Covariate balancing using the integral probability metric for causal inference

TL;DR

This paper introduces a covariate balancing method using the integral probability metric (IPM) that ensures consistent causal effect estimation without requiring correct model specification, and demonstrates superior finite-sample performance.

Contribution

The paper proposes a novel IPM-based weighting method for covariate balancing that guarantees consistency without model correctness and outperforms existing methods in finite samples.

Findings

Method achieves model-free consistency.

Outperforms existing weighting methods in finite samples.

Empirical results show significant improvements over traditional approaches.

Abstract

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.