Confounder Balancing for Instrumental Variable Regression with Latent Variable

TL;DR

This paper introduces the CB-IV and CB-IV-L algorithms for unbiased causal effect estimation in IV regression, effectively addressing confounding bias and imbalanced confounders, even in scenarios without pre-defined valid IVs.

Contribution

The paper proposes a novel confounder balanced IV regression method and extends it to handle latent and mixed-variable IV challenges, improving causal inference accuracy.

Findings

CB-IV achieves unbiased treatment effect estimation with lower variance.

CB-IV-L effectively handles latent and mixed-variable IV scenarios.

Experimental results show superior performance over existing methods.

Abstract

This paper studies the confounding effects from the unmeasured confounders and the imbalance of observed confounders in IV regression and aims at unbiased causal effect estimation. Recently, nonlinear IV estimators were proposed to allow for nonlinear model in both stages. However, the observed confounders may be imbalanced in stage 2, which could still lead to biased treatment effect estimation in certain cases. To this end, we propose a Confounder Balanced IV Regression (CB-IV) algorithm to jointly remove the bias from the unmeasured confounders and the imbalance of observed confounders. Theoretically, by redefining and solving an inverse problem for potential outcome function, we show that our CB-IV algorithm can unbiasedly estimate treatment effects and achieve lower variance. The IV methods have a major disadvantage in that little prior or theory is currently available to pre-define a valid IV in real-world scenarios. Thus, we study two more challenging settings without pre-defined valid IVs: (1) indistinguishable IVs implicitly present in observations, i.e., mixed-variable challenge, and (2) latent IVs don't appear in observations, i.e., latent-variable challenge. To address these two challenges, we extend our CB-IV by a latent-variable module, namely CB-IV-L algorithm. Extensive experiments demonstrate that our CB-IV(-L) outperforms the existing approaches.