  Selecting causal inference models for estimating individualized treatment
effects (ITE) from observational data presents a unique challenge since the
counterfactual outcomes are never observed. The problem is challenged further
in the unsupervised domain adaptation (UDA) setting where we only have access
to labeled samples in the source domain, but desire selecting a model that
achieves good performance on a target domain for which only unlabeled samples
are available. Existing techniques for UDA model selection are designed for the
predictive setting. These methods examine 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. Because of this, two models with
identical performance on the source domain would receive the same risk score by
existing methods, but in reality, have significantly different performance in
the test domain. We leverage the invariance of causal structures across domains
to propose a novel model selection metric specifically designed for ITE methods
under the UDA setting. In particular, we propose selecting models whose
predictions of interventions' effects satisfy known causal structures in the
target domain. Experimentally, our method selects ITE models that are more
robust to covariate shifts on several healthcare datasets, including estimating
the effect of ventilation in COVID-19 patients from different geographic
locations.
