Assessing causal effects in the presence of unmeasured confounding is a challenging problem. It has been previously shown that the causal effect is identifiable when noise variables of the treatment and outcome are both non-Gaussian under linear model setting with hidden variables. In this paper, we investigate the problem of identifying the causal effect using the auxiliary covariate and non-Gaussianity from the treatment. Our key idea is to characterize the impact of unmeasured confounders using an observed covariate, assuming they are all Gaussian. We demonstrate that the causal effect can be identified using a measured covariate, and then extend the identification results to the multi-treatment setting. We further develop a simple estimation procedure for calculating causal effects.

翻译：在存在未测量混杂因素的情况下评估因果效应是一个具有挑战性的问题。已有研究表明，在线性模型设置中，当处理变量和结果变量的噪声均服从非高斯分布且存在隐藏变量时，因果效应是可识别的。本文探讨了利用辅助协变量和处理变量的非高斯性来识别因果效应的问题。我们的核心思想是，假设未测量混杂因素均服从高斯分布，通过使用一个观测到的协变量来刻画其影响。我们证明了因果效应可以通过一个测量到的协变量进行识别，并将这一识别结果扩展至多处理设置。此外，我们进一步提出了一种用于计算因果效应的简单估计方法。