Advancing Counterfactual Inference through Quantile Regression

The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference usually assumes the availability of a structural causal model. Yet, in practice, such a causal model is often unknown and may not be identifiable. This paper aims to perform reliable counterfactual inference based on the (learned) qualitative causal structure and observational data, without necessitating a given causal model or even the direct estimation of conditional distributions. We re-cast counterfactual reasoning as an extended quantile regression problem, implemented with deep neural networks to capture general causal relationships and data distributions. The proposed approach offers superior statistical efficiency compared to existing ones, and further, it enhances the potential for generalizing the estimated counterfactual outcomes to previously unseen data, providing an upper bound on the generalization error. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.