Causal Inference with Noisy and Missing Covariates via Matrix Factorization
This addresses bias reduction in causal inference for observational studies, particularly in domains like clinical data, but is incremental as it builds on existing matrix factorization and causal methods.
The paper tackles bias in causal effect estimation from noisy and missing confounder measurements by using matrix factorization to infer confounders from many noisy covariates, showing consistency in linear regression and effectiveness in synthetic and clinical data experiments.
Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the bias caused by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates, a flexible and principled framework that adapts to missing values, accommodates a wide variety of data types, and can augment many causal inference methods. We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing. We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data.