Invariant and Transportable Representations for Anti-Causal Domain Shifts

Real-world classification problems must contend with domain shift, the (potential) mismatch between the domain where a model is deployed and the domain(s) where the training data was gathered. Methods to handle such problems must specify what structure is held in common between the domains and what is allowed to vary. A natural assumption is that causal (structural) relationships are invariant in all domains. Then, it is tempting to learn a predictor for label Y that depends only on its causal parents. However, many real-world problems are anti-causal'' in the sense that Y is a cause of the covariates X ---in this case, Y has no causal parents and the naive causal invariance is useless. In this paper, we study representation learning under a particular notion of domain shift that both respects causal invariance and that naturally handles the anti-causal'' structure.