Partial Identification with Noisy Covariates: A Robust Optimization Approach

Wenshuo Guo, Mingzhang Yin, Yixin Wang, Michael Jordan
Proceedings of the First Conference on Causal Learning and Reasoning, PMLR 177:318-335, 2022.

Abstract

Causal inference from observational datasets often relies on measuring and adjusting for covariates. In practice, measurements of the covariates can often be noisy and/or biased, or only measurements of their proxies may be available. Directly adjusting for these imperfect measurements of the covariates can lead to biased causal estimates. Moreover, without additional assumptions, the causal effects are not point-identifiable due to the noise in these measurements. To this end, we study the partial identification of causal effects given noisy covariates, under a user-specified assumption on the noise level. The key observation is that we can formulate the identification of the average treatment effects (ATE) as a robust optimization problem. This formulation leads to an efficient robust optimization algorithm that bounds the ATE with noisy covariates. We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification, including backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment. Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v177-guo22a, title = {Partial Identification with Noisy Covariates: A Robust Optimization Approach}, author = {Guo, Wenshuo and Yin, Mingzhang and Wang, Yixin and Jordan, Michael}, booktitle = {Proceedings of the First Conference on Causal Learning and Reasoning}, pages = {318--335}, year = {2022}, editor = {Schölkopf, Bernhard and Uhler, Caroline and Zhang, Kun}, volume = {177}, series = {Proceedings of Machine Learning Research}, month = {11--13 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v177/guo22a/guo22a.pdf}, url = {https://proceedings.mlr.press/v177/guo22a.html}, abstract = {Causal inference from observational datasets often relies on measuring and adjusting for covariates. In practice, measurements of the covariates can often be noisy and/or biased, or only measurements of their proxies may be available. Directly adjusting for these imperfect measurements of the covariates can lead to biased causal estimates. Moreover, without additional assumptions, the causal effects are not point-identifiable due to the noise in these measurements. To this end, we study the partial identification of causal effects given noisy covariates, under a user-specified assumption on the noise level. The key observation is that we can formulate the identification of the average treatment effects (ATE) as a robust optimization problem. This formulation leads to an efficient robust optimization algorithm that bounds the ATE with noisy covariates. We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification, including backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment. Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.} }
Endnote
%0 Conference Paper %T Partial Identification with Noisy Covariates: A Robust Optimization Approach %A Wenshuo Guo %A Mingzhang Yin %A Yixin Wang %A Michael Jordan %B Proceedings of the First Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2022 %E Bernhard Schölkopf %E Caroline Uhler %E Kun Zhang %F pmlr-v177-guo22a %I PMLR %P 318--335 %U https://proceedings.mlr.press/v177/guo22a.html %V 177 %X Causal inference from observational datasets often relies on measuring and adjusting for covariates. In practice, measurements of the covariates can often be noisy and/or biased, or only measurements of their proxies may be available. Directly adjusting for these imperfect measurements of the covariates can lead to biased causal estimates. Moreover, without additional assumptions, the causal effects are not point-identifiable due to the noise in these measurements. To this end, we study the partial identification of causal effects given noisy covariates, under a user-specified assumption on the noise level. The key observation is that we can formulate the identification of the average treatment effects (ATE) as a robust optimization problem. This formulation leads to an efficient robust optimization algorithm that bounds the ATE with noisy covariates. We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification, including backdoor adjustment, inverse propensity score weighting, double machine learning, and front door adjustment. Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.
APA
Guo, W., Yin, M., Wang, Y. & Jordan, M.. (2022). Partial Identification with Noisy Covariates: A Robust Optimization Approach. Proceedings of the First Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 177:318-335 Available from https://proceedings.mlr.press/v177/guo22a.html.

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