# Partial Identification with Noisy Covariates: A Robust Optimization Approach

**Authors:** Wenshuo Guo, Mingzhang Yin, Yixin Wang, Michael I. Jordan  
**arXiv:** [2202.10665](https://arxiv.org/abs/2202.10665)  
**Date:** 2022-02-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2202.10665v1/

## Key points

- Accurate measurement and adjustment of covariates are crucial for determining causal effects
- Imperfect measurements of covariates can lead to biased estimates of causal effects
- Causal effects may not be point-identifiable due to noise in measurements
- Study on partial identification of causal effects with noisy covariates involved user-specified assumptions about noise levels
- Formulation of identifying average treatment effects (ATE) as a robust optimization problem emerged as a key insight
- Efficient robust optimization algorithm developed to establish bounds on ATE with noisy covariates
- Robust optimization methodology extended to various causal adjustment methods including backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment
- Experiments showed that the robust optimization approach yielded ATE bounds with higher coverage probability compared to existing techniques
- Research contributes significantly to advancing understanding and application of causal inference methodologies in scenarios with noisy or biased covariate data

## Summary

In the field of causal inference from observational datasets, the accurate measurement and adjustment of covariates play a crucial role in determining causal effects. However, in practical scenarios, these measurements can often be subject to noise or bias, or only proxies of the actual covariates may be available. Adjusting for such imperfect measurements directly can result in biased estimates of causal effects. Additionally, due to the inherent noise in these measurements, without additional assumptions, the causal effects may not be point-identifiable. To address this challenge, a study was conducted on the partial identification of causal effects when dealing with noisy covariates. This study involved making a user-specified assumption regarding the level of noise present in the measurements. The key insight that emerged from this research was the formulation of identifying average treatment effects (ATE) as a robust optimization problem. By adopting this approach, an efficient robust optimization algorithm was developed to establish bounds on ATE when noisy covariates are involved. Furthermore, it was demonstrated that this robust optimization methodology could be extended to various causal adjustment methods for performing partial identification. These methods include backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment. Through experiments conducted on both synthetic and real-world datasets, it was observed that this robust optimization approach yielded ATE bounds with a higher coverage probability compared to existing techniques. Overall, this research contributes significantly to advancing the understanding and application of causal inference methodologies in scenarios where covariate measurements are noisy or biased. The development of a robust optimization framework provides a valuable tool for researchers seeking to obtain reliable estimates of causal effects despite imperfect covariate data.