Counterfactual Cross-Validation: Effective Causal Model Selection from Observational Data

What is the most effective way to select the best causal model among potential candidates? In this paper, we propose a method to effectively select the best individual-level treatment effect (ITE) predictors from a set of candidates using only an observational validation set. In model selection or hyperparameter tuning, we are interested in choosing the best model or the value of hyperparameter from potential candidates. Thus, we focus on accurately preserving the rank order of the ITE prediction performance of candidate causal models. The proposed evaluation metric is theoretically proved to preserve the true ranking of the model performance in expectation and to minimize the upper bound of the finite sample uncertainty in model selection. Consistent with the theoretical result, empirical experiments demonstrate that our proposed method is more likely to select the best model and set of hyperparameter in both model selection and hyperparameter tuning.