Causal Effect Estimation from Observational and Interventional Data Through Matrix Weighted Linear Estimators
This work addresses causal inference challenges for researchers and practitioners dealing with mixed data sources, but it is incremental as it builds on existing linear regression models with a focus on estimator combination.
The paper tackles the problem of estimating causal effects from a mix of observational and interventional data in a confounded linear regression model, showing that combining estimators improves statistical efficiency in terms of expected squared error, with synthetic studies confirming theoretical findings and outperforming baselines like a Stein-type estimator in settings with substantial confounding and large observational-to-interventional data ratios.
We study causal effect estimation from a mixture of observational and interventional data in a confounded linear regression model with multivariate treatments. We show that the statistical efficiency in terms of expected squared error can be improved by combining estimators arising from both the observational and interventional setting. To this end, we derive methods based on matrix weighted linear estimators and prove that our methods are asymptotically unbiased in the infinite sample limit. This is an important improvement compared to the pooled estimator using the union of interventional and observational data, for which the bias only vanishes if the ratio of observational to interventional data tends to zero. Studies on synthetic data confirm our theoretical findings. In settings where confounding is substantial and the ratio of observational to interventional data is large, our estimators outperform a Stein-type estimator and various other baselines.