A Proxy Variable View of Shared Confounding

Yixin Wang, David Blei
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:10697-10707, 2021.

Abstract

Causal inference from observational data can be biased by unobserved confounders. Confounders{—}the variables that affect both the treatments and the outcome{—}induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-wang21c, title = {A Proxy Variable View of Shared Confounding}, author = {Wang, Yixin and Blei, David}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {10697--10707}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/wang21c/wang21c.pdf}, url = {https://proceedings.mlr.press/v139/wang21c.html}, abstract = {Causal inference from observational data can be biased by unobserved confounders. Confounders{—}the variables that affect both the treatments and the outcome{—}induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables.} }
Endnote
%0 Conference Paper %T A Proxy Variable View of Shared Confounding %A Yixin Wang %A David Blei %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-wang21c %I PMLR %P 10697--10707 %U https://proceedings.mlr.press/v139/wang21c.html %V 139 %X Causal inference from observational data can be biased by unobserved confounders. Confounders{—}the variables that affect both the treatments and the outcome{—}induce spurious non-causal correlations between the two. Without additional conditions, unobserved confounders generally make causal quantities hard to identify. In this paper, we focus on the setting where there are many treatments with shared confounding, and we study under what conditions is causal identification possible. The key observation is that we can view subsets of treatments as proxies of the unobserved confounder and identify the intervention distributions of the rest. Moreover, while existing identification formulas for proxy variables involve solving integral equations, we show that one can circumvent the need for such solutions by directly modeling the data. Finally, we extend these results to an expanded class of causal graphs, those with other confounders and selection variables.
APA
Wang, Y. & Blei, D.. (2021). A Proxy Variable View of Shared Confounding. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:10697-10707 Available from https://proceedings.mlr.press/v139/wang21c.html.

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