Causal Effect Estimation from Observational and Interventional Data Through Matrix Weighted Linear Estimators
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Date
2023
Publication Type
Conference Paper
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yes
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Abstract
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.
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Publication status
published
Book title
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence
Journal / series
Volume
216
Pages / Article No.
1087 - 1097
Publisher
PMLR
Event
39th Conference on Uncertainty in Artificial Intelligence (UAI 2023)
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Methods
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Organisational unit
09664 - Schölkopf, Bernhard / Schölkopf, Bernhard