Learning Counterfactual Outcomes Under Rank Preservation

Kun Zhang (CMU & MBZUAI) · Haoxuan Li (Peking University) · Yang Liu (CUHK) · Jiawei Chen (Zhejiang University) · Yan Zeng (Beijing Technology and Business University) · Peng Wu (Beijing Technology and Business University) · Chunyuan Zheng (meituan) · Ruocheng Guo (Intuit AI Research)

causal inferenceconvexitycounterfactual inferenceempirical estimationexogenous variablehomogeneityideal losskernel-based estimatorrank preservation assumptionreal-world experimentssemi-synthetic experimentsstrict monotonicitystructural causal model theoretical analysisunbiased learning

Counterfactual inference aims to estimate the counterfactual outcome at the individual level given knowledge of an observed treatment and the factual outcome, with broad applications in fields such as epidemiology, econometrics, and management science. Previous methods rely on a known structural causal model (SCM) or assume the homogeneity of the exogenous variable and strict monotonicity between the outcome and exogenous variable. In this paper, we propose a principled approach for identifying and estimating the counterfactual outcome. We first introduce a simple and intuitive rank preservation assumption to identify the counterfactual outcome without relying on a known structural causal model. Building on this, we propose a novel ideal loss for theoretically unbiased learning of the counterfactual outcome and further develop a kernel-based estimator for its empirical estimation. Our theoretical analysis shows that the rank preservation assumption is not stronger than the homogeneity and strict monotonicity assumptions, and shows that the proposed ideal loss is convex, and the proposed estimator is unbiased. Extensive semi-synthetic and real-world experiments are conducted to demonstrate the effectiveness of the proposed method.