibitbetter OOD generalization but do not learn stable features. Further, for thesame provable differential privacy guarantees, a model that learns stablefeatures provides higher utility as compared to others. Our results offer thefirst extensive empirical study connecting stable features and privacy, andalso have a takeaway for the domain generalization community; MI attack can beused as a complementary metric to measure model quality.

The Connection between Out-of-Distribution Generalization and Privacy of ML Models