Identifiable Causal Inference with Noisy Treatment and No Side Information
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: We fixed mistakes in the previous revision:
- Removed repetition from the fourth-last paragraph of the introduction
- Section 2.1 last paragraph replaced “CEME is our main method” with “CEME is our proposed method”
- In several places, we previously referred to the CEME method as the algorithm/method defined in Section 1. This is however wrong in Revision 1 as the definition was moved to Section 2.1. Fixed these references to now refer to the CEME method and/or equations (3)--(5).
- Removed the words “accurately enough” from the second paragraph of Section 3.2 to make it match what we said in our response comment that we would write there.
- In the caption of Figure 9 we made the change “CEME/CEME$^+$ are misspecified here, unlike Oracle and Naive” -> “CEME/CEME$^+$ incorrectly assume a continuous $X^*$, unlike Oracle and Naive” (this is more accurate as Naive is also misspecified because it incorrectly assumes that the observed treatment is accurate)
Additionally, there are minor style and grammar improvements.
.
Assigned Action Editor: ~Yu_Yao3
Submission Number: 2626
Loading