Estimating causal effects by bounding confounding

Philipp Geiger, Dominik Janzing
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:833-842, 2014.

Abstract

Assessing the causal effect of a treatment variable X on an outcome variable Y is usually difficult due to the existence of un- observed common causes. Without further assumptions, observed dependences do not even prove the existence of a causal effect from X to Y . It is intuitively clear that strong statistical dependences between X and Y do provide evidence for X influenc- ing Y if the influence of common causes is known to be weak. We propose a framework that formalizes effect versus confounding in various ways and derive upper/lower bounds on the effect in terms of a priori given bounds on confounding. The formalization includes information theoretic quantities like informa- tion flow and causal strength, as well as other common notions like effect of treatment on the treated (ETT). We discuss several sce- narios where upper bounds on the strength of confounding can be derived. This justifies to some extent human intuition which assumes the presence of causal effect when strong (e.g. close to deterministic) statistical relations are observed.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-geiger14a, title = {Estimating causal effects by bounding confounding}, author = {Geiger, Philipp and Janzing, Dominik}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {833--842}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/geiger14a/geiger14a.pdf}, url = {https://proceedings.mlr.press/r12/geiger14a.html}, abstract = {Assessing the causal effect of a treatment variable X on an outcome variable Y is usually difficult due to the existence of un- observed common causes. Without further assumptions, observed dependences do not even prove the existence of a causal effect from X to Y . It is intuitively clear that strong statistical dependences between X and Y do provide evidence for X influenc- ing Y if the influence of common causes is known to be weak. We propose a framework that formalizes effect versus confounding in various ways and derive upper/lower bounds on the effect in terms of a priori given bounds on confounding. The formalization includes information theoretic quantities like informa- tion flow and causal strength, as well as other common notions like effect of treatment on the treated (ETT). We discuss several sce- narios where upper bounds on the strength of confounding can be derived. This justifies to some extent human intuition which assumes the presence of causal effect when strong (e.g. close to deterministic) statistical relations are observed.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Estimating causal effects by bounding confounding %A Philipp Geiger %A Dominik Janzing %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-geiger14a %I PMLR %P 833--842 %U https://proceedings.mlr.press/r12/geiger14a.html %V R12 %X Assessing the causal effect of a treatment variable X on an outcome variable Y is usually difficult due to the existence of un- observed common causes. Without further assumptions, observed dependences do not even prove the existence of a causal effect from X to Y . It is intuitively clear that strong statistical dependences between X and Y do provide evidence for X influenc- ing Y if the influence of common causes is known to be weak. We propose a framework that formalizes effect versus confounding in various ways and derive upper/lower bounds on the effect in terms of a priori given bounds on confounding. The formalization includes information theoretic quantities like informa- tion flow and causal strength, as well as other common notions like effect of treatment on the treated (ETT). We discuss several sce- narios where upper bounds on the strength of confounding can be derived. This justifies to some extent human intuition which assumes the presence of causal effect when strong (e.g. close to deterministic) statistical relations are observed. %Z Reissued by PMLR on 04 October 2026.
APA
Geiger, P. & Janzing, D.. (2014). Estimating causal effects by bounding confounding. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:833-842 Available from https://proceedings.mlr.press/r12/geiger14a.html. Reissued by PMLR on 04 October 2026.

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