Conditional Instrumental Variable Regression with Representation Learning for Causal Inference

This paper studies the challenging problem of estimating causal effects from observational data, in the presence of unobserved <PRE_TAG>confounders</POST_TAG>. The two-stage least square (TSLS) method and its variants with a standard instrumental variable (IV) are commonly used to eliminate confounding bias, including the bias caused by unobserved <PRE_TAG>confounders</POST_TAG>, but they rely on the linearity assumption. Besides, the strict condition of unconfounded instruments posed on a standard IV is too strong to be practical. To address these challenging and practical problems of the standard IV method (linearity assumption and the strict condition), in this paper, we use a conditional IV (CIV) to relax the unconfounded instrument condition of standard IV and propose a non-linear CIV regression with Confounding Balancing Representation Learning, CBRL.CIV, for jointly eliminating the confounding bias from unobserved <PRE_TAG>confounders</POST_TAG> and balancing the observed confounders, without the linearity assumption. We theoretically demonstrate the soundness of CBRL.CIV. Extensive experiments on synthetic and two real-world datasets show the competitive performance of CBRL.CIV against state-of-the-art IV-based estimators and superiority in dealing with the non-linear situation.