Causal effect estimation from observational and interventional data through matrix weighted linear estimators

Klaus-Rudolf Kladny, Julius von Kügelgen, Bernhard Schölkopf, Michael Muehlebach
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:1087-1097, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-kladny23a, title = {Causal effect estimation from observational and interventional data through matrix weighted linear estimators}, author = {Kladny, Klaus-Rudolf and von K{\"u}gelgen, Julius and Sch{\"o}lkopf, Bernhard and Muehlebach, Michael}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {1087--1097}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/kladny23a/kladny23a.pdf}, url = {https://proceedings.mlr.press/v216/kladny23a.html}, 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.} }
Endnote
%0 Conference Paper %T Causal effect estimation from observational and interventional data through matrix weighted linear estimators %A Klaus-Rudolf Kladny %A Julius von Kügelgen %A Bernhard Schölkopf %A Michael Muehlebach %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-kladny23a %I PMLR %P 1087--1097 %U https://proceedings.mlr.press/v216/kladny23a.html %V 216 %X 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.
APA
Kladny, K., von Kügelgen, J., Schölkopf, B. & Muehlebach, M.. (2023). Causal effect estimation from observational and interventional data through matrix weighted linear estimators. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:1087-1097 Available from https://proceedings.mlr.press/v216/kladny23a.html.

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