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 common between the domains and what varies. 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. We show how to leverage the shared causal structure of the domains to learn a representation that both admits an invariant predictor and that also allows fast adaptation in new domains. The key is to translate causal assumptions into learning principles that disentangle"invariant"and"non-stable"features. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed learning algorithm. Code is available at https://github.com/ybjiaang/ACTIR.