Symmetry as Intervention; Causal Estimation with Data Augmentation

To our knowledge, we provide the first analysis of causal estimation under hidden confounding using only observational $(X, Y)$ data and knowledge of symmetries in data generation via data augmentation (DA) transformations. We show that such DA is equivalent to interventions on the treatment $X$, mitigating bias from hidden confounding, and that framing DA as a relaxation of instrumental variables (IVs)-sources of $X$ randomization that are conditionally independent of the outcome $Y$-can further improve causal estimation beyond simple DA.