An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation
UZAIR AKBAR, Niki Kilbertus, Hao Shen, Krikamol Muandet, Bo Dai
The technique of data augmentation (DA) is often used in machine learning for regularization purposes to better generalize under i.i.d. settings. In this work, we make a case for the use of DA beyond just the i.i.d. setting, but for generalization across interventions as well by presenting a unifying framework with topics in causal inference. Specifically, we argue that when the outcome generating mechanism is invariant to our choice of DA, then such augmentations can effectively be thought of as interventions on the treatment generating mechanism itself. This can potentially help to reduce the amount of bias in our estimation of causal effects arising from hidden confounders. In the presence of such unobserved confounding we typically make use of instrumental variables (IVs) -- sources of treatment randomization that are conditionally independent of the outcome. However, IVs may not be as readily available as DA for many applications, which is the main motivation behind this work. By appropriately regularizing IV based estimators, we introduce the concept of IV-like (IVL) regression for when treatment randomization sources may carry no information about the outcome and the possibility of its use for improving predictive performance across treatment interventions and reducing confounding bias. Finally, we cast parameterized DA as a IVL regression problem and show that when used in composition can simulate a worst-case application of such DA, further improving performance on causal estimation and generalization tasks beyond what simple DA may offer. This is shown both theoretically for the population case and via simulation experiments for the finite sample case using a simple linear example. We also present real data experiments to support our case.