Partial Identification with Noisy Covariates: A Robust Optimization
Approach
- URL: http://arxiv.org/abs/2202.10665v1
- Date: Tue, 22 Feb 2022 04:24:26 GMT
- Title: Partial Identification with Noisy Covariates: A Robust Optimization
Approach
- Authors: Wenshuo Guo, Mingzhang Yin, Yixin Wang, Michael I. Jordan
- Abstract summary: Causal inference from observational datasets often relies on measuring and adjusting for covariates.
We show that this robust optimization approach can extend a wide range of causal adjustment methods to perform partial identification.
Across synthetic and real datasets, we find that this approach provides ATE bounds with a higher coverage probability than existing methods.
- Score: 94.10051154390237
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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