On Positivity Condition for Causal Inference

Inwoo Hwang, Yesong Choe, Yeahoon Kwon, Sanghack Lee
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:20818-20841, 2024.

Abstract

Identifying and estimating a causal effect is a fundamental task when researchers want to infer a causal effect using an observational study without experiments. A conventional assumption is the strict positivity of the given distribution, or so called positivity (or overlap) under the unconfounded assumption that the probabilities of treatments are positive. However, there exist many environments where neither observational data exhibits strict positivity nor unconfounded assumption holds. Against this background, we examine the graphical counterpart of the conventional positivity condition so as to license the use of identification formula without strict positivity. In particular, we explore various approaches, including analysis in a post-hoc manner, do-calculus, $Q$-decomposition, and algorithmic, to yielding a positivity condition for an identification formula, where we relate them, providing a comprehensive view. We further discuss the design of a positivity-aware identification algorithm based on the theoretical characterization of identification formulas.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-hwang24a, title = {On Positivity Condition for Causal Inference}, author = {Hwang, Inwoo and Choe, Yesong and Kwon, Yeahoon and Lee, Sanghack}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {20818--20841}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/hwang24a/hwang24a.pdf}, url = {https://proceedings.mlr.press/v235/hwang24a.html}, abstract = {Identifying and estimating a causal effect is a fundamental task when researchers want to infer a causal effect using an observational study without experiments. A conventional assumption is the strict positivity of the given distribution, or so called positivity (or overlap) under the unconfounded assumption that the probabilities of treatments are positive. However, there exist many environments where neither observational data exhibits strict positivity nor unconfounded assumption holds. Against this background, we examine the graphical counterpart of the conventional positivity condition so as to license the use of identification formula without strict positivity. In particular, we explore various approaches, including analysis in a post-hoc manner, do-calculus, $Q$-decomposition, and algorithmic, to yielding a positivity condition for an identification formula, where we relate them, providing a comprehensive view. We further discuss the design of a positivity-aware identification algorithm based on the theoretical characterization of identification formulas.} }
Endnote
%0 Conference Paper %T On Positivity Condition for Causal Inference %A Inwoo Hwang %A Yesong Choe %A Yeahoon Kwon %A Sanghack Lee %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-hwang24a %I PMLR %P 20818--20841 %U https://proceedings.mlr.press/v235/hwang24a.html %V 235 %X Identifying and estimating a causal effect is a fundamental task when researchers want to infer a causal effect using an observational study without experiments. A conventional assumption is the strict positivity of the given distribution, or so called positivity (or overlap) under the unconfounded assumption that the probabilities of treatments are positive. However, there exist many environments where neither observational data exhibits strict positivity nor unconfounded assumption holds. Against this background, we examine the graphical counterpart of the conventional positivity condition so as to license the use of identification formula without strict positivity. In particular, we explore various approaches, including analysis in a post-hoc manner, do-calculus, $Q$-decomposition, and algorithmic, to yielding a positivity condition for an identification formula, where we relate them, providing a comprehensive view. We further discuss the design of a positivity-aware identification algorithm based on the theoretical characterization of identification formulas.
APA
Hwang, I., Choe, Y., Kwon, Y. & Lee, S.. (2024). On Positivity Condition for Causal Inference. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:20818-20841 Available from https://proceedings.mlr.press/v235/hwang24a.html.

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