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.

本文研究了在存在未观察到的混淆因素的情况下，从观察数据中估计因果效应的复杂问题。我们使用条件性工具变量（CIV）来缓解标准工具变量方法中的无混淆工具变量条件，并提出一种基于混淆平衡表征学习的非线性 CIV 回归，CBRL.CIV，以非线性情况下共同消除未观察到的混淆因素的混淆偏差并平衡观察到的混淆因素，无需线性假设。我们从理论上证明了 CBRL.CIV 的合理性。对合成数据集和两个实际数据集进行的大量实验证明了 CBRL.CIV 与最先进的基于工具变量的估计器相比的竞争性能以及在处理非线性情况方面的优越性。

条件工具变量回归与表示学习用于因果推断

Conditional Instrumental Variable Regression with Representation  Learning for Causal Inference

The instrumental variable (IV) approach is a widely used way to estimate the
causal effects of a treatment on an outcome of interest from observational data
with latent confounders. A standard IV is expected to be related to the
treatment variable and independent of all other variables in the system.
However, it is challenging to search for a standard IV from data directly due
to the strict conditions. The conditional IV (CIV) method has been proposed to
allow a variable to be an instrument conditioning on a set of variables,
allowing a wider choice of possible IVs and enabling broader practical
applications of the IV approach. Nevertheless, there is not a data-driven
method to discover a CIV and its conditioning set directly from data. To fill
this gap, in this paper, we propose to learn the representations of the
information of a CIV and its conditioning set from data with latent confounders
for average causal effect estimation. By taking advantage of deep generative
models, we develop a novel data-driven approach for simultaneously learning the
representation of a CIV from measured variables and generating the
representation of its conditioning set given measured variables. Extensive
experiments on synthetic and real-world datasets show that our method
outperforms the existing IV methods.

本文提出了一种基于深度生成模型的数据驱动方法，用于从含有潜在混淆因素的数据中学习条件工具变量及其调节集的信息表示，并实现平均因果效应估计。通过大量的合成和实际数据实验，证明该方法优于现有的 IV 方法。