Selecting Treatment Effects Models for Domain Adaptation Using Causal Knowledge

While a large number of causal inference models for estimating individualized treatment effects (ITE) have been developed, selecting the best one poses a unique challenge, since the counterfactuals are never observed. The problem is challenged further in the unsupervised domain adaptation (UDA) setting where we have access to labeled samples in the source domain but desire selecting an ITE model that achieves good performance on a target domain where only unlabeled samples are available. Existing selection techniques for UDA are designed for predictive models and are sub-optimal for causal inference because they (1) do not account for the missing counterfactuals and (2) only examine the discriminative density ratios between the input covariates in the source and target domain and do not factor in the model’s predictions in the target domain. We leverage the invariance of causal structures across domains to introduce a novel model selection metric specifically designed for ITE models under UDA. We propose selecting models whose predictions of the effects of interventions satisfy invariant causal structures in the target domain. Experimentally, our method selects ITE models that are more robust to covariate shifts on a variety of datasets, including estimating the effect of ventilation in COVID-19 patients.