Approximate Causal Effect Identification under Weak Confounding

Ziwei Jiang, Lai Wei, Murat Kocaoglu
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:15125-15143, 2023.

Abstract

Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding’" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-jiang23h, title = {Approximate Causal Effect Identification under Weak Confounding}, author = {Jiang, Ziwei and Wei, Lai and Kocaoglu, Murat}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {15125--15143}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/jiang23h/jiang23h.pdf}, url = {https://proceedings.mlr.press/v202/jiang23h.html}, abstract = {Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding’" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.} }
Endnote
%0 Conference Paper %T Approximate Causal Effect Identification under Weak Confounding %A Ziwei Jiang %A Lai Wei %A Murat Kocaoglu %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-jiang23h %I PMLR %P 15125--15143 %U https://proceedings.mlr.press/v202/jiang23h.html %V 202 %X Causal effect estimation has been studied by many researchers when only observational data is available. Sound and complete algorithms have been developed for pointwise estimation of identifiable causal queries. For non-identifiable causal queries, researchers developed polynomial programs to estimate tight bounds on causal effect. However, these are computationally difficult to optimize for variables with large support sizes. In this paper, we analyze the effect of "weak confounding’" on causal estimands. More specifically, under the assumption that the unobserved confounders that render a query non-identifiable have small entropy, we propose an efficient linear program to derive the upper and lower bounds of the causal effect. We show that our bounds are consistent in the sense that as the entropy of unobserved confounders goes to zero, the gap between the upper and lower bound vanishes. Finally, we conduct synthetic and real data simulations to compare our bounds with the bounds obtained by the existing work that cannot incorporate such entropy constraints and show that our bounds are tighter for the setting with weak confounders.
APA
Jiang, Z., Wei, L. & Kocaoglu, M.. (2023). Approximate Causal Effect Identification under Weak Confounding. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:15125-15143 Available from https://proceedings.mlr.press/v202/jiang23h.html.

Related Material