Identifiable Causal Inference with Noisy Treatment and No Side Information

Antti Pöllänen, Pekka Marttinen

Abstract: 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 side information and knowledge of the measurement error variance. 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.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

- Added the "accepted" flag so latex compiles the camera-ready version
- On the first page added author information and a link to the review on OpenReview
- In two places in the text added a link to our Github repository that contains code and data for replicating the experiments
- Added Author Contributions and Acknowledgments sections

Code: https://github.com/antti-pollanen/ci_noisy_treatment

Assigned Action Editor: ~Yu_Yao3

Submission Number: 2626