Scalable Out-of-distribution Robustness in the Presence of Unobserved Confounders

Abstract

We consider the task of out-of-distribution (OOD) generalization, where the distribution shift is due to an unobserved confounder (Z) affecting both the covariates (X) and the labels (Y). In this setting, traditional assumptions of covariate and label shift are unsuitable due to the confounding, which introduces heterogeneity in the predictor, i.e., Y = f_Z(X). OOD generalization differs from traditional domain adaptation by not assuming access to the covariate distribution (X^te) of the test samples during training. These conditions create a challenging scenario for OOD robustness: (a) Z^tr is an unobserved confounder during training, (b) P^teZ P^trZ, (c) X^te is unavailable during training, and (d) the posterior predictive distribution depends on P^te(Z), i.e., Y = E_P^te(Z)[f_Z(X)]. In general, accurate predictions are unattainable in this scenario, and existing literature has proposed complex predictors based on identifiability assumptions that require multiple additional variables. Our work investigates a set of identifiability assumptions that tremendously simplify the predictor, whose resulting elegant simplicity outperforms existing approaches.

Tasks

Reproductions