Advancing Counterfactual Inference through Nonlinear Quantile Regression

The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference, under Pearls' counterfactual framework, typically depends on having access to or estimating a structural causal model. Yet, in practice, this causal model is often unknown and might be challenging to identify. Hence, this paper aims to perform reliable counterfactual inference based solely on observational data and the (learned) qualitative causal structure, without necessitating a predefined causal model or even direct estimations of conditional distributions. To this end, we establish a novel connection between counterfactual inference and quantile regression and show that counterfactual inference can be reframed as an extended quantile regression problem. Building on this insight, we propose a practical framework for efficient and effective counterfactual inference implemented with neural networks under a bi-level optimization scheme. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data, thereby providing an upper bound on the generalization error. Furthermore, empirical evidence demonstrates its superior statistical efficiency in comparison to existing methods. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.