  This paper studies the challenging problem of estimating causal effects from
observational data, in the presence of unobserved confounders. 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 confounders, 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 confounders 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.
