We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We do so by generalizing estimation in the instrumental variable setting. Despite significant work on regression with measurement error, additionally handling unobserved confounding in the continuous setting is non-trivial: we have seen little prior work. As a by-product of our investigation, we clarify a connection between mean embeddings and characteristic functions, and how learning one simultaneously allows one to learn the other. This opens the way for kernel method research to leverage existing results in characteristic function estimation. Finally, we empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error and to the type of error distributions.

翻译：我们提出一个以内核为基础的非参数估计器,以衡量因果结果因果结果因误差而受损。我们这样做的方法是在工具变量设置中进行一般估计。尽管在测量误差的回归方面做了大量工作,但在连续环境中处理未观察到的混乱却是非三重的:我们很少看到先前的工作。作为我们调查的副产品,我们澄清了中值嵌入和特性功能之间的联系,以及同时学习一个功能又如何让一个同时学习一个功能学习另一个功能之间的联系。这为内核方法研究开辟了途径,以利用现有结果来进行特性函数估计。最后,我们从经验上表明,我们拟议的方法(MEKIV)超越基线,在测量误差强度和误差分布类型的变化下是稳健的。