In some causal inference scenarios, the treatment (i.e. cause) variable is measured inaccurately, for instance in epidemiology or econometrics. Failure to correct for the effect of this measurement error can lead to biased causal effect estimates. Previous research has not studied methods that address this issue from a causal viewpoint while allowing for complex nonlinear dependencies and without assuming access to side information. For such as scenario, this paper proposes a model that assumes a continuous treatment variable which is inaccurately measured. Building on existing results for measurement error models, we prove that our model's causal effect estimates are identifiable, even without knowledge of the measurement error variance or other side information. Our method relies on a deep latent variable model where Gaussian conditionals are parameterized by neural networks, and we develop an amortized importance-weighted variational objective for training the model. Empirical results demonstrate the method's good performance with unknown measurement error. More broadly, our work extends the range of applications where reliable causal inference can be conducted.

翻译：在某些因果推断场景中，如流行病学或计量经济学，处理变量（即原因）的测量存在误差。若不纠正这种测量误差的影响，可能导致有偏的因果效应估计。现有研究尚未从因果视角出发，在允许复杂非线性依赖且无需辅助信息的前提下，提出解决该问题的方法。针对此类场景，本文提出一种假设连续处理变量存在测量误差的模型。基于测量误差模型的现有成果，我们证明该模型的因果效应估计即使在未知测量误差方差或其它辅助信息的情况下仍具有可辨识性。本方法采用深度潜变量模型，其中高斯条件分布由神经网络参数化，并开发了用于模型训练的分摊重要性加权变分目标函数。实验结果表明，该方法在未知测量误差下表现良好。更广泛地，本研究拓展了可开展可靠因果推断的应用范围。