Identifiable causal inference with noisy treatment and no side
  information
Antti Pöllänen Pekka Marttinen
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.