Asymmetry Learning for Counterfactual-invariant Classification in OOD Tasks

Generalizing from observed to new related environments (out-of-distribution) is central to the reliability of classifiers. However, most classifiers fail to predict label $Y$ from input $X$ when the change in environment is due a (stochastic) input transformation $T^\text{te} \circ X'$ not observed in training, as in training we observe $T^\text{tr} \circ X'$, where $X'$ is a hidden variable. This work argues that when these transformations are induced by a collection of known $m$ equivalence relations, the task of finding a robust OOD classifier can be defined as finding the simplest causal model that defines a causal connection between the transformations and the target labels. We then propose a new learning paradigm, asymmetry learning, that identifies which symmetries the classifier must break in order to correctly predict $Y$ in both train and test. Asymmetry learning performs a causal model search that, under certain identifiability conditions, finds classifiers that perform equally well in-distribution and out-of-distribution.