Identifiable causal inference with noisy treatment and no side information

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.