Before revision:  We show both theoretically and empirically that this causally-motivated regularization scheme yields robust predictors that generalize well both in-distribution and under distribution shifts, and does so with better sample efficiency than standard regularization or weighting approaches .
After revision:  We show both theoretically and empirically that this causally-motivated regularization scheme yields robust predictors that generalize well under distribution shift, and (b) have better finite sample efficiency compared to usual regularization schemes, even in the absence of distribution shifts. Our analysis highlights important theoretical properties of training techniques commonly used in causal inference, fairness, and disentanglement literature .