Learning Counterfactual Outcomes Under Rank Preservation

TL;DR

This paper introduces a new method for counterfactual inference that relies on a rank preservation assumption, enabling unbiased estimation without requiring a known structural causal model, and demonstrates its effectiveness through experiments.

Contribution

It proposes a novel rank preservation assumption for identifying counterfactuals and develops an unbiased kernel-based estimator, advancing counterfactual inference methods.

Findings

The rank preservation assumption is weaker than traditional assumptions.

The proposed estimator is theoretically unbiased and convex.

Experiments show improved accuracy in counterfactual estimation.

Abstract

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.