In some causal inference scenarios, the treatment 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 a scenario, this study proposes a model that assumes a continuous treatment variable that 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 in which 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 in which reliable causal inference can be conducted.

翻译：在某些因果推断场景中，处理变量存在测量不准确的问题，例如流行病学或计量经济学领域。若未能校正此类测量误差的影响，将导致因果效应估计产生偏倚。现有研究尚未从因果视角探讨同时允许复杂非线性依赖且无需辅助信息假设的解决方法。针对该场景，本研究提出一种假设存在连续但测量不准确的处理变量的模型。基于测量误差模型的现有结论，我们证明了即便缺乏测量误差方差或其他辅助信息，该模型的因果效应估计仍具有可辨识性。本方法采用深度潜变量模型，其中高斯条件分布通过神经网络参数化，并开发了用于模型训练的摊销重要性加权变分目标函数。实验结果表明，该方法在测量误差未知的情况下表现优异。更广泛而言，本研究拓展了可开展可靠因果推断的应用范围。