# Identifiable causal inference with noisy treatment and no side information

arXiv: https://arxiv.org/abs/2306.10614 · HTML: https://mlsanity.com/paper/2306.10614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 18 Jun 2023.

## Builds on (most cited first, 8 of 8)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach](https://mlsanity.com/paper/2206.09186/) (2022)
- [Measurement error models: from nonparametric methods to deep neural networks](https://mlsanity.com/paper/2007.07498/) (2020)

## Abstract (arXiv)

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.