Advancing Counterfactual Prediction through Nonlinear Quantile Regression

TMLR Paper7367 Authors

Abstract: The ability to address counterfactual “what if” inquiries is essential for understanding and leveraging causal relationships. Traditional counterfactual prediction, under Pearl’s framework, typically relies on access to or estimation of a structural causal model (SCM). In practice, however, the underlying causal model is often unknown and difficult to identify. To overcome this limitation, we present a method for answering counterfactual queries without explicitly estimating the SCM. We establish a novel connection between counterfactual prediction and quantile regression, showing that counterfactual prediction can be reframed as an extended quantile regression problem. Building on this insight, we propose a practical framework for efficient and effective counterfactual prediction using neural networks under a bi-level optimization scheme. The proposed framework is theoretically shown to yield a unique and well-posed solution, providing a principled basis for reliable counterfactual estimation. Moreover, it improves the ability to generalize estimated counterfactual outcomes to unseen data, for which we further derive an upper bound on the generalization error. Empirical evaluations across multiple datasets offer strong evidence supporting the proposed framework and its theoretical properties.

Submission Type: Regular submission (no more than 12 pages of main content)

Previous TMLR Submission Url: https://openreview.net/forum?id=CijeUSJWeQ

Changes Since Last Submission: The modified font issue has been resolved. In addition, we corrected typographical errors, citation formatting issues, and table caption placement.

Assigned Action Editor: ~Fredrik_Daniel_Johansson1

Submission Number: 7367